Abstract. The paper introduces an analysis of a real in-ter-organizational innovation network with a network science approach. The study is integrated with a Social Network Analysis referring to the EEN. Keywords. Network science, social network analysis, chore-ography, inter-organizational networks, innovation.

1 Introduction Network Science is an emerging, interdisciplinary re-search field aiming to understand the structure, devel-opment and weaknesses of networks through different methods attained to different disciplines as mathematics, statistics, physics and computer science. It is “an at-tempt to understand networks emerging in nature, tech-nology and society using a unified set of tools and prin-ciples. Despite apparent differences, many networks emerge and evolve, driven by a fundamental set of laws and mechanisms and these are the provinces of network science” [3].

The purpose of this paper is to consider the Network Science paradigm as a tool to study inter-organizational innovation networks by means of graph theory as mathematical abstraction and other multidisciplinary approaches to infer behaviors of various phenomena.

Innovation networks are defined as: “a basic institu-tional arrangement to cope with systemic innovation. Networks can be viewed as an inter-penetrated form of market and organization … .!!They include joint ven-tures, licensing arrangements, management contracts, sub-contracting, production sharing and R&D collabo-ration” ([14], [16]).

Among them, inter-organizational innovation net-works are characterized by recurring exchange interac-tions between members that retain residual control of their individual resources yet periodically jointly decide

1 Giovanna Ferraro and Antonio Iovanella are with Department of

Enterprise Engineering, University of Rome Tor Vergata, Italy. E-mails: giovanna.ferraro@uniroma2.it, antonio.iovanella @uniroma2.it.

2 Manuscript received April 17, 2014; revised May 21, 2014.

over their use [11]. Members of such systems can be firms, organizations or research centers, located in dif-ferent regions and specialized in particular sectors, linked by common interests, technologies and skills and networked by the decision to collaborate according to specific rules. Technological districts, business incuba-tors and consortia created by international initiatives financed by the European Commission are some exam-ples of such kind of networks.

Herein by means of the Enterprise Europe Network (EEN), a real case study, we model an in-ter-organizational innovation network as a complex network and infer the main properties that characterize the structure and behavior of the system selecting an appropriate set of tools to measure them.

Although real networks may appear very different from each other with respect to their functions and at-tributes, the analysis of their structure shows the ubiqui-ty of several asymptotic features and reveals the emer-gence of general and common self-organizing rules.

Such systems, denoted by a significant number of nodes, are characterized by a structure that is irregular, complex and dynamically evolving in time. The study thereof, focused on the network topology, identifies a series of principles and statistical properties common to the majority of real systems. The networks’ structure has relevant consequences on systems’ robustness and reac-tion to external perturbations. The topology is likewise important in determining the emergence of collective dynamical behavior, such as synchronization [21], or in managing the most important features of relevant pro-cesses [22].

Network science includes the Social Network Anal-ysis (SNA) as a tool to conceptualize and investigate interactions among social entities. In general terms, SNA can be considered as an archetype that abstracts social life in terms of structures of relationships among actors [19].

SNA concerns issues of centrality, meaning the indi-viduals which are best connected to others or have most influences, connectivity, showing how individuals are connected to one another through the network and

Proceedings of ICCSA 2014 Normandie University, Le Havre, France – June 23-26, 2014

A NETWORK SCIENCE APPROACH TO INTER-ORGANIZATIONAL INNOVATION NETWORKS:

THE CASE STUDY OF ENTERPRISE EUROPE NETWORK

Giovanna Ferraro and Antonio Iovanella1, 2

ICCSA 2014, Normandie University, Le Havre, France – June 23-26, 2014 117

Giovanna Ferraro and Antonio Iovanella

community, indicating the nodes that are highly and tightly linked.

The paper is organized as follows: section 2 de-scribes the case study and the network modelization, section 3 introduces the analysis of the network struc-ture, section 4 presents the case study in terms of a scale-free network, section 5 describes the emergence of the network choreography, section 6 reports the final thoughts and the key issues that require further research.

2 EEN as a case study Here, we deem as case study, the Enterprise Europe Network (EEN) that was launched in 2008 by the Euro-pean Commission’s Directorate-General for Enterprise and Industry. It builds on the former Euro Info Centre (EIC) and Innovation Relay Centre (IRC) Networks, established in 1987 and 1995 respectively.

EEN can be considered a key instrument in the Eu-ropean Union’s strategy to boost growth and jobs. The network brings together as members, more than 600 different and independent organizations as chambers of commerce, technology centers, universities, research institutes and development agencies, from 54 countries. EEN’s mission is helping small companies make the most of the business opportunities in the European Un-ion by offering combined services according to the prin-ciple of one-stop shop for small business. The services offered concern technology transfer, access to finance, advice on EU law and standards, intellectual property rights, research funding and internationalization.

Partners of the networks are independent organiza-tions organized in consortia at country level. We con-sider the collaborations among partners through the analysis of the Partnership Agreements (PAs). The aim of the partnership process is to get clients to sign-up a long-term collaboration with companies or researchers that match their needs and expectations. Therefore, PAs represent important performance indicators for measur-ing the effectiveness and efficiency of the activities un-dertaken by the Network. PAs comprise different ser-vices such as technological and commercial cooperation and collaborative research.

The examined data have been collected by the Exec-utive Agency of the EEN – EASME – and concern 54 members countries and 4940 PAs signed during the pe-riod from 1st January 2011 to 31st December 2012 - 1910 PAs in 2011 and 3030 in 2012.

The data processing and the network analysis are conducted using the software R3 with the igraph4 pack-age.

3 http://www.r-project.org 4 http://igraph.sourceforge.net

2.1 Modelization The classical mathematical abstraction of the network is a graph G. A graph G = (V, E) is composed of a set V of n nodes and a set E of m links defining a relationship among these nodes. We refer to a member by an index i meaning that we allow a one-to-one correspondence between an index and a member.

Each member of EEN represents a node of a graph: two members, says i and j, are adjacent through a link if and only if there is a connection between i and j and a weight wij equal to the number of PAs signed between two members.

The granularity of the available data being at country level, the network is composed as follows: each node is a centroid that represents a country inside which there are independent organizations, as network partners, while links exist if two countries share at least one PA.

To the graph G is associated an adjacency matrix A, where its elements are defined as aij = wij if nodes i, j of G are connected, aij = 0 otherwise. Since the said graph represents reciprocal relationships, the matrix is sym-metric (i.e. aij = aji) with zero elements on the main di-agonal.

In this work, we are interested on the structure of the connections among members rather than on their inten-sity. Therefore we focus the analysis on EEN as an un-weighted network where the links between nodes are either present or not and the network can be denoted by (0, 1), 1 if i and j are connected, 0 otherwise - or binary matrices. The study of EEN weighted graph representa-tion and the relative evidences will be presented in a forthcoming paper.

3 Analysis of the network structure Most of real networks, despite intrinsic differences, are described by similar structural features, as for instance relatively small path lengths, high clustering coeffi-cients, fat tailed shapes in degree distributions and de-gree correlations. Such properties make real networks different from the traditional models studied in the graph theory like regular lattices and random graphs. Indeed, real networks meet the scale-free structure and the evi-dence comes from the convergence between empirical data and analytical models that foresee the network structure [7].

In this section, we describe some structural proper-ties observed in the topology of the EEN.

118 ICCSA 2014, Normandie University, Le Havre, France – June 23-26, 2014

A Network Science Approach To Inter-Organizational Innovation Networks

3.1 Network parameters We set two different graphs for each year, namely G2011 and G2012 where the nodes n2011 and n2012 are, respec-tively, the countries with at least one PA signed and where links m2011 and m2012 reflect interactions among countries, rather than the entire set of 4940 PAs, thus decreasing the number to m2011 = 285 and m2012 = 357. After this pre-processing, the network graph configura-tion is composed by n2011 = 48 and n2012 = 49 and it is illustrated in Figure 1 and 2 where node labels are the official country codes.

The EEN countries that have not signed any PA in the period 2011-2012 are not considered in the analysis. One of the basic characteristics of a graph G is its den-sity d that measures the portion of links in the set E compared to the maximum possible number of links between nodes in set V (equal to nx(nx - 1)/2, x = {2011, 2012}) and assumes values from 0 to 1. Density indi-cates how the communication paths in the system are able to get information out to the members. In EEN graphs, the value of the density is low (0.25 and 0.30) denoting that the network is sparse. Such sparsely con-nected networks show the typical power-law node-degree distribution in which most nodes have only few links while some few nodes are extremely connect-ed.

Table 1 gives some basic information about EEN in the two different years. The reported network measures will be explained throughout the paper.

The diameter D is the length of the shortest path be-tween the most distanced nodes measuring the extent of a graph and the topological length between two nodes. It characterizes the ability of two nodes to communicate with each other. The smaller is D, the shorter is the ex-

pected path between them as the hubs act as bridges between the many small nodes. In EEN graphs the value of D is 4, i.e. the path among farthest nodes is very short; in consequence all nodes appear strongly con-nected due also to EEN modest size in terms of number of nodes. Table 1: EEN graph parameters

Network measures 2011 2012 Nodes (n) 48 49 Links (m) 285 357 Density (d) 0.25 0.30 Diameter (D) 4 4 Clique number (χ) 12 12 Average shortest path (L) 1.91 1.78 Cluster coefficient (C) 0.65 0.67 Degree exponent (γ) 2.82 2.69 Second eigenvalue (λ2) 0.84 0.92

3.2 Community, clique and dendrograms In a network a community is a sub-graph whose nodes are tightly connected. The requirement that all pairs of community members choose each other leads to the definition of a clique. A clique is a maximal complete sub-graph of three or more nodes, i.e. a subset of nodes all of which are adjacent to each other, and such that no other nodes exist adjacent to all of them. The cardinality of the maximal clique is indicated with χ and in EEN the value is 12 for both years. Table 2 resumes the mem-bership in each clique.

From the analysis it results that in 2011 the EEN has only one clique of 12 members while in 2012 the net-work contains 6 cliques each having 12 members. There is a relevant overlapping represented by 8 countries,

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

AL

AM

AT

BA

BE

BG

BY

CA

CHCL

CN

CY

CZDE

DK

EE

ES

FIFR

GR

HRHU

IE

IL

IS

IT

JP

KR

LT

LU

LV

ME

MK

MT

NL

NO

PL

PT

RO

RS

RU

SE

SI

SK

TN

TRUK

US

Figure 2: The 2012 EEN graph (G2012). Figure 1: The 2011 EEN graph (G2011).

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

AL

AM

AT

BE

BG

BY

CACH

CL

CN

CY

CZ

DE

DK

EEES

FI

FRGR

HR

HUIE

IL

IS

IT

JP

KRLTLU

LV

MEMK

MTMX

NL

NO

PL

PT

RO

RS

RU

SE

SI

SK

TN

TR

UA

UK

US

ICCSA 2014, Normandie University, Le Havre, France – June 23-26, 2014 119

Giovanna Ferraro and Antonio Iovanella

namely IT, UK, DE, ES, PL, TR, NL and BE constant overtime; in 2012 the overlapping is extended to IL. In the system there is indeed, a group of countries strictly inter-connected surrounded by partners having different level of membership in terms of clique. Figure 3 shows all cliques for 2012. Table 2: Clique compositions in years 2011 and 2012.

2011 IT UK DE ES PL FR TR NL BE SE CZ CH 2012 IT UK DE ES PL FR TR NL BE SE IL FI IT UK DE ES PL FR TR NL BE SE IL CZ IT UK DE ES PL FR TR NL BE GR IL FI IT UK DE ES PL FR TR NL BE GR IL CZ IT UK DE ES PL HU TR NL BE SE IL CZ IT UK DE ES PL HU TR NL BE GR IL CZ

The hierarchy of communities in the network is usu-

ally represented by a dendrogram that graphically de-notes through splitting in a tree. The horizontal position of the split indicates the distance at which communities were connected.

Figure 3: The highlighted links for 2012 EEN cliques.

Figure 4 reports the dendrogram for the year 2012, where communities are detected by means of the edge shortest path betweenness measure [18], which itera-tively extract community from the graphs considering at each step geodesic network paths.

The dendrogram reveals information concerning which countries are grouped together at various levels of dissimilarity and at the right of the dendrogram each country forms its own cluster.

The dendrogram confirms what we reported in Table 2, i.e. the presence of a core of countries closely con-nected in one community while the others follow at dif-

ferent level of the hierarchy.

Figure 4: The EEN dendrogram for 2012.

3.3 Centrality measures The topology of several real networks is related to the possibility of identifying the properties of every node. Usually, nodes with similar characteristics tend to link to each other. They have features that carry relevant information regarding their role in the network. Specifi-cally, we refer to centrality value that represents the node’s relative importance within a graph, the higher is the centrality index of a node, the higher is its perceived centrality in the graph. Moreover, centrality measures assess the nodes involvement in or contribution to the cohesiveness of the network [6].

The concept of centrality has an inherent ambiguity; there is no point in including all measures in one meth-od. The best ones are related to the applications de-pending on the degrees of the local and overall struc-tures. There is a similarity in certain measures indeed a node rank can depend on the status to which, it is con-nected to. Centrality measures in some cases provide considerably various results. The choice of them re-quires the consideration of the specificity of the measures and the requirements of different applications.

There are several measures describing the centrality; the most commonly used are the degree centrality, the closeness, the betweenness, the eigenvector centrality and the Bonacich index.

The degree centrality of a node is the number of links incident upon a node and can be interpreted in terms of the size of members’ neighborhoods within the network. The degree defines the immediate risk of a member to catch whatever is flowing through the net-work. It quantifies how well it is connected to the other elements of the graph.

BE CZDE ES

HU

IL

IT

NLPL

SE

TR

UK

2.5 2.0 1.5 1.0 0.5 0.0

EEN 2012

● JP● TN● MX● US● KR● MT● IS● PT● LV● NO● SI● LT● RU● RO● SK● UK● TR● SE● PL● NL● IT● IL● HU● ES● DE● CZ● BE● GR● FR● FI● AT● EE● BG● DK● CH● IE● LU● RS● MK● CN● HR● CY● CL● ME● AM● AL● UA● CA● BY

120 ICCSA 2014, Normandie University, Le Havre, France – June 23-26, 2014

A Network Science Approach To Inter-Organizational Innovation Networks

Table 3: Centrality measures for the EEN in 2012.

Country ID De-gree

Close-ness

Between-tween-ness

Eigen-vector

Bonacich Index

Italy IT 40 0.857 173.795 1.000 1.110 United Kingdom UK 37 0.814 112.440 0.981 0.627 France FR 35 0.787 143.730 0.914 -1.740 Spain ES 34 0.762 77.512 0.927 -1.112 Germany DE 32 0.750 36.406 0.928 -0.690 Poland PL 31 0.738 44.689 0.891 -0.529 Greece GR 29 0.716 62.175 0.792 -1.750 Sweden SE 28 0.706 22.489 0.838 -0.784 Turkey TR 28 0.696 20.339 0.850 -0.567 The Netherlands NL 26 0.686 21.366 0.800 -0.920 Hungary HU 22 0.632 10.199 0.698 -0.952 Czech Republic CZ 21 0.632 56.780 0.672 1.162 Belgium BE 21 0.632 14.168 0.682 -0.449 Austria AT 19 0.615 9.657 0.612 -0.140 Denmark DK 18 0.608 9.910 0.587 -0.042 Finland FI 18 0.608 5.252 0.610 -1.140 Bulgaria BG 17 0.593 10.612 0.559 -1.494 Romania RO 16 0.600 3.620 0.577 -0.732 Slovenia SI 16 0.585 10.423 0.526 -1.458 Estonia EE 15 0.593 1.906 0.552 0.269 Israel IL 15 0.585 2.803 0.559 -1.108 Lithuania LT 13 0.571 47.563 0.450 0.103 Slovakia SK 13 0.571 0.455 0.500 -0.300 Norway NO 13 0.565 1.389 0.482 -0.249 Russia RU 12 0.565 0.380 0.474 -1.653 Ireland IE 12 0.558 2.769 0.432 -1.717 Portugal PT 12 0.558 4.189 0.437 0.149 Switzerland CH 12 0.558 0.454 0.459 -1.395 Serbia RS 12 0.552 6.381 0.363 0.010 Latvia LV 11 0.558 0.133 0.432 1.220 Macedonia MK 10 0.545 4.340 0.322 1.197 Luxembourg LU 10 0.545 0.458 0.378 -0.057 Iceland IS 9 0.527 0.114 0.365 -0.065 Croatia HR 8 0.533 0.282 0.300 -0.685 China CN 8 0.533 0.272 0.306 -1.253 Malta MT 7 0.495 1.203 0.221 -0.623 Cyprus CY 6 0.511 0.840 0.212 -0.147 Chile CL 4 0.485 0.200 0.140 0.266 U.S.A. US 4 0.485 0.000 0.160 1.019 South Korea KR 4 0.480 0.000 0.161 0.750 Montenegro ME 4 0.466 0.307 0.101 -0.185 Armenia AM 3 0.475 0.000 0.111 -0.780 Mexico MX 2 0.471 0.000 0.087 -1.948 Albania AL 2 0.471 0.000 0.085 0.263 Tunisia TN 1 0.466 0.000 0.047 1.561 Ukraine UA 1 0.453 0.000 0.047 1.078 Canada CA 1 0.444 0.000 0.043 -1.288 Japan JP 1 0.390 0.000 0.032 1.613 Belarus BY 1 0.366 0.000 0.021 0.554

The closeness centrality refers to a natural distance between all pairs of nodes defined by the length of their shortest paths. Thus, the more central a node is, the lower is its distance to all other nodes. This value measures how long it will take to spread information from a member to all others sequentially.

The betweenness centrality determines the number of times a node acts as bridge along the shortest path between two other nodes. This measure reveals the members that are essential for connecting different re-gions of the network.

The Eigenvector centrality measures the node’s in-fluence in a network according to the number and the quality of its connections. Indeed a member with a smaller number of high quality links has more power than one with a larger number of mediocre contacts.

The Bonacich index refers to the notion that the power of a node is recursively defined by the sum of the power of its alters. Positive values imply that members become more powerful as their the alter (neighbor) comes to be more powerful, while negative values imply that members are more powerful only as their alters be-come weaker, as occurs in competitive or antagonistic relations.

Table 3 reports the centrality measures referred to EEN members in 2012.

The crosscheck between degree and centrality scores clearly shows the presence of the three classes of mem-bers, i.e. hubs, semi-peripherals and peripherals.

The Table highlights the presence of more than one hub since nodes as IT, UK, DE, ES, FR and PL have a neighbor value greater than 30 meaning that they are well connected to the other countries due to the high number of links. These countries have also a high rank of closeness signifying their relevant involvement in the network and their contribution to spread more easily information within the system even if they connect dif-ferent regions of the graph due to the higher between-ness values. Indeed, hubs act as bridges between the many small nodes.

DE, PL, SE, TR and NL show a low value of be-tweenness maintaining a high rank of eigenvector cen-trality meaning a relevant influence of these nodes in the network even without acting as a bridge in connecting the different region of the graph.

There are some interesting cases as for CZ and LT where a high score in betweenness corresponds to rela-tively small values in eigenvector centrality, intending that these countries lay on many shortest paths but they are connected mostly to low score members.

ICCSA 2014, Normandie University, Le Havre, France – June 23-26, 2014 121

Giovanna Ferraro and Antonio Iovanella

Regarding the Bonacich index, some countries as IT, UK, CZ, LV, MK, US, SK, JP, TN and UA have posi-tive and high values denoting that these nodes become more influent as their neighbors come to be more pow-erful. The majority of negative scores means that nodes are more powerful only if their neighbours become weaker as in competitive relations.

4 EEN as a scale-free network We propose complex networks with the scale-free fea-ture ([22] and references therein) an adequate frame-work within which to represent EEN. We refer mainly to the Barabási-Albert (BA) scale-free network model [4], [2],[13]. BA networks are open and dynamically formed by continuous addition of new nodes that represent members, while links mimic collaborative agreements. Links’ inhomogeneity reflects the degree of members’ involvement in the network and the difference among hubs, semi-peripheral and peripheral nodes.

Scale-free networks emerge in real situations in which the kind of inhomogeneity in the degree distribu-tion represents few nodes having many links whereas the majority of them has few connections. Therefore, a single node or hub cannot be considered representative since these networks are held together by a different, although limited, number of highly connected hubs while the majority of nodes has smaller connection de-gree than the average. All nodes are linked with a rather short path due to the small world characteristic [22] even in case of large and sparse systems.

Scale-free networks are mainly identifiable by three characteristics: the average path length, the clustering coefficient and the degree distribution.

The average shortest path in EEN is 1.91 in 2011 and 1.78 in 2012 meaning that in the time period considered,

the distance among members decreases shaping the small world characteristic of the network.

Clustering is introduced by structural embeddedness that is the existence of dense ties among nodes. In inno-vation networks, members sharing common partners have knowledge about each other’s trustworthiness, ca-pabilities, competences, and reputation and thus miti-gating the effects of power asymmetries [9]. In the case study this value is C2011 = 0.65 and C2012 = 0.67 indicat-ing the presence of dense local subgroups of intercon-nected nodes.

Regarding the degree distribution, the degree ki of a node i represents the number of its links; the larger the degree, the more significant the node is in a network. The average of ki over all i is the network average de-gree and the spread of node degrees over a network is characterized by a distribution function P(k) that repre-sents the probability that a randomly selected node has exactly k links.

The BA model asserts that growth and preferential attachments determine the self-organization of a net-work with scale-free structure. Actually, real networks constantly grow by adding new nodes that at each time-step join the network and link to other nodes al-ready present in the system. New nodes tie preferentially to those that are more highly connected, following a “rich get richer” phenomenon [4].

The probability ∏(ki) that a new node will be con-nected to an already existing node i depends on the de-gree ki for the property of the preferential attachments:

Π k! = k!k!!

!!!

In BA model, the connectivity distribution follows a

power law function, i.e. the probability P(k) that a node

● ●

●

●● ●

● ●●

● ●

●●

●

●

●●●●

●●●●

●●●●

●●●●

●

●

●

1 2 5 10 20

0.02

0.05

0.10

0.20

0.50

1.00

Degree

Cum

ulat

ive fr

eque

ncy

● EEN modelER model

● ●

●● ●

● ● ● ●● ●

● ●

●

●●●

●●

●●●

●●●●●

●●

●

●●

●

●●

●

●●

●●●

1 2 5 10 20

0.02

0.05

0.10

0.20

0.50

1.00

Degree

Cum

ulat

ive fr

eque

ncy

● EEN modelER model

Figure 5: Degree distribution for the 2011 EEN and the Erdös and Rényi model.

Figure 6: Degree distribution for the 2012 EEN and the Erdös and Rényi model.

122 ICCSA 2014, Normandie University, Le Havre, France – June 23-26, 2014

A Network Science Approach To Inter-Organizational Innovation Networks

in the network interacts with k other vertices decays with the law P(k) ~ k-γ with slope γ as the scaling expo-nent.

The values of the average path length, the cluster coefficient and γ reported in Table 1 meet the three scale-free properties required and they are comparable with the values of other real networks as reported in [22]. As a consequence, EEN exhibits the scale-free properties and is represented by the BA model.

The power law degree distribution is tested by com-paring the slope of the degree distribution of the EEN and that of a classic random graph having the same number of nodes and links, and generated using the Erdös and Rényi model. Figures 5 and 6 depict the comparison between the two distributions. The power law slope of the EEN clearly decays less quickly than that of the random graph.

4.1 Network robustness Network robustness permits to understand the behavior of certain systems under failures and attacks and allows to protect them against assaults or to exploit their weak-nesses.

In the BA model, the network is robust if it contains a giant cluster comprised of most of the nodes even after a fraction of its nodes is removed.

Robustness refers to the capacity of the network to perform its basic functions even in case of nodes and links missing. Related to robustness, the resilience is the dynamical feature that entails a change in the network’s essential activities. Resilience is the capacity of the network to adapt to internal and external errors by alter-ing its processes while continuing to perform [5].

Real networks exhibit an unexpected degree of tol-erance to the random deletion of their nodes due to their heterogeneity. Indeed, such breakdowns affect mainly the various small nodes that play a limited role in main-taining the networks’ integrity and their removal has limited impact on their structure.

The random failure or error is the capacity of the network to uphold its connectivity features even in case of casual deletion of a portion of its nodes or links.

Scale-free networks with γ ≤ 3 show a high robust-ness to random failure meaning that to break such net-works apart, virtually all nodes should be removed.

In general, once a small fraction of nodes is re-moved, the distance among the remaining nodes in-creases, since some paths that contribute to the network connectivity are eliminated. Thus, for the remaining nodes, it is more difficult to communicate with each other.

In scale-free networks the diameter remains un-changed under an increasing level of errors, even when more than 5% of the nodes fail. The connections among the remaining nodes are unaffected due to the inhomo-geneous connectivity distribution. Indeed, scale-free

networks are characterized by the majority of nodes having few links, therefore nodes with small connectiv-ity will be selected with much higher probability than hubs and their removal does not alter the path structure and has no influence on the overall network structure [1].

The attack refers to a removal process targeted to specific nodes i.e. the highly connected. In real net-works, the deletion of a single hub does not fragment the system as the remaining hubs can still hold the system’s integrity. However if the number of removed nodes reaches a critical threshold, the network suddenly breaks in disconnected components.

To simulate a deliberate attack, the most connected nodes are eliminated and, in sequence, the others in de-creasing order of connectivity. In scale-free networks, when the most linked nodes are removed, the diameter increases rapidly doubling its original value if 5% of hubs are eliminated [1]. This vulnerability to attacks is due to the inhomogeneity of the connectivity distribu-tion. Indeed, the removal of the few highly linked nodes alters the network topology and decreases the capacity of the remaining nodes to communicate with each other.

Hence, the structural robustness is not valid against a deliberate attack, as the simultaneous removal of the most connected nodes will destroy any system showing its fragility or its own Achilles’ Heel [1]: the network behind is robust to random failures but vulnerable to-ward attacks.

Figure 7: The effects on EEN diameter of error tolerance and attack tolerance in 2012.

Despite in the observed network we do not expect a random failure or a deliberate attack due to the fact that the nodes of the graph represent countries, we have im-plemented a double analysis – the Error Tolerance and the Attack Tolerance – and its effects on the network’s diameter to detect the general features.

0 10 20 30 40 50

02

46

810

Error Tolerance

Fraction removed nodes

Dia

met

er

0 10 20 30 40 50

02

46

810

Attack Tolerance

Fraction removed nodes

Dia

met

er

ICCSA 2014, Normandie University, Le Havre, France – June 23-26, 2014 123

Giovanna Ferraro and Antonio Iovanella

Due to modest size of the graph, EEN tends to retain its diameter at each time step a random node is removed, as in the case of error, almost at 70% oscillations not-withstanding.

The attack tolerance analysis is carried out removing at each time step the node with the highest degree, sim-ulating an attack to the most connected nodes. The EEN diameter increases for growing percentage of nodes’ removals and it suddenly decreases when almost 50% of the nodes are erased. Figure 7 shows the effects on EEN diameter of error tolerance and attack tolerance.

5 Network choreography The network choreography is the system’s capacity to address collaboration among multiple members. Chore-ography is focused on inter-organization coordination for external perspectives while collaboration is ad-dressed by self-organizing interactions.

It requires some structural hypothesis on network topology and some membership characteristics and in-volves the accomplishment of certain activities among network members to reach the innovation outcome.

We refer to [13] for a complete description of net-work choreography.

5.1 Synchronization Scale-free networks exhibit several interesting dynam-ical phenomena; in particular, we focus on the synchro-nization motion of their dynamical elements [21] and on a qualitative and paradigmatic correspondence between the emergence of synchronization in a network and the establishment of the choreography phenomenon.

In complex networks, nodes are characterized by a collection of variables that identifies a state. Such varia-bles tend to synchronize in an equilibrium point that represents the state of choreography and the synchroni-zation enables the homogeneity of state variables of the members involved in choreography. Moreover, due to the self-organization process of scale-free networks, their syncronizability holds even when new nodes are constantly added.

The study of the synchronization can not be de-tailedly performed because not all state variables of each member are known. Nevertheless, in [21] it is sustained that if we contemplate the Laplacian matrix L = A – D where A is the adjacency matrix and D is the diagonal degree element matrix with dii = ki and 0 elsewhere, its largest eigenvalue is λ1 = 0 and if the second eigenvalue λ2 is positive and not close to λ1, then the synchroniza-tion state is exponentially stable.

In the case study, the EEN adjacency matrixes for the years 2011 and 2012 have λ1 = 0 in both cases and, respectively, λ2 = 0.84 and λ2 = 0.92. Therefore the synchronization is a stable state and, consequently, the

choreography is a stable state for the EEN during the years under evaluation.

5.2 Network membership Inter-organizational innovation networks require peculi-ar membership characteristics for the potential members that are attracted to join networks to get some benefits. Network membership characteristics are expressed by means of ontology and homophily properties. 5.2.1 Ontology The term ontology is relevant in many fields as knowledge engineering and artificial intelligence. Sev-eral definitions and a wide range of applications are considered in different topics (e.g. see [8] and references therein).

We consider the definition of ontology provided in [20]: “An ontology is a formal explicit specification of a shared conceptualization”. Ontology is therefore: • Formal: it communicates the intended meaning of

defined terms, independent on social or computa-tional context. Formalism is a complete set of defini-tions express as logical axioms and documented in natural languages [15].

• Explicit: it defines the design of decisions, concepts and constrains.

• Shared: it regards a knowledge accepted by a group in which the members agree about the objects and the relations of such knowledge.

• Conceptualized: it concerns an abstract, simplified view of the world that we wish to represent. Every knowledge base, knowledge-based system or knowledge-level agent is committed to some con-ceptualization [15].

Table 4: EEN ontology.

Ontology

features EEN

Formal

Network members are grouped in Consortia and are legally bound with the network executive agency by Framework Partner-ship Agreements.

Explicit

Operational manual and guidelines contain all the key information regarding the work-ing practices. These documents contain the obligations and formalities that members should follow.

Shared

All rules and procedures are shared. A common language is accepted and used among members. The exchange of good practices is encouraged to spread knowledge, enhance excellence and profes-sionalism across the network.

Conceptualized Rules and guidelines are conceptualized. Members sign a “code of conduct”.

124 ICCSA 2014, Normandie University, Le Havre, France – June 23-26, 2014

A Network Science Approach To Inter-Organizational Innovation Networks

In this way, the state variables given for every member and the matrix A above mentioned are parts of the conceptualization, are formal since they respect a mathematical modelization, are explicit because every member knows its composition and shared since each member commits to have a state variable identically composed following the coupling rules.

In EEN the set of rules, guidelines and common language are formalized, explicit, shared and conceptu-alized among network members. The features remain valid also for the mathematical model given by the ad-jacency matrix A, while it is worthwhile to mention that for the complexity of a real case it is virtually impossi-ble to explicit the state variables and the matrix Γ.

5.2.2 Homophily Homophily is the tendency of nodes to link with others that are similar to them or, in other words, the members’ attitude to associate and connect with similar [17]. Indi-viduals in homophily relationships share common char-acteristics that make communication and relationships easier. Inter-organizational networks foresee similar interests among members that share innovation attitude, goals and believes.

In the literature, homophily in scale-free network is related to network topological aspects in terms of node similitude related to preferential attachment. It repre-sents a relevant aspect leading the growth of networks. In particular, homophily refers to how the preferential attachment privileges the bond between new nodes and those having high number of nearest neighbors and high similitude jointly [10].

Concerning the homophily, in this case study nodes represent countries, therefore, this property is not partic-ular meaningful as they are similar by definition. Nev-ertheless, in all the other general cases is important to consider.

6 Conclusions This paper shows the use of network science paradigm as a tool to study inter-organizational innovation net-works. The real case study is modeled by means of graph theory and other multidisciplinary tools to gather behavior of various phenomena.

We perform a network analysis of the case study aiming to generate a descriptive model that explain and describe EEN basic features and a network modeling that permits to design process models that reproduce the collected data but can also be utilized to infer predic-tions.

We suggest the BA model as an adequate framework to represent real inter-organizational innovation net-works as in this model the network structure and its evolution are strictly correlated.

Further research should be conducted to extend the analysis in a broader range of contexts and networks, especially for macroeconomics considerations. Never-theless, some essential characteristics have been studied. In particular, network topology influences connections among members; scale-free networks are able to spread and uphold interactions among nodes; robustness con-cerns the network capacity to face changes in the eco-nomic environment; ontology provides a shared com-mon vision of the network and homophily enables cohe-sive relationships among members.

The network topology allows affirming the existence of a synchronizations state and its similarity to the phe-nomenon of choreography. Although this similarity is only paradigmatic, it permits to give some hints about the state stability as showed in the case study. The anal-ysis of the data shows the presence of such stable state of choreography, which ensures members to profit from the value-added of the network according to their con-nections: members join EEN to get benefits from the network itself and from the networking processes to improve their competitiveness and innovation capability.

Acknowledgment Authors would like to thank the Executive Agency for Small and Medium-sized Enterprises and the Evaluation and Monitoring Unit for the support to data retrieving.

References [1] R. Albert, H. Jeong, A.-L. Barabási, “Error and attack

tolerance of complex networks“, Nature, 406, pp. 378–382, 2000.

[2] R. Albert, A.-L. Barabási, “Statistical Mechanics of Complex Networks“, Reviews of Modern Physics, vol. 74, nr. 1, pp. 47-97, 2002.

[3] A.-L. Barabási, “Network science“, Philosophical Trans-action of The Royal Society A, 371, 2013.

[4] A.-L. Barabási and R. Albert, “Emergence of scaling in random networks“, Science, 286, pp. 509-512, 1999.

[5] A.-L. Barabási, Network Science, available from http://barabasilab.neu.edu/networksciencebook/, 2014.

[6] S.P. Borgatti, M.G. Everett, “A Graph-theoretic perspec-tive on centrality”, Social Networks, SON 499, pp. 1-19, 2005.

[7] G. Caldarelli, Scale-Free Networks, Oxford Univ. Press, Oxford, 2007.

[8] B. Chandrasekaran, J.R. Josephson, V.R. Benjamins, “What are ontologies and why do we need them?”, IEEE Intelligent Systems, 14(1), pp. 20-26, 1999.

[9] R. Cowan, N. Jonard, “Knowledge portfolios and the organization of innovation networks”, Academy of Man-agement Review, 34 (2), pp. 320-342, 2009.

[10] M.L. de Almeida, G.A. Mendes, G.M. Viswanathan, L. R. da Silva, “Scale-free homophilic network”, The Euro-pean Physical Journal B, 86:38, 2013.

[11] M. Ebers, Explaining Inter-Organizational Network For-mation in M. Ebers (ed), The Formation of In-ter-Organizational Networks, 1997.

ICCSA 2014, Normandie University, Le Havre, France – June 23-26, 2014 125

Giovanna Ferraro and Antonio Iovanella

[12] P. Erdös, A. Rényi, “On random graphs”, Publicationes Mathematicae, 6, pp. 290-297, 1959.

[13] G. Ferraro, A. Iovanella, “Choreography in in-ter-organizational innovation networks”, arXiv:1311. 6609v2, 2013.

[14] C. Freeman, “Networks of innovator: A synthesis of re-search issue”, Research Policy, 20, pp. 499-514, 1991.

[15] T.R. Gruber, “Toward principles for the design of ontolo-gies used for knowledge sharing?”, International Journal of Human-Computer Studies, 43, (5–6), pp. 907–928, 1995.

[16] K. Imai, Y. Baba, “Systemic Innovation and Cross-border Networks: Transcendent Markets and hierarchies to create a new techno-economic system”, International Seminar on Contributions of Science and Technology to Economic Growth, OECD, Paris, 1989.

[17] M. McPherson, L. Smith-Lovin, J.M. Cook, “Birds of a Feather: Homophily in Social Networks”, Annual Review of Sociology 27, pp. 415–444, 2001.

[18] M. E. J. Newman, M. Girvan, “Finding and evaluating community structure in networks”, Physical Review E, 69, 026113, 2004.

[19] J. Scott, P.J. Carrington eds. The SAGE Handbook of Social Network Analysis, SAGE Publications, London, 2012.

[20] R. Studer, V. Richard Benjamins, D. Fensel, “Knowledge Engineering: Principles and methods”, Data & Knowledge Engineering, 25, pp. 161-197, 2006.

[21] X.F. Wang, G. Chen, “Synchronization in scale-free dy-namical networks: robustness and fragility”, IEEE Trans-actions on Circuits and Systems I: Fundamental Theory and Applications, 49 (1), pp. 54-62, 2002.

[22] X.F. Wang, G. Chen, “Complex networks: small-world, scale-free and beyond”, Circuits and Systems Magazine, IEEE Circuit and System Magazine, 3 (1), pp. 6-20, 2003.

126 ICCSA 2014, Normandie University, Le Havre, France – June 23-26, 2014