Bibliometric Networks

Bibliometric Networks

Frank Havemann and Andrea Scharnhorst

Institut fur Bibliotheks- und Informationswissenschaft der Humboldt-Universitat zuBerlin

Data Archiving and Networked Services (DANS) Den Haag

Abstract

This text is based on a translation of a chapterin a handbook about network analysis (publishedin German) where we tried to make beginners fa-miliar with some basic notions and recent devel-opments of network analysis applied to bibliomet-ric issues (Havemann and Scharnhorst 2010) Wehave added some recent references

Contents

1 Introduction 1

2 Citation Networksof Articles 2

3 Bibliographic Coupling 5

4 Co-citation Networks 6

5 Citation Networksof Journals 8

51 Citation FlowsBetween Journals 9

52 Citation Environmentsof Individual Journals 10

6 Lexical Couplingand Co-Word Analysis 10

7 Co-authorship Networks 11

8 Outlook 14

1 Introduction

Bibliometrics is a research field that deals withthe statistical analysis of bibliographic informa-tion Most bibliometric research can be catego-rized as scientometric because it relates to scien-tific publication output in particular to journalarticles Informetrics captures flows of informa-tion not just within but also beyond the world ofbooks and periodicals including communicationover the Web (Webometrics) and the Internet1

The bibliographic description of a written workcontains a number of elements such as the name(s)of the author(s) title of the piece keywords anddata necessary for locating the document (e gtitle of the journal or edited volume in which anarticle appears year of publication volumeissuenumber page numbers) This information is oftencollected and archived in databases All of theseelements constitute the bibliographic attributes ofa document also called the metadata

A documentrsquos attributes are connected to oneanother through the document itselfmdashauthor(s)to journal keywords to publication date etcThese connections of different attributes gener-

1For an introduction to these overlapping fields we re-fer the reader to the Introduction to Informetrics a text-book by Egghe and Rousseau (1990) to the Handbookof Quantitative Science and Technology Research editedby Moed Glanzel and Schmoch (2004) to Bibliometricsand Citation Analysis the most recent English languagemonograph by De Bellis (2009) and to the recent open-access electronic book by Havemann (2009) Einfuhrungin die Bibliometrie (Introduction to Biblometrics someof the sections in this article are essentially abbreviatedversions of sections contained in chapter three of Have-mannrsquos book) Finally as a good starting point to initiatethe subject we refer the reader as well to the lecture textof Wolfgang Glanzel (2003) Bibliometrics as a ResearchField

1

arX

iv1

212

5211

v1 [

csD

L]

20

Dec

201

2

ate bipartite networks which can be representedas rectangular matrices Like attributes such asauthors with authors (see section 7 below on co-authorship networks) or keywords with keywords(see section 6 below on co-word analysis) canalso be coupled to one another this kind of cou-pling produces unipartite networks representedby square symmetrical matrices

Scientific publications are characterized by thefact that as a rule they contain references toother scientific works This generates a furthernetwork namely that of the publications them-selve This kind of self-reference has also beentaken up in models of the scientific publicationprocess (Bruckner et al 1990 Gilbert 1997 Ley-desdorff 2001 Morris et al 2003 Lucio-Arias andLeydesdorff 2009)

After Eugene Garfieldrsquos pioneering and seminalwork the Science Citation Index (SCI) in the1960s the SCI was used not only to navigate in-formation but it was also applied as a tool inscientific analysis (Garfield 1955 de Solla Price1965 Wouters 1999) The growing accessibility ofmachine-readable data (the SCI was already avail-able on magnet tapes relatively early on) and theappearance of the second big information networkthe World Wide Web (WWW) made large-scaleautomated data processing and analysis possibleThe WWWmdashin which pages constitute the net-work nodes and (hyper-)links the edgesmdashhas itselfbecome a popular object of research in networkanalysis (Huberman 2001)

Link analysis also proves fruitful when ap-plied to academic institutions or countries as wasshown by Thelwall (2004 2009) and also by Or-tega et al (2008) The position of links in anetwork allows us to draw conclusions about re-search collaboration and the function of differ-ent national scientific systems in international re-search landscape

In addition the Web remains today a mediumfor accessing data in part freely which we cananalyze according to their own particular net-work structures Consider for example the bio-information databases Ebay or Facebook Data-flow networks of this kind have resulted in the evo-lution of a new specialty within statistical physicsnamely that of complex networks (Scharnhorst2003 Morris and Yen 2004 Pyka and Scharnhorst2009) Within the multidisciplinary setting of net-work science the methods of social network analy-

sis (SNA) originally developed for smaller socialnetworks are combined with statistical analysisand dynamic modeling from physics with com-puter science algorithms for data mining and vi-sualization and with graph theory in mathemat-ics for the purpose of better grasping explainingand mastering existing complex networks in na-ture and society (NRC 2005) In recent years bib-liometrics and scientometrics have been stronglyinfluenced by these developments in new networkresearch (Borner et al 2007) We will examinethis more closely in section 8 below In what fol-lows immediately however we confine ourselvesto the network descriptions that have tradition-ally received special attention in scientometrics

In scientometrics we distinguish roughly be-tween the analysis of texts and the analysis ofactors Even if information on both elements iscontained in a single bibliographic record histor-ically speaking most bibliometric network analy-ses have concentrated on text elements (viz ci-tation co-citation bibliographic coupling or se-mantic networks) This stands in contrast tothe analysis of scientific collaboration networksmdasheither for cooperation on an individual level orcooperation between countries (Wagner 2008)Among the more interesting methods that haveevolved in the intermediate field of text and ac-tor is the HistCite method developed by EugeneGarfield et al which we discuss in section 2 be-low

2 Citation Networksof Articles

Articles in scientific periodicals base on otherknowledge and acknowledge this by referencingearlier articles and other publications This waythey build networks This view of a stream of pe-riodicals literature was already propagated morethan 40 years ago by Derek J de Solla Price(1965) Defining articles as nodes or vertices andcitations as the links or edges of a network graphallows us to apply graph theoretical methods tobibliometrics In view of the social nature of thescience system we will also consider how termsand concepts initially developed for SNA can befruitfully applied to explain scientific communica-tion

2

New nodes with directed edges pointing to pre-viously available nodes are continually added toboth the network of journal articles and the WebWhereas web pages can be modified (or even com-pletely deleted) a journal article remains an un-changed document once it has been publishedCorrections for example can only be added to thedocument subsequently as errata or corrigendaHyperlinks can be added to existing pages retroac-tively referring to pages that have been subse-quently produced In citation networks by con-trast there is temporal ordering but the orderas it were is not strict Because of the protract-edness of the publication process authors may beaware of not-yet-published works and cite thesebut citation network analysis usually does nottake this into account

Todayrsquos vast network of scientific journal arti-cles began to build up when the referencing ofolder publications became common practice Itmight be helpful to try to visualize the spacial ex-pansion of the whole article citation network asa continually growing sphere which adds a newldquogrowth ringrdquo every year in which articles are lo-cated through the sources that they cite TheHistCite method developed by Eugene Garfieldet al (2003) assumes that at the root of ev-

1

2

3

4

5

6

7

8

9

10

11

12

Figure 1 Temporally ordered graph of a cita-tion network for the first twelve articles on N-raysData source de Solla Price (1965)

ery citation network there is a single piece ofpath-breaking researchmdashnamely the major workof one scientist or the core works emanating froma specialist group or specialty area Successfulstrands of research can thus be extracted or dis-tilled from this work In easily accessible networksof frequently cited articles the paths of scientificinsight and knowledge are clearly visible Thismethod can also be used to show connections be-tween different scientific schools and communitiesor their relative isolation from each other (Lucio-Arias and Scharnhorst 2012)

As Lucio-Arias and Leydesdorff (2008) show amain path analysis of these temporally orderedgraphs reveals the mechanisms of disseminationand diversification (diffusion) as well as those ofconsolidation and standardization (codification)of scientific knowledge This kind of citation-based historiography complements biographic andscientific-historic investigation and in so doingbridges the graph-theoretical concept of networksand the role of social networks in structuralist so-cial theory (Merton 1957)

If we determine the actual location of a publica-tion only on the basis of information given in thesources cited then essentially we forgo other in-formation in the document which may be equallycrucial for this determination Therefore a recon-struction of knowledge transfer should not but-tress itself solely on the analysis of citation net-works Citation analysis does however have theadvantage of being able to use the mathemati-cal calculations of SNA and thereby achieves re-sults that hermeneutic historiography alone can-not Moreover the standard methods of informa-tion retrieval use the textual similarities betweendocuments to show users of specifically retrievedtexts further texts that might be relevant for them(see section 6 S 10) More recent approachesto information retrieval embrace also other bib-liometric regularities (Mutschke et al 2011) co-author patterns and journal distributions

Relations (edges links) in a network of nodescan be captured mathematically in a square ad-jacency matrix A whose elements aij ge 0 are dif-ferent from zero if node i is related to node j Ifwe do not differentiate between relations of dif-ferent strengths then aij has a value of 1 if arelationship exists

In his above-mentioned article Derek Jde Solla Price (1965) presented the adjacency

3

matrix for citations between articles in a self-contained bibliography on N-rays whereby theones were symbolized with dots and the placesthat would have been filled by the zeros were leftblank (de Solla Price 1965 p 514 figure 6)2 Heordered the articles in temporal sequence accord-ing to their date of publication and omitted cita-tions of all sources external to the bibliographyThe adjacency matrix for the first twelve articlesis thus

A =

0 0 0 0 0 0 0 0 0 0 0 01 0 0 0 0 0 0 0 0 0 0 01 1 0 0 0 0 0 0 0 0 0 01 1 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 00 0 0 0 1 0 0 0 0 0 0 00 0 0 0 1 0 0 0 0 0 0 00 0 0 0 0 0 1 0 0 0 0 00 0 0 0 0 0 0 1 0 0 0 00 0 0 0 0 0 0 1 1 0 0 00 0 0 0 0 0 0 1 1 0 0 00 0 0 0 0 0 0 1 1 1 0 0

Because future articles could not be cited onesoccur in rows of this matrix only to the left of (orbelow) the main diagonal Thus because of thetemporal sequencing of the citation network deSolla Pricersquos adjacency matrix takes the form of atriangle along the main diagonal and to the rightof (or above) it occur only zeros (aij = 0forallj ge i)3

In figure 1 the graph of the first twelve arti-cles in the citation network disaggregate into twopartial graphs Each of these graphs representsindependently achieved results which could onlyat a subsequent point in timemdashnamely with theappearance of the first overview article on N-rays(number 75 in the bibliography)mdashbe interpretedas belonging together4 The adjacency matrixA of a citation network can be used to model areaderrsquos behavior moving from article to article byfollowing the cited sources For example a readermay begin with article 12 the starting time thusnoted is t = 0 Heshe can be described by thecolumn vector ~r(0) which contains eleven zerosand one one as the twelfth component By multi-plying this vector from the left with the transpose

2N-rays turned out to be fictive so for that reasonthe bibliography qualifies as self-contained This concreteexample of a citation graph will accompany us through thesubsequent sections of this paper

3Temporally ordered networks are acyclic Withinacyclic graphs there is no path along the directed linkswhich loops back to return to the starting point

4This expresses itself as co-citation (cf section 4 p 6)

of A one finds the reader by articles 8 9 and 10In the next step by means of the rule ~r larr AT~rheshe wanders from there to articles 7 8 and 9and so forth

~r(0) =

000000000001

~r(1) =

000000011100

~r(2) =

000000121000

We can refine this model to one of the randomreader5 whereby each component of the vectorscales to one ~R = ~r

sumri equiv ~rr+ Thus for a

given time t = 2 for example the componentsof the reader vector different from zero will beR7(2) = 14 R8(2) = 12 R9(2) = 14 Byscaling to one we can interpret these fractions asa probability namely the probability that at timet = 2 we would encounter the reader by article 78 or 9 should heshe upon completion of hisherreading randomly select one of the sources citedWe have a double chance of finding the reader byarticle 8 because heshe can arrive at 8 via 9 aswell as 10 This makes it clear why scaling to oneallows us now to designate the reader as a randomreader

Today with the aid of citation indexes readersare not only able to search for articles in the refer-ence lists of cited sources retrospectively but theycan also navigate temporally forward in citationnetworks We can model this process by using thetranspose of the transposed adjacency matrix thatis A itself (AT)T = A because reflection alongthe main diagonals reverses all of the arrows inthe graph of a directed network which is easy toshow

The adjacency matrix A gives the direct pathsbetween the nodes in the network along the di-rected edges For the model of the reader weused powers of A (or AT) A1 A2 A3 For ex-ample if we compare A2 with the graph in figure1 we see that the components of A2 indicate howmany (indirect) paths of length 2 there are be-tween the nodesmdashfor instance there are two such

5This refers to the random surfer model upon whichBrin and Page (1998) based their PageRank algorithm

4

paths between node 8 and node 12 (between theremaining pairs of nodes there is at most one pathof length 2) In general then a matrix Ak con-tains the number of ways of length k between thevertexes

3 Bibliographic Coupling

In accordance with Kessler (1963) two articles aresaid to be bibliographically coupled if at least onecited source appears in the bibliographies or ref-erence lists of both articles If we look for suchbibliographic couplings in the graph of the firsttwelve articles on N-rays (figure 1 p 3) we dis-cover a number of these Nodes 2 and 3 are bib-liographically coupled over node 1 as are nodes 2and 4 Nodes 3 and 4 are coupled over node 1 andover node 2 Nodes 6 and 7 are coupled over node5 Nodes 9 through 12 are coupled in pairs overnode 8 and nodes 10 to 12 are coupled in pairsadditionally over node 9

If a reader desires to locate a bibliographicallycoupled article in a citation network heshe mustfirst move one step along an arrow to the nextvertex and then from that node in the oppo-site direction of the next arrow As known fromgraph theory this process is described by the ma-trix B = AAT Its element bij in accordance withthe rules for matrix multiplication is the scalarproduct of the row vectors from A Because A isa binary matrix summation results in the numberof matching components of both row vectors thatis the number of common sources

Thus element bij indicates how many biblio-graphic couplings exist between articles i and jIn other words bij gives the number of paths oflength 2 via which one moves from i along the ar-row and then to j in the opposite direction Thesymmetry of the coupled pairs corresponds to thatof the matrix B = BT The main diagonal con-tains the numbers of bibliographic self-couplingsof an article namely the numbers of all of theirreferences to other articles in the network

Citation databases enable users to move tem-porally forward backward and laterally (by zig-zagging) Thematically similar articles appearingin the same volume of a journal are often tempo-rally so proximate that the earlier article cannotbe cited in the later one But they also reveal theirlikeness through similar reference lists that isthrough strong bibliographic coupling As early

as the late-1980s with the old CD-ROM edition ofthe Science Citation Index the user was directedfrom an article which heshe located to the twentymost strongly bibliographically coupled articlesvia the rdquorelated recordsldquo option6 The strengthof the coupling of two articles i and j is definedhere simply by the number of references that thearticles have in common as given by the elementbij of matrix B

In our example of the bibliography on N-rayswe can only include in our analysis the citation re-lations between articles in the N-ray bibliographyalthough clearly other sources have been cited inthe articlesrsquo reference lists which do not belongto the bibliography In an alternative approachwe can analyze a complete body of scientific litera-ture of a publication period together with all citedsources Using the SCI we could for instance an-alyze the publications in one specific year Ratherthan selecting a thematic excerpt or segment fromthe citation graph we then consider all of thejournal articles of that year with all of their citedsources including books patents newspaper ar-ticles etc Accordingly the resultant matrix isnot a square adjacency matrix A whose rows andcolumns represent the same vertexes but rather arectangular matrix each of whose rows representsan article and each of whose columns representsa cited source Only a few of the journal articlesfor that particular year will appear as a sourceThus we arrive at citation network consisting ofjust two types of nodes articles and sources Notethat the articles carry the same publication yearand the sources can be from any year Withinthis network only edges between nodes of differ-ent type are permitted Networks of this typeare also called bipartite the rectangular matrixis termed an affiliation matrix7

For the rectangular affiliation matrix A withm rows (articles) and n columns (sources) wecan also calculate the matrix of bibliographic cou-plings B = AAT Matrix B is also square in thiscase and contains for each of the m articles onerow and one column

Two articles both with long reference listscould contain many sources in common in whichcase they would be said to be strongly bibliograph-

6This use of bibliographic coupling for information re-trieval is still part of the on-line edition of the ScienceCitation Index now part of the Web of Knowledge (seehttpwokinfocom)

7From the Latin ad-filiare meaning to adopt as a son

5

ically coupled Articles with only a few referencestherefore would tend to be more weakly biblio-graphically coupled if coupling strength is mea-sured simply according to the number of refer-ences articles contain in common This suggeststhat it might be more practicable to switch to arelative measure of bibliographic coupling whichwe can define most simply by using set theoryIn references lists each cited source appears onlyonce thus we can see a reference list as a set ofcited sources In set theory language we formulatethis thus

bij = |Ri capRj |

that is the element bij of matrix B equals the sizeof the intersection of the reference lists in articlesi and j The Jaccard index (or Jaccard similar-ity coefficient) gives us a relative measure of theoverlap of two sets8

Jij =|Ri capRj ||Ri cupRj |

(1)

The Jaccard index of bibliographic coupling iszero if the intersection of the reference lists isempty it reaches a maximum of one if both listsare identical (because in this case the intersec-tion would be equal to the union)

Another relative measure of similarity betweensets which we can use here is the so-called Saltonindex9

Sij =|Ri capRj |radic|Ri||Rj |

(2)

In this case the average size of the sets is relatedto the geometric mean of the size of both setsHere too the index reaches a maximum of one foridentical sets and a minimum of zero for disjointones

4 Co-citation Networks

We speak of the co-citation of two articles whenboth are cited in a third article Thus co-citation

8The Swiss botanist and plant physiologist Paul Jac-card (1868ndash1944) defined this index in 1901

9The computer scientist Gerard Salton (1927ndash1995)who lived and worked in the United States was oneof the pioneers in the area of information retrieval (cfWikipedia) This index was introduced in Salton andMcGill (1983) In section 36 of the above-cited biblio-metrics textbook Havemann (2009) shows how Salton andMcGill define their index alternatively as the cosine of theangle between the row vectors of matrix A

can be seen as the counterpart of bibliographiccoupling Returning to our example we can alsofind a number of instances of co-citation amongthe first twelve articles on N-rays (figure 1) arti-cles 1 and 2 are co-cited twice (in articles 3 and4) articles 8 and 9 are co-cited three times (inarticles 10 11 and 12 respectively) and article10 is co-cited once with article 8 and once witharticle 9 (in article 12)

In the previous section we explained how thebibliographic coupling matrix B can be obtainedfrom the scalar product of the row vectors of theadjacency matrix A Now we have to constructthe scalar product of the column vectors fromA in order to calculate the elements for the co-citation matrix C

cij =sumk

akiakj

Since A is a binary matrix the summation yieldsthe number of common components of the respec-tive column vectors that is the number of cases inwhich articles appear in the same row or referencelist Written compactly we calculate C = ATAThus our model reader moves within the graphfirst in the opposite direction of the arrow andthen in a second step with the arrow Like ma-trix B matrix C is also symmetric The main di-agonal of C contains the number of cases in whichan article is co-cited with itself (which is the casefor every citation) The number cii is thereforethe number of all citations of article i in otherarticles in the network

Most of the elements in the co-citation ma-trix C of our example are equal to zero Thisis so because the content-related connections be-tween both citation strands only became apparentas co-citation of these papers initially with thepublication of the first overview article on N-rays(number 75 in the N-rays bibliography and thusnot visible in figure 1) Co-citation relations un-like bibliographic couplings are subject to changeMany content-related connections can or may onlybe recognized by later authors at some subse-quent point in time or conversely can or maybe deemed as no longer essential by later authors

As with the bibliographic coupling of articlesit is equally reasonable for purposes of co-citationanalysis to consider all of the journal articles ofa year with all of their cited sources We willnow analyze the bipartite network of articles and

6

sources introduced in the previous section notaccording to how the articles are coupled oversources but rather just the opposite that ishow co-citation in articles connects the sourcesto one another We can also calculate matrix Cin accordance with the bipartite network yieldingC = ATA

In the co-citation analysis of two successivevolumes of a bibliographic database many co-cited sources in the first yearrsquos papers will ap-pear again as co-cited sources in the second Cou-pling strength will vary however many new co-cited pairs of sources will join the old ones Thereference lists for a given yearrsquos papers practi-cally speaking are analogous to the results of anopinion survey designed to ascertain which citedsources are currently seen to be related to one an-other

The principle of co-citation was first applied byIrina Marshakova (1973) in Moscow in a studyon laser physics Independently from Marshakovathe principle was also propagated by Henry Small(1973) a scientist from the Institute for Scien-tific Information (ISI) in Philadelphia founded byEugene Garfield in 1960 Since the 1970s the co-citation perspective has been at the core of bib-liometric analyses of specialties fields scientificschools or paradigms in the sense of Kuhnmdashinother words co-citation has provided the mainthrust underlying our understanding of the socialand cognitive theoretical structure of science (DeBellis 2009)

All bibliometric networks can be visualized ormodeled graphically (We will come back to thisin section 8 below) Historically co-citation anal-ysis data were used for the mapping of scienceand for the first Atlas of Science project (Garfield1981) For such purposes the network of co-citedsources is calculated or derived from the referencelists of publications from a single yearrsquos paperswhereby only those sources are considered the ci-tation numbers of which exceed a certain thresh-old value (e g a threshold value of 5) Thesesources were seen by Henry G Small (1978) asconcept symbols In a network thus constructedthe next step is to try to determine clusters ofsources whose members have a strong relation-ship to each other but relate only weakly tosources in other clusters10

10In network analysis such clusters of nodes are alsocalled communities

To determine clusters of similar objects in ac-cordance with the above criteria a set of algo-rithms was developed If we wish to apply thesealgorithms we first have to decide which measureof co-citation strength between two sources bestapplies the absolute number of co-citations orfor instance one of the two relative measures pre-sented abovemdashthe Jaccard or Salton indexes

Relative measures of co-citation result in a weakcoupling strength among frequently cited sourceswhich are only rarely co-cited This seems appro-priate because many of the citing authors do notsee a closer relationship between those cited con-cept symbols At the ISI Henry Small first startedworking with the Jaccard index and later withthe Salton index (Small and Sweeney 1985) IrinaMarshakova (1973) did not use a relative measureInstead she calculated the expected values for co-citation numbers based upon the independence ofboth citation processes and accepted only thosenumbers that exceeded the expected values signif-icantly

In order to get from clusters of concept symbolsto a map the next step is aggregation Hereby wetake all of the nodes in one cluster and draw themtogether into a point Then we take all of thelinks between each set of two clusters and drawthese together into a single link of a determinedstrength that corresponds to the specific factualdistance between those clusters In this way wecreate a network of clusters that can be visual-ized The technique of multidimensional scalingor MDS has been frequently used to visualize com-plex networks on a twondashdimensional plane Todaynetworks are often visualized using force directedplacement or FDP

Since the clusters of nodes thus produced inturn represent the vertexes in a co-citation net-work using an analogous clustering procedure wecan now generate clusters of clusters and so onuntil all of the cited sources of a given yearrsquos pa-pers are united in a single cluster that representsthat part of science indexed by the database used

Co-citation cannot only be applied on arti-cles We can also inquire for example how of-ten authors are cited together in order to modelor map the structure of the expert communityOr we can analyze co-citations of entire jour-nals (see section 5) In neither case how-ever can we expect that aggregations of pa-pers represent just one specific subject Authors

7

for instance usually deal with several themesmdashsometimes simultaneouslymdashwhich can also belongto different specialized areas of expertise Anotherproblem of author co-citation is the growing ten-dency toward more research collaboration whichbecomes visible in the increasing number of au-thors per article in some fields The thematic flex-ibility of authors leads in fact to a real problemIf we wish to determine or define authorsrsquo areasof activity thematic flexibility turns out to be acrucial factor whenever we seek to trace dynamicprocesses in science (on this matter see section 8below)

5 Citation Networksof Journals

Research has been able to expand so much overthe centuries only because new areas of exper-tise have continually opened up and the variousresearch tasks have been distributed accordinglyamong the expert communities representing thesenew fields of scientific endeavor Each communityhas created its own specialized journal Along-side to these specialized journals journals coexistin which research results of general interest arepublished Currently the open-access movementchanges the journal landscape profoundly11 Stillwe can assume that the foundation of a journalis a response of a communicative need of a scien-tific community in one field one country or acrossseveral

But even the most highly specialized journalscontain more than just those articles contributedby the experts in their respective fields of researchthese periodicals also contain articles from otherresearch areas that could be of interest for anyreader of a particular journal at a given time Theresult of this is that the literature from one sci-entific area is not just to be found in the corejournals of that area but rather that it is broadlyscattered according to Bradfordrsquos law (Bradford1934)

Nevertheless despite the addition of literatureexternal to a core research field and in accordancewith the Porphyrian tree of knowledge articlesin one journal should cite the articles of journalsfrom contiguous fields more often than they wouldthose from fields or disciplines further away The

11see the Public Knowledge Project httppkpsfuca

early study by Gross and Gross (1927) was basedon this plausible assumption already They de-termined the number of citations of other jour-nals in the general chemistry publication Journalof the American Chemical Societymdashfor the pur-pose of providing librarians with data relevantfor library journal selection However number-of-journal-citations data gathered in this way arenot just influenced by thematic proximity or dis-tance but also simply by the quantity and qualityof the articles in the journal referenced Journalswith similar topics compete for the articles thatare most important for further research For thatreason articles submitted to a journal for publica-tion must undergo a qualitative appraisal processthe so-called peer review The bigger a journalrsquosreputation the more articles it will be offered andhence the more rigorous its review process is likelyto be Thus scientific periodicals differ not onlyaccording to area of expertise but also accordingto reputation

In sum then the citation flows in a networkof scientific journals are influenced by three mainfactors thematic contiguity the size of a journaland the reputation of a journal As a further in-fluencing variable can be added the usual numberof cited sources per article for the particular areaof specialty in question

We can correct for journal size by relating thenumber of citations to the corresponding numberof articles available to be cited as Garfield andSher (1963) did when they introduced the journalimpact factor (JIF) In order to take account ofthe different citation behavior customary in dif-ferent fields Pinski and Narin (1976) suggestedthat instead of relating the number of journal cita-tions to the number of citable articles this numbershould be related to the total number of referencesin all of the cited journalrsquos articles This is tan-tamount to a kind of import-export relationshipthat would also take into account that review ar-ticles with long reference lists are on average citedmore frequently than original articles publishingresearch results Thus journal citation networksconstructed with such a normalization will justmirror the actual thematic relationships of thoseperiodicals and their respective reputations

Compared to article citation networks journalsnetworks will naturally have substantially fewernodes and are for that reason not only moretransparent but also lend themselves more easily

8

to numeric analysis The citation numbers nec-essary to construct a journals network are pre-sented in aggregated form in the Journal CitationReports of the Science Citation Index and the So-cial Sciences Citation Index In the following wepresent two examples of journal network analyses

51 Citation FlowsBetween Journals

First we will examine different variants of a net-work consisting of five information science jour-nals (1) Information Processing and Manage-ment (2) Journal of the American Society for In-formation Science and Technology (3) Journal ofDocumentation (4) Journal of Information Sci-ence and (5) Scientometrics

We begin by constructing a network thathas been weighted with reciprocal citation num-bers (including self-citations by the journals in thenetwork) With data from the Social Sciences Edi-tion of the Journal Citation Reports we derive thefollowing adjacency matrix for the citation win-dow 2006 and the publication window 2002ndash2006

A =

79 65 15 6 2442 182 11 15 446 22 37 8 6

20 26 13 30 117 48 7 10 254

(3)

Matrix A contains only elements aij 6= 0 becauseall five journals cite each other as well as them-selves The main diagonal contains the journalself-citations In the graph of A edges (links) be-tween all the five vertices flow in both directionsLoops represent self-citations

Let us now like Pinski and Narin (1976) switchto a network where the number of citations aij ofjournal j by journal i are divided by the sum aj+of the number of references to j in the 5-journalsnetwork yielding γij = aijaj+12

Pinski and Narin go even further They arguethat citation in a prestigious journal should countmore than citation in a less important one Butprecisely because they measure prestige itself bynumber of citations (per cited source) they end upwith a recursive concept of that notion like theconcept of prestige that has been debated sincethe 1940s for social network analysis (Wasserman

12The actual data can be found in the book by Have-mann (2009)

and Faust 1994) In social networking it is notonly important how many people one knows onemust know the ldquorightrdquo people namely those whoknow a lot of others who are the ldquorightrdquo ones

How do we conceptualize this recursive notionof prestige mathematically To this end we willexamine a model of prestige redistribution for thefive information science journals under consider-ation here To begin (t = 0) all five journalsshould have the same weight so we fix this at 1The weights are written as a column vector Anal-ogous to our procedure for the reader model inan article citation network we then multiply thecolumn vector from the left with the transpose ofthe adjacency matrix ~w(1) = γT ~w(0) In this wayweights are redistributed within the network Thenew column vector contains exactly the row sumsof γT i e wj(1) = γ+j = a+jaj+ the import-export ratios of journals By repeating this proce-dure many times over we can see that the weightsiteratively approach fixed limit values In accor-dance with this for trarrinfin the following equationholds13

~w = γT ~w

This means that the weights determined by the it-eration fulfill an equation which can be seen as anexpression of the recursive definition of prestigeviz that the weight of journal j results from thecitation relations to all of the other journals (aswell as to itself) according to how close these rela-tions are factored by the weight of the other jour-nals Pinski and Narin call this influence weightDetermination equations of this type are also re-ferred to as bootstrap relations

Important to note here is that the iteration pro-cedure is somewhat incorrectly labeled ldquoredistri-butionrdquo The sum of the five weights after thefirst iteration step is 476 lt n = 5 In other wordsweight is lost (because the import-export relationsof the larger journals are more propitious thanthose of the smaller ones) However this discrep-ancy can be corrected through scaling for trarrinfinwe obtain the normalized components 076 133103 064 and 125 By scaling to n it becomespatently clear who the winners and losers of re-distribution are

13That this relationship holds not just in our special casebut in every case is guaranteed by the theory of eigenval-ues Matrices of type γT have a principal (maximal) eigen-value of 1 and the iteration determines the correspondingeigenvector

9

Following Pinski and Narin Nancy Geller(1978) considered a kind of modified redistribu-tion of journal weights Her starting point wasthe theory of Markov chains a special class ofstochastic or random processes in which (justas it is for our case here) the situation at timet + 1 is completely determined by the situationat time t Instead of using γ she took a some-what differently scaled matrix γlowast with the ele-ments γlowastij = aijai+ whose transpose belongs tothe stochastic matrices Stochastic matrices havethe property that they leave the sum of vector ele-ments unchanged Such matrices describe true re-distribution they are therefore well-suited for thedescription of random processes in which proba-bility is redistributed over possible system statesNancy Gellerrsquos algorithm is also interesting be-cause there are only a few steps that separate itfrom Googlersquos PageRank algorithm as presentedin the textbook by Havemann (2009 section 33)This is an example for a method developed for ci-tation networks which became useful also for Webanalysis

52 Citation Environmentsof Individual Journals

If we consider citation matrices for large groups ofjournals we see that many cells in such a matrixare empty and that citation tends to be confinedto smaller more densely networked groups (Ley-desdorff 2007) This is not surprising it mirrorsthe real-world design and relations of scientificspecialty areas and disciplines Nevertheless thedelineation of areas remains a problem which hasnot been satisfactorily resolved the borders arefluid

Leydesdorff (2007) suggested another methodfor determining the position of individual jour-nals within the mass of and relative to all of theareas of science The starting point is an ego net-work let us take for example the journal SocialNetworks Social Networks has two citation envi-ronments The first consists of those journals ina specific time frame that cite articles in SocialNetworks from a unique time period We couldcall this group or set of journals the awarenessarea spillover area or influence area of SocialNetworksmdashin other words its citation impact en-vironment The second environment consists ofthose journals that are cited in articles in Social

Networksmdashthat is its knowledge base For eachgroup of journals then it is possible to carry outthe following analysis independently We ascer-tain all of the reciprocal citation links for eachrespective group with the aid of the Journal Cita-tion Reports Social Networks our starting pointis a member of both environments For these cita-tion environments we obtain asymmetric matriceslike in equation 3 (p 9)

By applying the process described above weobtain groups of journals that have similar cita-tion behaviors these groups can thus be inter-preted or defined as specialty areas The po-sition of the journal whose ego network was atthe starting point gives us information about as-pects of interdisclipinarity (for example by ap-plying betweenness centrality) and a possible in-terface function (Leydesdorff 2007) If we repeatthis analysis over a sequence of years the some-times changing function of a journal in an equallydynamic journal environment becomes visible Inthe case of Social Networks what was revealed wasthat this journalrsquos functioning as a possible bridgebetween traditional areas of social science and newmethods and approaches from network theory inphysics could be reduced to a single year namely2004 (Leydesdorff and Schank 2008)

6 Lexical Couplingand Co-Word Analysis

For computer-supported information retrieval(IR) documents are characterized by the termsused in them A manageable (not too big) butnevertheless informative set of such terms com-prised mainly of keywords supplied by authors orindexers or significant words in a documentrsquos ti-tle can serve well for IR In the extreme all ofthe words in a document can be taken into ac-count What is interesting then is the frequencywith which these words occur not counting stopwords like ldquotherdquo ldquoandrdquo ldquoofrdquo and others Theappearance of terms in a collection or set of docu-ments is described by the term-document matrixA whose element aij tells us how often in docu-ment i the term j occurs

The term-document matrix like the matrix in-troduced above consisting of documents and citedsources (see section 3) describes a bipartite net-work namely one of terms and documents In

10

this case however by taking into account the fre-quency with which terms occur in a document weweight the network

The so-called vector-space model of IR not onlyreveals the similarity between documents based onthe terms used in them (this is lexical coupling)it also shows the relationships between the termsbased on their common usage in the documents(this is the basis of co-word analysis) The formercorresponds to bibliographic coupling of articlesthe latter refers to the co-citation of sources (sec-tion 4)

At the beginning of the 1980s Michel Callonand his group in France proposed co-word anal-yses as an alternative or supplement to prevail-ing co-citation methods (Callon Courtial Turnerand Bauin 1983) So-called ldquocognitive sciento-metricsrdquo is supposed to make the relationshipsbetween documents clearly evident where forwhatever reason reciprocal citation has occurredonly sparsely Anthony van Raanrsquos group in theNetherlands developed interactive tools for co-word based science maps in the context of eval-uations These maps can make the activities ofinstitutions or countries in specific fields of sciencevisible (Noyons 2004) Clusters in these networkswere interpreted as themes or topics and tempo-rally hierarchically branched trees provided someinsight into the dynamics of scientific areas (Ripand Courtial 1984)

Co-word analyses can be understood as theempirical method of the so-called actor-networktheory a social theory in the field of scienceand technology studies (Latour 2005 De Bellis2009) Despite more recent and promising text-based network analyses for identifying innovation-relevant scientific researchmdashsome researchers evenspeak of literature-based discoveries (Swanson1986 Kostoff 2007)mdashexpert knowledge for the in-terpretation of text-based agglomerations is stillnecessary And despite decades-long efforts bymany groups as Howard White put it succinctlyin a 2007 discussion we are still not able to an-alyze and visualize the development and changeof scientific paradigms or scientific controversiesin such a way that they are accessible to non-experts14

14Howard White 11th International Conference of Sci-entometrics and Informetrics Madrid 2007 workshop onmapping personal notes

This deficit may be due in part to the ambiva-lence of language In a study by Leydesdorff andHellsten (2006) the authors pointed to the signif-icance of context for words and they suggestedreturning to the text-document matrices for wordanalyses as well in order to gain more completeinformation Probably the answer also lies in theclever selection of a base unit for statistical proce-dures An analysis of developing discussion focalpoints in online forums has shown that alreadyin one single post contributors brought up or re-ferred to different topics Therefore in this partic-ular case the choice of sentences as the base unitfor statistical network analyses produced betterresults than did the longer text passages of onepost (Prabowo Thelwall Hellsten and Scharn-horst 2008)

In text mining in sources (such as all key-words all titles abstracts or full text) extrac-tion of terms or phrases is performed according todifferent algorithms and statistical measures forfrequency and correlation (including network in-dicators) are applied for which the reference unitsuch as a phrase a sentence a document is an im-portant parameter The plethora of combinationsof these elements presents a great challenge to textanalysis and text miningmdasha challenge which canonly be addressed through strong networking of alltext-based structural searches including semanticWeb research (van der Eijk van Mulligen KorsMons and van den Berg 2004)

One method of information retrieval devel-oped for extracting topics from corpora whichuses both types of links in bipartite networks ofdocuments and termsmdashnamely co-word analysisand lexical couplingmdashis latent semantic analysis(LSA) proposed by Deerwester Dumais FurnasLandauer and Harshman (1990) This method isbased on singular value decomposition (SVD) ofthe term-document matrix By means of SVD bi-partite networks of articles and cited sources canalso be analyzed thematically (Janssens Glanzeland De Moor 2008 Mitesser Heinz Havemannand Glaser 2008)

7 Co-authorship Networks

Co-authorship is considered an indicator of coop-eration If two or more authors share the respon-sibility for a publication presenting particular re-search results then in the course of the research

11

process that led to those results these individu-als ought to have worked together in some way oranother at one time

It is appropriate and important to agree ona concept of cooperation before the structureof co-authorship networks is analyzed or inter-preted (Sonnenwald 2007) To discuss this in-depth however would exceed the scope of thisarticle so we refer the reader to the definition ofresearch collaboration in the aforementioned bib-liometrics textbook (Havemann 2009 section 37)where the author relies on work of Grit Laudel(1999 S 32ndash40) see also Laudel (2002)

Not every form of collaboration finds its ulti-mate expression in a co-authored work On theother hand a certain tendency to arbitrarily as-sign co-authorship to individuals (or force one onthem) cannot be denied On the other handshared responsibility for an article in a renownedjournal is only rarely possible without some formof cooperation The co-authors one would ex-pect at least know each other15 and this realis-tic expectation is what makes the analysis of co-authorship networks interesting

Co-authorship networks are usually introducedas networks of authors In its simplest form theco-authorship network is unweighted A link be-tween two authors exists if both appear togetheras authors of at least one publication in the bib-liography or body of literature under investiga-tion Weighting the link with the number of ar-ticles in which both appear together as authorssuggests itself but this kind of modeling still usesonly part of the information about cooperationthat can actually be extracted from a bibliogra-phy What it fails to capture is whether the rela-tionships between authors are purely bilateral orwhether these researchers work together in largergroups If for example three authors cooperateon one article then between them in total threelinks of weight 1 can be found this is exactly thesame as if three pairs of them had each publishedone article together (in total then three articles)

Another aspect which could be taken into ac-count is the sequence in which the co-authors arelisted Though in different communities thereare different rules whom to place first and last ithas been proposed to include information on au-thor sequence in bibliometric indicators (Galam

15The likely exception here being articles with 100 ormore authors

2011) More complete information is used if co-authorship is presented as a bipartite network ofauthors and articles Element aij of affiliation ma-trix A is equal to 1 if author i appears among theauthors listed for article j otherwise it is equal tozero

Up to now most investigations have confinedthemselves to co-authorship networks in whichonly authors are represented as nodes and pub-lications are not The adjacency matrix B of sucha network can be calculated from the affiliationmatrix A whereby B = AAT This becomes im-mediately apparent if we carry our deliberationson networks of bibliographically coupled articles(section 3) over to the authors-articles networkIn a bipartite network a co-author is someonewhom we reach whenever we take a step towarda publication (AT) and then back again to an au-thor (A) We derive the co-authorship figures fortwo authors from the scalar product of the (bi-nary) row vectors of A The diagonal element biiin matrix B is therefore equal to the number ofpublications to which author i was a contributor

So how are co-authorship networks structuredFirst of all we frequently find that an overwhelm-ing majority of specialty area authors (more than80 ) are grouped together in a single componentof the network namely the so-called main com-ponent The remaining authors conversely of-ten comprise only small groups of researchers con-nected to one another (at least indirectly) overco-authorship links All of the distances occur-ring between the cooperation partnersmdashwhetherthese are functional (subject-related) institu-tional geographical language-related cultural orpoliticalmdashcannot prevent the emergence of onebig interrelated network of cooperating scientists

Equally worthy of note in comparison to sizeare the very slight distances between authorsin the main components of co-authorship net-works In a co-authorship network consisting ofmore than one million biomedical science authorswhose combined output for the period 1995ndash99was more than two million published articles (ver-ified in Medline) the statistical physicist MarkE J Newman (2001a) found that over 90 of theauthors were grouped together in the main com-ponent16 The second largest component of this

16Because authors in bibliographic databases are not al-ways clearly identifiable the figures vary according to themethod of identification used Newman found that if he

12

network contained only 49 authors The maximaldistance between two authors in the main compo-nent (also called the network diameter) is a matterof only 24 steps or hops that is on the shortestpath between two arbitrary nodes lie a maximumof 23 other nodes The average length of all of theshortest paths between nodes in the main compo-nent is less than five hops (Newman 2001b)

This ldquosmall worldrdquo effect first described

by Milgram17 is like the existence of a giant

component18 probably a good sign for sci-

ence it shows that scientific informationmdash

discoveries experimental results theoriesmdash

will not have far to travel through the net-

work of scientific acquaintance to reach the

ears of those who can benefit by them

(Newman 2001b p 3)

Newmanrsquos statement restricts itself to the in-formal communication of results between re-searchers which so often precedes formal publi-cation This observation confirms one of the twobehavioral principles of science Manfred Bonitz(1991) formulated early in the history of sciento-metrics They read as

Holographic principle Scientific infor-mation ldquoso behavesrdquo that it is eventuallystored everywhere Scientists ldquoso behaverdquothat they gain access to their informationfrom everywhere

Maximum speed principle Scientific in-

formation ldquoso behavesrdquo that it reaches its

destination in the shortest possible time

Scientists ldquoso behaverdquo that they acquire

their information in the shortest possible

time

Newmanrsquos observation confirms the second ofBonitzrsquo principles

The famous ldquosmall worldrdquo experiment referredto above undertaken by social psychologist Stan-ley Milgram (1967) for the acquaintance network

took into account authorsrsquo full names the main componentwould comprise 15 million different authors however ifhe included the surnames and only initials for first namethen this figure shrank to just under 11 million individu-als For statistical analysis purposes this ambiguity is onlyof minor importance but it strongly impairs the system-atic pursuit of individual research Newer methods dependon a combination of names addresses channels of publica-tion and citation behavior in order to automatically andunambiguously ascribe researcher identification

17Milgram (1967)18Newman (2001a)

in the US resulted in an average distance of sixhops19 Newman explains the small-world ef-fect taking himself as an example he has 26 co-authors who in turn author publications togetherwith a total of 623 other researchers

The ldquoradiusrdquo of the whole network

around me is reached when the number

of neighbors within that radius equals the

number of scientists in the giant component

of the network and if the increase in num-

bers of neighbors with distance continues

at the impressive rate [ ] it will not take

many steps to reach this point (Newman

2001b p 3)

The number of co-authors that an author hasis a measure of hisher interconnectedness Itis equal to the number of hisher links (degreeof the node) in the co-authorship network In agiven specialty area marginal or peripheral au-thors have only a few cooperation partners Innetwork analysis therefore the degree of a nodeis also a measure of its centrality Often the distri-bution of co-authorship is skewed a few authorshave many co-authors many authors have only afew co-authors (Newman 2001a p 5)

Another measure of centrality is the between-ness of a given node i Betweenness is defined asthe total number of shortest paths between arbi-trary pairs of nodes which run through node iConceivable then is that nodes with higher val-ues of betweenness are responsible for shorter dis-tances in networks and also for the emergence oflarge main components And in terms of be-tweenness centrality a number of frontrunnersalso set themselves clearly apart from the remain-ing authors (Newman 2001b p 2)

Finally the different roles and functions of re-searchers in co-authorship networks is a topic thathas begun to receive increasing attention Lam-biotte and Panzarasa (2009) have recently con-sidered the importance of a researcherrsquos function(viz having a high level of connectivity and au-thority within a community versus being an facil-itator or communicator between communities) forthe dissemination of new ideas

19Milgramrsquos subjects had the task of sending a lettervia their acquaintances as close as possible to a recipientunknown to themselves The letters that actually reachedthe targeted individual had been forwarded on average bysix persons (including the subject)

13

8 Outlook

Paul Otlet the pioneer in knowledge organizationinherited us a wealth of drawings of the evolv-ing universe of knowledge (van den Heuvel andRayward 2011) Among them he depicted themain classes of his decimal classification scheme20

as longitudes of a globe of knowledge (van denHeuvel and Rayward 2005 van den Heuvel 2008)Katy Borner has inspired an artistic visualizationof the sciences as a growing ldquoorganismrdquo (Bornerand Scharnhorst 2009) Recent efforts for a ge-ography or geology of the expanding globe of sci-entific literature have led to a revival of ldquosciencemapsrdquo The Atlas of Science presented by the ISIin the early 1980s (Garfield 1981) has been fol-lowed by a New Atlas of Science (Borner 2010)21

Nevertheless scientists are still struggling to findadequate imagery or as the case may be an ap-propriate mathematical model to represent thedeeper understanding we have of the dynamic pro-cesses of evolving science networks

Against this backdrop of the ldquonew network sci-encerdquo the future of bibliometric network analyseslies in the incorporation of methods and tools fromother disciplinary areas Visualizations representa possible platform for interdisciplinary encoun-ters (Borner 2010) These new ldquomaps of sciencerdquohave met with similar controversy to that whichwe know from the history of geographical mapsIt therefore comes as no surprise that mappersof science have sought to build bridges to car-tography If we apply the methods of structureidentification (self-organized maps) as they weredeveloped for complexity research (Agarwal andSkupin 2008) then it is just a small step from thequestion of possible models to the explication ofcomplex structure formation

20Universal Decimal Classification UDC see also http

udccorg21The Atlas of Science of Katy Borner captures parts of a

remarkable long-term project called ldquoPlaces and Spacesrdquowhich is a growing exhibition of science maps This exhibi-tion is particularly interesting for one because the publicinvitation and selection process enables highly varied andunique depictions to achieve greater visibility through pub-lic display and second because the themes of the yearlyiterations embrace such a broad and diverse spectrum ofsubject mattermdashrunning for example from the history ofcartography over maps as deceptive or phantasy picturesup to maps drawn by children Many of the maps on dis-play are based on network data For more information seehttpwwwscimapsorg

For bibliometric networks next to the tradi-tional topic of structure identity the topic ofstructure formationmdashand with it the dimensionof timemdashsteps more forcefully into the foregroundof interest All of the methods we have used up tonow in the global cartography of science or knowl-edge landscapes (Scharnhorst 2001) confirm theexistence of collectively generated self-organizingstructures in the form of scientific disciplines andscientific communities On the macro-level thesepatterns are so persistent that as Klavans andBoyack (2009) have recently shown they mani-fest themselves recurrently relatively independentof the respective research methods22

It is more difficult to find general patterns orregularities on the micro-level for the interactionsbetween authors or for those between authorsand documented knowledge What remains is adeeper understanding of the dynamic mechanismsthat describe the emergence of a science land-scape and individual navigation within it Weexpect dynamic mathematical models to repro-duce already known statistical bibliometric lawslike Lotkarsquos law of scientific productivity (Lotka1926) or Bradfordrsquos law of scattering (Bradford1934) mentioned above Complexity researchwith notions like energy entropy or fitness land-scapes (Scharnhorst 2001) offers a rich repertoireof contemporary analytical methods and modelswhich can do justice to the network character ofcomplex systems (Fronczak Fronczak and Ho lyst2007) Recent empirical research in this area isdevoted to contemporary effects in evolving bib-liometric networks (Borner Maru and Goldstone2004) and the search for burst phenomena (ChenChen Horowitz Hou Liu and Pellegrino 2009) orthe application of epidemic models to the dissem-ination of ideas (Bettencourt Kaiser and Kaur2009) But also on the level of conceptual modelsphilosophy and sociology of science have embracedthe idea of an epistemic landscape and mathemat-ical models for the search behavior of researcherin it (Payette 2012 Edmonds Gilbert Ahrweilerand Scharnhorst 2011)

Topic delineation on both the micro as themacro level is a pertinent problem of sciencestudies in general and bibliometrics in particu-lar However the problem of topic delineation

22The ring structure of the consensus map bears as-tounding similarity to Otletrsquos historical visions of a globeof knowledge

14

in citation-based networks of papers might bea consequence of the overlap of thematic struc-tures The overlap of themes in publications iswell known to science studies A recent study byHavemann Glaser Heinz and Struck (2012) onthe meso level tests three local approaches to theidentification of overlapping communities devel-oped in the last years (Fortunato 2010)

The heuristic value of dynamic models lies intheir broad range of available possible mecha-nisms forms of interaction and feedback whichcan be connected to distinctive types of structureformation Thus for example the topically rele-vant notion of field mobility23 can be drawn uponfor the explication of growth processes in compet-ing scientific areas for which in addition schoolsof knowledge as sources of self-accelerating growthare also highly relevant (Bruckner and Scharn-horst 1986) Through mobility a network is cre-ated between scientific areas and at the sametime all of the elementary dynamic model mech-anisms and a quasi ldquometabolic networkrdquo of knowl-edge systems are formed (Ebeling and Scharn-horst 2009) The wanderings of the researchercan be followed or read from hisher self-citationsWhereas self-referencing is usually ignored in sci-entometrics these citations constitute an excel-lent source for the investigation and analysis ofmobility in scientific fields Structures in theself-citation network can be interpreted as the-matic areas which become visible through differ-ent groups of keywords and co-authorships Thewandering of an individual between research ar-eas as shown by hisher lifework of collected sci-entific output can be displayed or represented asa unique bar code pattern (Hellsten LambiotteScharnhorst and Ausloos 2007) This creativefuzziness of the scientist can also be shown on sci-ence maps as a spreading phenomenon wherebythe scientist instead of the wandering dot is de-picted as a flow field (Skupin 2009)

The use of models as generators of hypothe-ses presupposes that the hypotheses have beenempirically tested and accordingly put into thecontext of social communication socioeconomicand political theories of ldquoscience qua social sys-

23The term ldquofield mobilityrdquo was introduced in bibliomet-rics by Jan Vlachy (1978) to describe the thematic wander-ing of scientists Thematic wandering results from new dis-coveries as well as other grounds such as the connectivitybetween scientific areas (Bruckner Ebeling and Scharn-horst 1990)

temrdquo (Glaser 2006) This connection to tradi-tionally strongly sociologically anchored SNAmdashespecially the proposed inclusion of social cogni-tive and personality attributes of actors for mod-eling the evolution of networks and dissemina-tion phenomena within networksmdashand the inclu-sionapplication of dynamic modeling approachesin SNA provide an excellent basic framework forusing models to generate theory (Snijders van deBunt and Steglich 2010)

Semantic web applications creating new linkedrepositories of data publication and conceptslarge scale data mining techniques (as originat-ing from Artificial Intelligence) meaningful visu-alizations and mathematical models of science allcontribute to a better understanding of the sciencesystem However similar to the variety of possi-ble network visualizations is the variety of math-ematical and conceptual models of science Of-ten knowledge about data mining modeling andvisualizing is inherited by different relative iso-lated academic tribes (Becher and Trowler 2001)Translating and linking concepts and methodswhere appropriate and possible is one remainingtask Exploring and better understanding ourown science history is another one Only if we suc-ceed in bridging unique individual science biogra-phies with the laws and regularities of the sciencesystem as a whole will we be able to learn moreabout the development of new ideasmdashknowledgegenerationmdashand be better able to intervene in thisprocess in a more controlled and supportive man-ner

Acknowledgement

We thank Mary Elizabeth Kelley-Bibra for help-ing us with the translation of the text into English

References

Agarwal P and A Skupin (2008) Self-organising maps applications in geographicinformation science Wiley-Blackwell

Becher T and P R Trowler (2001) AcademicTribes and Territories Intellectual enquiryand the culture of disciplines (2nd ed) So-ciety for Research into Higher Education Open University Press

15

Bettencourt L M D I Kaiser and J Kaur(2009) Scientific discovery and topologicaltransitions in collaboration networks Jour-nal of Informetrics 3 (3) 210ndash221 SpecialEdition on the Science of Science Concep-tualizations and Models of Science ed byKaty Borner amp Andrea Scharnhorst

Bonitz M (1991) The impact of behav-ioral principles on the design of the sys-tem of scientific communication Sciento-metrics 20 (1) 107ndash111

Borner K (2010) Atlas of Science VisualizingWhat We Know MIT Press

Borner K J T Maru and R L Goldstone(2004) The simultaneous evolution of au-thor and paper networks Proceedings of theNational Academy of Sciences of the UnitedStates of America 101 5266ndash5273

Borner K S Sanyal and A Vespignani(2007) Network science Annual Reviewof Information Science and Technology 41537ndash607

Borner K and A Scharnhorst (2009) Vi-sual conceptualizations and models of sci-ence Journal of Informetrics 3 (3) 161ndash172Science of Science Conceptualizations andModels of Science

Bradford S C (1934) Sources of informationon specific subjects Engineering 137 85ndash86

Brin S and L Page (1998) The anatomy ofa large-scale hypertextual Web search en-gine Computer Networks and ISDN Sys-tems 30 (1ndash7) 107ndash117

Bruckner E W Ebeling and A Scharnhorst(1990) The application of evolution modelsin scientometrics Scientometrics 18 (1) 21ndash41

Bruckner E and A Scharnhorst (1986)Bemerkungen zum Problemkreis einerwissenschafts-wissenschaftlichen Interpreta-tion der Fisher-Eigen-Gleichung dargestelltan Hand wissenschaftshistorischer Zeug-nisse Wissenschaftliche Zeitschrift derHumboldt-Universitat zu Berlin Mathema-tisch-naturwissenschaftliche Reihe 35 (5)481ndash493

Callon M J P Courtial W A Turnerand S Bauin (1983) From translations to

problematic networks An introduction toco-word analysis Social Science Informa-tion 22 (2) 191ndash235

Chen C Y Chen M Horowitz H HouZ Liu and D Pellegrino (2009) Towardsan Explanatory and Computational Theoryof Scientific Discovery Journal of Informet-rics Special Edition on the Science of Sci-ence Conceptualizations and Models of Sci-ence ed by Katy Borner amp Andrea Scharn-horst

De Bellis N (2009) Bibliometrics and CitationAnalysis From the Science Citation Indexto Cybermetrics Lanham The ScarecrowPress ISBN-13 978-0-8108-6713-0

de Solla Price D J (1965) Networks of scien-tific papers Science 149 510ndash515

Deerwester S S T Dumais G W FurnasT K Landauer and R Harshman (1990)Indexing by latent semantic analysis Jour-nal of the American Society for InformationScience 41 (6) 391ndash407

Ebeling W and A Scharnhorst (2009)Selbstorganisation und Mobilitat von Wis-senschaftlern ndash Modelle fur die Dynamik vonProblemfeldern und WissenschaftsgebietenIn W Ebeling and H Parthey (Eds) Selb-storganisation in Wissenschaft und TechnikWissenschaftsforschung Jahrbuch 2008 pp9ndash27 Wissenschaftlicher Verlag Berlin

Edmonds B N Gilbert P Ahrweiler andA Scharnhorst (2011) Simulating the socialprocesses of science Journal of ArtificialSocieties and Social Simulation 14 (4) 1ndash6 httpjassssocsurreyacuk14

414html (Special issue)

Egghe L and R Rousseau (1990) Introductionto Informetrics Quantitative Methods in Li-brary and Information Science Elsevier

Fortunato S (2010) Community detection ingraphs Physics Reports 486 (3-5) 75ndash174

Fronczak P A Fronczak and J A Ho lyst(2007) Analysis of scientific productiv-ity using maximum entropy principle andfluctuation-dissipation theorem PhysicalReview E 75 (2) 26103

Galam S (2011) Tailor based allocations formultiple authorship a fractional gh-indexScientometrics 89 (1) 365ndash379

16

Garfield E (1955) Citation indexes for scienceA new dimension in documentation throughassociation of ideas Science 122 (3159)108ndash111

Garfield E (1981) Introducing the ISI At-las of Science Biochemistry and Molec-ular Biology Current Contents 42 279ndash87 Reprinted Essays of an Infor-mation Scientist Vol 5 p 279ndash2871981ndash82 httpwwwgarfieldlibrary

upenneduessaysv5p279y1981-82pdf

Garfield E A I Pudovkin and V S Istomin(2003) Why do we need algorithmic his-toriography Journal of the American So-ciety for Information Science and Technol-ogy 54 (5) 400ndash412

Garfield E and I H Sher (1963) Newfactors in the evaluation of scientificliterature through citation indexingAmerican Documentation 14 (3) 195ndash201httpwwwgarfieldlibraryupenn

eduessaysv6p492y1983pdf 2005-4-28

Geller N L (1978) On the citation influencemethodology of Pinski and Narin Informa-tion Processing amp Management 14 (2) 93ndash95

Gilbert N (1997) A simulation of the struc-ture of academic science

Glanzel W (2003) Bibliometrics as a researchfield A course on theory and applicationof bibliometric indicators Courses Hand-out httpwwwnorslisnet2004Bib_

Module_KULpdf

Glaser J (2006) Wissenschaftliche Produk-tionsgemeinschaften Die soziale Ordnungder Forschung Campus Verlag

Gross P L K and E M Gross (1927) Col-lege Libraries and Chemical Education Sci-ence 66 (1713) 385ndash389

Havemann F (2009) Einfuhrung in die Bib-liometrie Berlin Gesellschaft fur Wis-senschaftsforschunghttpd-nbinfo993717780

Havemann F J Glaser M Heinz andA Struck (2012 March) Identifying over-lapping and hierarchical thematic structuresin networks of scholarly papers A compar-ison of three approaches PLoS ONE 7 (3)e33255

Havemann F and A Scharnhorst (2010) Bib-liometrische Netzwerke In C Stegbauerand R Hauszligling (Eds) Handbuch Net-zwerkforschung pp 799ndash823 VS Ver-lag fur Sozialwissenschaften 101007978-3-531-92575-2 70

Hellsten I R Lambiotte A Scharnhorstand M Ausloos (2007) Self-citations co-authorships and keywords A new approachto scientistsrsquo field mobility Scientomet-rics 72 (3) 469ndash486

Huberman B A (2001) The laws of the Webpatterns in the ecology of information MITPress

Janssens F W Glanzel and B De Moor(2008) A hybrid mapping of informationscience Scientometrics 75 (3) 607ndash631

Kessler M M (1963) Bibliographic couplingbetween scientific papers American Docu-mentation 14 10ndash25

Klavans R and K Boyack (2009) Toward aconsensus map of science Technology 60 2

Kostoff R N (2007) Literature-related dis-covery (LRD) Introduction and back-ground Technological Forecasting amp SocialChange 75 (2) 165ndash185

Lambiotte R and P Panzarasa (2009) Com-munities knowledge creation and informa-tion diffusion Journal of Informetrics 3 (3)180ndash190

Latour B (2005) Reassembling the social Anintroduction to actor-network-theory Ox-ford University Press USA

Laudel G (1999) InterdisziplinareForschungskooperation Erfolgsbedin-gungen der Institution rsquoSonderforschungs-bereichrsquo Berlin Edition Sigma

Laudel G (2002) What do we measure by co-authorships Research Evaluation 11 (1) 3ndash15

Leydesdorff L (2001) The Challenge of Scien-tometrics the development measurementand self-organization of scientific communi-cations Upublish Com

Leydesdorff L (2007) Visualization of the cita-tion impact environments of scientific jour-nals An online mapping exercise Jour-

17

nal of the American Society for InformationScience and Technology 58 (1) 25ndash38

Leydesdorff L and I Hellsten (2006) Measur-ing the meaning of words in contexts Anautomated analysis of controversies aboutrsquoMonarch butterfliesrsquo rsquoFrankenfoodsrsquo andrsquostem cellsrsquo Scientometrics 67 (2) 231ndash258

Leydesdorff L and T Schank (2008) Dynamicanimations of journal maps Indicators ofstructural changes and interdisciplinary de-velopments Journal of the American Soci-ety for Information Science and Technol-ogy 59 (11) 1810ndash1818

Lotka A J (1926) The frequency distribu-tion of scientific productivity Journal of theWashington Academy of Sciences 16 (12)317ndash323

Lucio-Arias D and L Leydesdorff (2008)Main-path analysis and path-dependenttransitions in HistCite-based historiogramsJournal of the American Society for In-formation Science and Technology 59 (12)1948ndash1962

Lucio-Arias D and L Leydesdorff (2009)The dynamics of exchanges and referencesamong scientific texts and the autopoiesisof discursive knowledge Journal of Infor-metrics

Lucio-Arias D and A Scharnhorst (2012)Mathematical approaches to modeling sci-ence from an algorithmic-historiographyperspective In A Scharnhorst K Bornerand P Besselaar (Eds) Models of Sci-ence Dynamics Understanding ComplexSystems pp 23ndash66 Springer Berlin Heidel-berg

Marshakova I V (1973) System of documentconnections based on references Nauchno-Tekhnicheskaya Informatsiya Seriya 2 ndash In-formatsionnye Protsessy i Sistemy 6 3ndash8(in Russian)

Merton R K (1957) Social theory and socialstructure Free Press New York

Milgram S (1967) The small world problemPsychology Today 2 (1) 60ndash67

Mitesser O M Heinz F Havemann andJ Glaser (2008) Measuring Diversity of Re-search by Extracting Latent Themes from

Bipartite Networks of Papers and Refer-ences In H Kretschmer and F Havemann(Eds) Proceedings of WIS 2008 FourthInternational Conference on WebometricsInformetrics and Scientometrics NinthCOLLNET Meeting Berlin Humboldt-Universitat zu Berlin Gesellschaft furWissenschaftsforschung ISBN 978-3-934682-45-0 httpwwwcollnetde

Berlin-2008MitesserWIS2008mdrpdf

Moed H F W Glanzel and U Schmoch(Eds) (2004) Handbook of QuantitativeScience and Technology Research The Useof Publication and Patent Statistics in Stud-ies of SampT Systems Dordrecht KluwerAcademic Publishers

Morris S A G Yen Z Wu and B Asnake(2003) Time line visualization of researchfronts Journal of the American Society forInformation Science and Technology 54 (5)413ndash422

Morris S A and G G Yen (2004) CrossmapsVisualization of overlapping relationships incollections of journal papers Proceedings ofthe National Academy of Sciences of TheUnited States of America 101 5291ndash5296

Mutschke P P Mayr P Schaer and Y Sure(2011) Science models as value-added ser-vices for scholarly information systems Sci-entometrics 89 (1) 349ndash364

Newman M E J (2001a) Scientific collabora-tion networks I Network construction andfundamental results Physical Review E 64016131

Newman M E J (2001b) Scientific collabora-tion networks II Shortest paths weightednetworks and centrality Physical ReviewE 64 016132

Noyons E C M (2004) Science maps withina science policy context In H F MoedW Glanzel and U Schmoch (Eds) Hand-book of Quantitative Science and Technol-ogy Research The Use of Publication andPatent Statistics in Studies of SampT Systemspp 237ndash256 Dordrecht Kluwer AcademicPublishers

NRC (2005) Network science National Re-search Council of the National AcademiesWashington DC

18

Ortega J L I Aguillo V Cothey andA Scharnhorst (2008) Maps of the aca-demic web in the European Higher Educa-tion Areamdashan exploration of visual web in-dicators Scientometrics 74 (2) 295ndash308

Payette N (2012) Agent-based models of sci-ence In A Scharnhorst K Borner andP Besselaar (Eds) Models of Science Dy-namics Understanding Complex Systemspp 127ndash157 Springer Berlin Heidelberg

Pinski G and F Narin (1976) Citation influ-ence for journal aggregates of scientific pub-lications theory with application to liter-ature of physics Information Processing ampManagement 12 297ndash312

Prabowo R M Thelwall I Hellsten andA Scharnhorst (2008) Evolving debates inonline communication ndash a graph analyti-cal approach Internet Research 18 (5) 520ndash540

Pyka A and A Scharnhorst (2009) Introduc-tion Network perspectives on innovationsInnovative networks ndash network innovationIn A Pyka and A Scharnhorst (Eds) Inno-vation Networks ndash New Approaches in Mod-elling and Analyzing Berlin Springer

Rip A and J Courtial (1984) Co-word mapsof biotechnology An example of cognitivescientometrics Scientometrics 6 (6) 381ndash400

Salton G and M J McGill (1983) Introduc-tion to Modern Information Retrieval NewYork NY USA McGraw-Hill Inc

Scharnhorst A (2001) Constructing Knowl-edge Landscapes within the Framework ofGeometrically Oriented Evolutionary The-ories In M Matthies H Malchow andJ Kriz (Eds) Integrative Systems Ap-proaches to Natural and Social Sciences ndashSystems Science 2000 pp 505ndash515 BerlinSpringer

Scharnhorst A (2003 July) Com-plex networks and the web Insightsfrom nonlinear physics Journal ofComputer-Mediated Communication 8 (4)httpjcmcindianaeduvol8issue4

scharnhorsthtml

Skupin A (2009) Discrete and continuous con-ceptualizations of science Implications for

knowledge domain visualization Journal ofInformetrics 3 (3) 233ndash245 Special Editionon the Science of Science Conceptualiza-tions and Models of Science ed by KatyBorner amp Andrea Scharnhorst

Small H (1973) Co-citation in the ScientificLiterature A New Measure of the Rela-tionship Between Two Documents Jour-nal of the American Society for InformationScience 24 265ndash269

Small H (1978) Cited documents as conceptsymbols Social studies of science 8 (3) 327

Small H and E Sweeney (1985) Cluster-ing the Science Citation index using co-citations Scientometrics 7 (3) 391ndash409

Snijders T A B G G van de Bunt andC E G Steglich (2010) Introduction tostochastic actor-based models for networkdynamics Social Networks 32 (1) 44ndash60

Sonnenwald D (2007) Scientific collaborationAnnual Review of Information Science andTechnology 41 (1)

Swanson D R (1986) Fish oil Raynauds syn-drome and undiscovered public knowledgePerspectives in Biology and Medicine 30 (1)7ndash18

Thelwall M (2004) Link analysis An infor-mation science approach Academic Press

Thelwall M (2009) Introduction to Webomet-rics Quantitative Web Research for the So-cial Sciences In Synthesis Lectures on Infor-mation Concepts Retrieval and ServicesVolume 1 pp 1ndash116 Morgan amp ClaypoolPublishers

van den Heuvel C (2008) Building SocietyConstructing Knowledge Weaving the WebOtletrsquos visualizations of a global informa-tion society and his concept of a universalcivilization In W B Rayward (Ed) Euro-pean Modernism and the Information Soci-ety Chapter 7 pp 127ndash153 London Ash-gate Publishers

van den Heuvel C and W Rayward (2011)Facing interfaces Paul Otletrsquos visualiza-tions of data integration Journal of theAmerican Society for Information Scienceand Technology 62 (12) 2313ndash2326

19

van den Heuvel C and W B Rayward(2005 July) Visualizing the Organizationand Dissemination of Knowledge PaulOtletrsquos Sketches in the Mundaneum MonsrsquoEnvisioning a Path to the Future Webloghttpinformationvisualization

typepadcomsigvis200507

visualizations_html

van der Eijk C C E M van Mulligen J AKors B Mons and J van den Berg (2004)Constructing an Associative Concept Spacefor Literature-Based Discovery Journal ofthe American Society for Information Sci-ence and Technology 55 (5) 436ndash444

Vlachy J (1978) Field mobility in Czechphysics-related institutes and facultiesCzechoslovak Journal of Physics 28 (2)237ndash240

Wagner C S (2008) The new invisible collegeScience for Development Brookings Institu-tion Washington DC

Wasserman S and K Faust (1994) Social Net-work Analysis Methods and ApplicationsCambridge University Press

Wouters P (1999) The citation cultureUnpublished Ph D Thesis University ofAmsterdam httpgarfieldlibrary

upenneduwouterswouterspdf

20

1 Introduction

2 Citation Networks of Articles



5 Citation Networks of Journals

51 Citation Flows Between Journals

52 Citation Environments of Individual Journals

6 Lexical Coupling and Co-Word Analysis


8 Outlook

ate bipartite networks which can be representedas rectangular matrices Like attributes such asauthors with authors (see section 7 below on co-authorship networks) or keywords with keywords(see section 6 below on co-word analysis) canalso be coupled to one another this kind of cou-pling produces unipartite networks representedby square symmetrical matrices

Scientific publications are characterized by thefact that as a rule they contain references toother scientific works This generates a furthernetwork namely that of the publications them-selve This kind of self-reference has also beentaken up in models of the scientific publicationprocess (Bruckner et al 1990 Gilbert 1997 Ley-desdorff 2001 Morris et al 2003 Lucio-Arias andLeydesdorff 2009)

After Eugene Garfieldrsquos pioneering and seminalwork the Science Citation Index (SCI) in the1960s the SCI was used not only to navigate in-formation but it was also applied as a tool inscientific analysis (Garfield 1955 de Solla Price1965 Wouters 1999) The growing accessibility ofmachine-readable data (the SCI was already avail-able on magnet tapes relatively early on) and theappearance of the second big information networkthe World Wide Web (WWW) made large-scaleautomated data processing and analysis possibleThe WWWmdashin which pages constitute the net-work nodes and (hyper-)links the edgesmdashhas itselfbecome a popular object of research in networkanalysis (Huberman 2001)

Link analysis also proves fruitful when ap-plied to academic institutions or countries as wasshown by Thelwall (2004 2009) and also by Or-tega et al (2008) The position of links in anetwork allows us to draw conclusions about re-search collaboration and the function of differ-ent national scientific systems in international re-search landscape

In addition the Web remains today a mediumfor accessing data in part freely which we cananalyze according to their own particular net-work structures Consider for example the bio-information databases Ebay or Facebook Data-flow networks of this kind have resulted in the evo-lution of a new specialty within statistical physicsnamely that of complex networks (Scharnhorst2003 Morris and Yen 2004 Pyka and Scharnhorst2009) Within the multidisciplinary setting of net-work science the methods of social network analy-

sis (SNA) originally developed for smaller socialnetworks are combined with statistical analysisand dynamic modeling from physics with com-puter science algorithms for data mining and vi-sualization and with graph theory in mathemat-ics for the purpose of better grasping explainingand mastering existing complex networks in na-ture and society (NRC 2005) In recent years bib-liometrics and scientometrics have been stronglyinfluenced by these developments in new networkresearch (Borner et al 2007) We will examinethis more closely in section 8 below In what fol-lows immediately however we confine ourselvesto the network descriptions that have tradition-ally received special attention in scientometrics

In scientometrics we distinguish roughly be-tween the analysis of texts and the analysis ofactors Even if information on both elements iscontained in a single bibliographic record histor-ically speaking most bibliometric network analy-ses have concentrated on text elements (viz ci-tation co-citation bibliographic coupling or se-mantic networks) This stands in contrast tothe analysis of scientific collaboration networksmdasheither for cooperation on an individual level orcooperation between countries (Wagner 2008)Among the more interesting methods that haveevolved in the intermediate field of text and ac-tor is the HistCite method developed by EugeneGarfield et al which we discuss in section 2 be-low

2 Citation Networksof Articles

Articles in scientific periodicals base on otherknowledge and acknowledge this by referencingearlier articles and other publications This waythey build networks This view of a stream of pe-riodicals literature was already propagated morethan 40 years ago by Derek J de Solla Price(1965) Defining articles as nodes or vertices andcitations as the links or edges of a network graphallows us to apply graph theoretical methods tobibliometrics In view of the social nature of thescience system we will also consider how termsand concepts initially developed for SNA can befruitfully applied to explain scientific communica-tion

2



1

2

3

4

5

6

7

8

9

10

11

12







3


A =

0 0 0 0 0 0 0 0 0 0 0 01 0 0 0 0 0 0 0 0 0 0 01 1 0 0 0 0 0 0 0 0 0 01 1 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 00 0 0 0 1 0 0 0 0 0 0 00 0 0 0 1 0 0 0 0 0 0 00 0 0 0 0 0 1 0 0 0 0 00 0 0 0 0 0 0 1 0 0 0 00 0 0 0 0 0 0 1 1 0 0 00 0 0 0 0 0 0 1 1 0 0 00 0 0 0 0 0 0 1 1 1 0 0







~r(0) =

000000000001

~r(1) =

000000011100

~r(2) =

000000121000







4













5


bij = |Ri capRj |



(1)




(2)








cij =sumk

akiakj




6











7











8





A =

79 65 15 6 2442 182 11 15 446 22 37 8 6

20 26 13 30 117 48 7 10 254

(3)







~w = γT ~w




9










10











11












12










(Newman 2001b p 3)








time














2001b p 3)





13

8 Outlook












14







Acknowledgement


References



15
























16










Module_KULpdf


















17






















18










scharnhorsthtml













19



visualizations_html







20

1 Introduction









8 Outlook



1

2

3

4

5

6

7

8

9

10

11

12







3


A =

0 0 0 0 0 0 0 0 0 0 0 01 0 0 0 0 0 0 0 0 0 0 01 1 0 0 0 0 0 0 0 0 0 01 1 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 00 0 0 0 1 0 0 0 0 0 0 00 0 0 0 1 0 0 0 0 0 0 00 0 0 0 0 0 1 0 0 0 0 00 0 0 0 0 0 0 1 0 0 0 00 0 0 0 0 0 0 1 1 0 0 00 0 0 0 0 0 0 1 1 0 0 00 0 0 0 0 0 0 1 1 1 0 0







~r(0) =

000000000001

~r(1) =

000000011100

~r(2) =

000000121000







4













5


bij = |Ri capRj |



(1)




(2)








cij =sumk

akiakj




6











7











8





A =

79 65 15 6 2442 182 11 15 446 22 37 8 6

20 26 13 30 117 48 7 10 254

(3)







~w = γT ~w




9










10











11












12










(Newman 2001b p 3)








time














2001b p 3)





13

8 Outlook












14







Acknowledgement


References



15
























16










Module_KULpdf


















17






















18










scharnhorsthtml













19



visualizations_html







20

1 Introduction









8 Outlook


A =

0 0 0 0 0 0 0 0 0 0 0 01 0 0 0 0 0 0 0 0 0 0 01 1 0 0 0 0 0 0 0 0 0 01 1 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 00 0 0 0 1 0 0 0 0 0 0 00 0 0 0 1 0 0 0 0 0 0 00 0 0 0 0 0 1 0 0 0 0 00 0 0 0 0 0 0 1 0 0 0 00 0 0 0 0 0 0 1 1 0 0 00 0 0 0 0 0 0 1 1 0 0 00 0 0 0 0 0 0 1 1 1 0 0







~r(0) =

000000000001

~r(1) =

000000011100

~r(2) =

000000121000







4













5


bij = |Ri capRj |



(1)




(2)








cij =sumk

akiakj




6











7











8





A =

79 65 15 6 2442 182 11 15 446 22 37 8 6

20 26 13 30 117 48 7 10 254

(3)







~w = γT ~w




9










10











11












12










(Newman 2001b p 3)








time














2001b p 3)





13

8 Outlook












14







Acknowledgement


References



15
























16










Module_KULpdf


















17






















18










scharnhorsthtml













19



visualizations_html







20

1 Introduction









8 Outlook













5


bij = |Ri capRj |



(1)




(2)








cij =sumk

akiakj




6











7











8





A =

79 65 15 6 2442 182 11 15 446 22 37 8 6

20 26 13 30 117 48 7 10 254

(3)







~w = γT ~w




9










10











11












12










(Newman 2001b p 3)








time














2001b p 3)





13

8 Outlook












14







Acknowledgement


References



15
























16










Module_KULpdf


















17






















18










scharnhorsthtml













19



visualizations_html







20

1 Introduction









8 Outlook


bij = |Ri capRj |



(1)




(2)








cij =sumk

akiakj




6











7











8





A =

79 65 15 6 2442 182 11 15 446 22 37 8 6

20 26 13 30 117 48 7 10 254

(3)







~w = γT ~w




9










10











11












12










(Newman 2001b p 3)








time














2001b p 3)





13

8 Outlook












14







Acknowledgement


References



15
























16










Module_KULpdf


















17






















18










scharnhorsthtml













19



visualizations_html







20

1 Introduction









8 Outlook











7











8





A =

79 65 15 6 2442 182 11 15 446 22 37 8 6

20 26 13 30 117 48 7 10 254

(3)







~w = γT ~w




9










10











11












12










(Newman 2001b p 3)








time














2001b p 3)





13

8 Outlook












14







Acknowledgement


References



15
























16










Module_KULpdf


















17






















18










scharnhorsthtml













19



visualizations_html







20

1 Introduction









8 Outlook











8





A =

79 65 15 6 2442 182 11 15 446 22 37 8 6

20 26 13 30 117 48 7 10 254

(3)







~w = γT ~w




9










10











11












12










(Newman 2001b p 3)








time














2001b p 3)





13

8 Outlook












14







Acknowledgement


References



15
























16










Module_KULpdf


















17






















18










scharnhorsthtml













19



visualizations_html







20

1 Introduction









8 Outlook





A =

79 65 15 6 2442 182 11 15 446 22 37 8 6

20 26 13 30 117 48 7 10 254

(3)







~w = γT ~w




9










10











11












12










(Newman 2001b p 3)








time














2001b p 3)





13

8 Outlook












14







Acknowledgement


References



15
























16










Module_KULpdf


















17






















18










scharnhorsthtml













19



visualizations_html







20

1 Introduction









8 Outlook










10











11












12










(Newman 2001b p 3)








time














2001b p 3)





13

8 Outlook












14







Acknowledgement


References



15
























16










Module_KULpdf


















17






















18










scharnhorsthtml













19



visualizations_html







20

1 Introduction









8 Outlook











11












12










(Newman 2001b p 3)








time














2001b p 3)





13

8 Outlook












14







Acknowledgement


References



15
























16










Module_KULpdf


















17






















18










scharnhorsthtml













19



visualizations_html







20

1 Introduction









8 Outlook












12










(Newman 2001b p 3)








time














2001b p 3)





13

8 Outlook












14







Acknowledgement


References



15
























16










Module_KULpdf


















17






















18










scharnhorsthtml













19



visualizations_html







20

1 Introduction









8 Outlook










(Newman 2001b p 3)








time














2001b p 3)





13

8 Outlook












14







Acknowledgement


References



15
























16










Module_KULpdf


















17






















18










scharnhorsthtml













19



visualizations_html







20

1 Introduction









8 Outlook

8 Outlook












14







Acknowledgement


References



15
























16










Module_KULpdf


















17






















18










scharnhorsthtml













19



visualizations_html







20

1 Introduction









8 Outlook







Acknowledgement


References



15
























16










Module_KULpdf


















17






















18










scharnhorsthtml













19



visualizations_html







20

1 Introduction









8 Outlook
























16










Module_KULpdf


















17






















18










scharnhorsthtml













19



visualizations_html







20

1 Introduction









8 Outlook










Module_KULpdf


















17






















18










scharnhorsthtml













19



visualizations_html







20

1 Introduction









8 Outlook






















18










scharnhorsthtml













19



visualizations_html







20

1 Introduction









8 Outlook










scharnhorsthtml













19



visualizations_html







20

1 Introduction









8 Outlook



visualizations_html







20

1 Introduction









8 Outlook

Bibliometric Networks

Documents

Transcript of Bibliometric Networks