Influence Patterns in Topic Communities of Social Media

Mania Kardara$, George Papadakis$,�,Thanos Papaoikonomou$, Konstantinos Tserpes$, Theodora Varvarigou$

� L3S Research Center, Hanover, Germany papadakis@L3S.de$ National Technical University of Athens, Greece {nkardara, gpapadis, tpap, tserpes, dora}@mail.ntua.gr

ABSTRACTUsers of Social Media typically gather into communities onthe basis of some common interest. Their interactions insidethese on-line communities follow several, interesting pat-terns. For example, they differ in the level of influence theyexert to the rest of the group: some community membersare actively involved, affecting a large part of the commu-nity with their actions, while the majority comprises plainparticipants (e.g., information consumers). Identifying usersof the former category lies on the focus of interest of manyrecent works, as they can be employed in a variety of appli-cations, like targeted marketing.

In this paper, we build on previous research that exam-ined influencers in the context of a popular Social Mediaweb site, namely Twitter. Unlike existing works that con-sider its user base as a whole, we focus on communities thatare created on-the-fly by people that post messages abouta particular topic (i.e., topic communities). We examine alarge and representative sample of real-world communitiesand evaluate to which extent their influential users deter-mine the aggregate behavior of the entire community. Tothis end, we consider a practical use case: we check whetherthe community’s overall sentiment stems from the aggregatesentiment of this core group. We also examine the dynam-ics of groups of influencers by assessing the strength of theties between them. In addition, we identify patterns in thecontent produced by influencers and the relation betweeninfluencers of different communities. Our experiments leadto interesting conclusions that highlight many aspects of in-fluencers’ activity inside topic communities; thus, they formthe basis for intelligent, data mining techniques that canautomatically discover influencers in the context of a com-munity.

Categories and Subject DescriptorsJ.4 [Computer Application]: Social and Behavioral Sci-ences—Sociology

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General TermsExperimentation, Human Factors

KeywordsSocial influence, Topic Communities, Social media

1. INTRODUCTIONSocial Media inherently support the rapid sharing of infor-

mation and opinions. With their help, the topics of interestand deliberation meet no boundaries and are only restrictedby time. Communities related to those topics are gener-ated in the “blink of an eye”, following the flow of events -global and local, significant and not - in the form of a chainreaction. The participation level of their members rangesfrom mere information consumers to information broadcast-ers and opinion-leaders. Identifying the role of individualusers and classifying them into these categories, especiallythe latter one, yields major business value [1]. Targetedmarketing, for instance, constitutes an application that cangreatly benefit from this practice.

In the context of a topic community, opinion-leaders arethose individuals that dominate it: the influence they ex-ert on the opinion-shaping (or even decision-making) of theother members is disproportionately high. Hence, they areoften referred to as highly influential users or simply influ-encers. Influence, however, constitutes a subjective conceptand, as such, is very hard to measure and track. So far,two theories for influence diffusion have been proposed inthe literature; the first one argues that a minority of highlypopular, but rather unrelated people influences all others [3];consider as examples celebrities, politicians and sportsmen.The second theory suggests that individuals are influencedby all their peers and, thus, all people are influencers [1, 3].

In this work, we examine the former theory with respectto its implications on the subgroup of influential users: weinvestigate how closely connected to each other they are,not only in terms of links on the social graph, but also interms of social interactions among them. We also examine towhich extent this elite group of people defines the aggregatebehavior of the community with respect to several aspectsof its activity. The objective of the present work is, there-fore, to unravel the relationships between the influencers ofa specific community as well as to investigate their ties withtheir peer members.

To this end, we conducted a large-scale qualitative andquantitative analysis of influence patterns in the context of

the most popular Social Media web site, namely Twitter1.We employed a large subset of Twitter’s content comprising100 topic communities that involve well over 1 million users.We recorded their activity over a period of seven monthsand gathered 11 million messages, in total. The reasons weselected Twitter for our study are the following:

Strict rules for social interaction. Twitter encompassesa limited, yet extremely flexible and expressive wayof communicating opinions and information: they arediffused through short messages of free text, followinga simple protocol for distinguishing between originalthoughts and the re-production of others’ opinions. Inaddition, the interaction of users is based on definiteroles, which specifies the direction of opinion diffusion.All these features make it easier to capture not onlythe context of an opinion (content-wise), but also thediffusion of its influence in the underlying social net-work (structure-wise).

Dynamicity of topic communities. Communities are cre-ated spontaneously and are characterized by a plaintopic tag. Users are, thus, free to participate in them,just by adding the corresponding tag in their messages.

Access to data. Twitter offers easy ways to access greatvolumes of real-world, user-generated data through itshandy API. There is, also, a standard and well-establishedrepresentation model for data, which allows for effi-ciently extracting the features of interest from debateson a topic (e.g., the users that are mentioned). Thus,it is easy to develop and integrate applications thatdetect influence patterns.

These characteristics make Twitter an ideal test-bed foranalyzing influence patterns and explain why it currentlylies on the focus of intensive research [1, 3, 12]. However,related work has primarily focused on identifying the criteriathat are suitable for measuring the influence exercised by (aset of) user(s), rather than examining their implications.In addition, the proposed criteria are typically applied outof context (i.e., on the entire user base of Twitter), thusignoring the individual communities that comprise it.

The work presented in this paper, builds on these efforts— by adopting their metrics — but emphasizes on their im-plications in the context of topic communities: we examinethe ties that bind the top influencers as well as their connec-tions with the rest of the community and the top influencersof other communities. Our aim is to identify useful pat-terns that form a precise model of influencers and can beemployed by machine learning algorithms to automaticallyestimate the influence of individual community members.

In more detail, we conducted the following experiments:

Experiment 1 : We first identified the most appropriateinfluence criteria — among those proposed in the lit-erature — and then examined whether they providesimilar results in the frame of a single community (i.e.,whether they place the same users in the top influencepositions). The outcomes of this analysis are crucialfor two reasons: first, an excessive correlation betweentwo criteria indicates that one of them is redundant

1See http://twitter.com.

and can be excluded from the analysis. Second, a mod-erate correlation indicates that influential users affectmultiple aspects of the activity of a topic community.

Experiment 2 : To evaluate the power of top influencers,we considered the use case of the community’s aggre-gate polarity. That is, we examined how closely theoverall disposition of the influencers is with the“mood”of the rest of the community. A high correlation be-tween them provides strong evidence for the authorityexercised by the top influencers over a community.

Experiment 3 : We analyzed the content produced by theinfluencers, with respect to both its volume and itsquality. Among others, we sought responses to the fol-lowing questions: does it consist of original opinionsor it merely reproduces opinions of others? Does it ex-press strong sentiments about the corresponding topicor it is rather impassive? Is it consumed at discussionswith other members of the community or it is ratherfocused on providing facts about the topic?

Experiment 4 : We continued by examining the ties be-tween the top influencers and the degree of homophilybetween them, in particular (i.e., how similar are theirbackgrounds). As suggested by [12], this is indirectlyindicated by the high link reciprocity among them inthe structure of the underlying social network.

Experiment 5 : An essential condition for the formationof a group is that the people comprising it are self-aware of its existence; that is, its members know andsocialize with each other. To estimate the strengthof the ties between influencers, we examine how oftenthey participate in discussions between them and howoften they cite the opinions of their peers.

Experiment 6 : Last but not least, we highlighted the re-lations between the top influencer groups of differentcommunities. In fact, we analyzed the conditions, un-der which the same people exert high levels of influenceamong multiple communities. The main point of refer-ence in this effort is the similarity of content betweena pair of communities.

The rest of the paper explains and analyzes these experi-ments. In particular, Section 2 introduces the reader to theTwitter-specific details, formulating the terminology and thebasic concepts used in this research. In Section 3, we elab-orate on the criteria we employed for measuring influenceand present the methodology and results for Experiment 1.The remaining sections 6, 7, 4, 5 and 8 do the same forExperiments 2, 3,4,5 and 6, respectively. Finally, Section 9analyzes prior works in this field, and Section 10 providesan overview of the lessons learned from this work along withsome thoughts for future work.

2. EVALUATION SETUP

2.1 Twitter OverviewTwitter is a microblogging service that was launched in

March 2006, and soon became the most popular of its kind:five years later, in May 2011, its user base comprised around200 million users that post 1 billion short messages per

week2. To this unprecedented success also attest the largenumber of specialized services that have been developed ontop of it, such as Topsy3.

Responsible for Twitter’s popularity are the unique char-acteristics that lie at its core: first, users are only allowed topost short messages of up to 140 characters, which are calledtweets. This urges content providers to put all their talentinto creating original, self-contained and witty messages thatrequire the minimum attention and time from their read-ers. Thus, they can be easily understood, memorized andshared with other people, strongly resembling marketing slo-gans. Second, Twitter encourages and inherently supportsthe interaction between its members: its accounts are pub-licly available by default so that users can freely register toany one of them, receiving notification for its latest activity.In fact, Twitter maintains a social graph that comprisesone node for each user and one link for each connection be-tween two users. These links are directed, pointing from thesubscriber to the content provider. In its terminology, theformer is called follower and the latter followee. By be-coming followers of a specific account, users explicitly denotethat the followee is of particular interest to them, either dueto a common background (e.g., a hobby) or because of thequality of her content (e.g., news services).

Also crucial for the success of Twitter are the usage pat-terns that emerged with the increase of the content and ofthe social interactions among its members:

1. Users typically categorize their tweets in topics thathave been freely defined by other users. This is doneby adding to a tweet a topic tag, which consists ofthe symbol # followed by one or more words — oralphanumerics — concatenated together (e.g., #fb).This kind of annotation — known as hashtag — canbe used, therefore, to identify groups of people thatare interested in the same subject. Note that a singletweet can be associated with multiple hashtags (i.e.,topics).

2. Twitter offers a platform for discussion among its mem-bers: by adding the annotation “@randomName” intheir tweet(s), users can directly address the userrandomName, who can later respond back in the sameway. This form of annotation — called mention —enables us to detect users that are engaged into bilat-eral discussions.

3. Users typically share with their followers tweets thatthey find quite appealing or interesting, but have beenposted other users. This is done by posting on theirown accounts the original tweet marked with the spe-cial annotation “RT @randomName” in order to givecredit to the first author, randomName. This prac-tice — called retweeting — enables us to track thediffusion of a particular tweet, and, thus, to estimateits influence; the larger the cascade it triggers (i.e., themore users retweet it), the more influential it is.

In the following, we consider all these characteristics ofTwitter with the aim of analyzing the interaction patternsbetween the members of specific communities. For brevity,

2See http://blog.twitter.com/2011/03/numbers.htmlfor more details.3See http://topsy.com.

the messages that contain a mention or the retweet symbolare called annotated tweets. In addition, a core part ofour analysis focuses on the polarized tweets: these aretweets that express a positive or a negative sentiment thatis explicitly denoted by the appropriate emoticon. Followingthe common practice in the liteature [2, 5, 11], we consideras positive a tweet that contains either of the followingsmileys: “:)”, “:-)”, “: )”, “:D” or “=)”. On the other hand,we classify as negative a tweet that is a marked with “:(”,“:-(”, or “: (”. Polarized tweets can be used to estimate theaggregate sentiment of an entire community (or of a partof it) towards the corresponding topic. Note that, in ouranalysis, we disregard tweets that contain both a positiveand a negative emoticon.

2.2 Problem FormulationThis work focuses on studying the dynamics of influence

in the context of specific topics in Twitter. Therefore, at itscore lies the notion of topic community, i.e., a four-partiteentity that consists of the following components: (i) a uniquehashtag, that describes the subject of the community, (ii) theset of users that have posted at least one tweet on the topic,(iii) all the messages that pertain to the particular topic (i.e.,the tweets that contain the corresponding hashtag), and (iv)the connections on the social graph between the users of thecommunity. Hence, a topic community consists not only ofpeople that share a common interest, but also of the linksbetween them and the relevant content they have produced.

The members of a topic community typically differ in thedegree of influence they exert over their peers; some usersare rather passive, while others excel in some aspect of thecommunity, affecting the behavior of their peers and set-ting relevant trends. The members that have established aprominent position within a community through their activeparticipation in it are called influencers.

The level of influence is usually measured with the helpof an influence criterion; that is, a metric that consid-ers a specific activity of a community and quantifies theinvolvement of every member in it. For instance, two impor-tant aspects of Twitter’s topic community are the internalmentions (i.e., mentions from one community member toanother) and the internal retweets (i.e., retweets postedby a member of the community, whose original author alsobelongs to the community).

The application of an influence criterion on a topic com-munity associates each person with an ordinal value thatdenotes her individual degree of influence (e.g., number ofinternal retweets). Users can be ranked, therefore, on a scaleof influence. The top k influential users are individuallycharacterized as core users, whereas the team they formis named the core@k group of the topic community withrespect to that particular criterion. For brevity, we also callit core group, while its size (k) is termed core size.

To analyze the results of our experimental study, we con-sidered the following core sizes: k = 10, k = 20, k = 50 andk = 100. The reason is that they are suitable for illustrat-ing the effect of this parameter on the aggregate dynam-ics of a community’s core group; sizes of finer granularity(e.g., k = 10, 20, 30, 40. . . ) result in negligible variations(especially between consecutive sizes), while sizes of coarsergranularity (e.g., k = 10, 100, 1000. . . ) hide a lot of informa-tion. This range of core sizes also allows for approximating

the size that corresponds to the maximum level of influenceamong most groups.

In the following, we consider several influence settings(i.e., the binding of an influence criterion and a core size) inorder to examine the activity of core groups. Our goal is toidentify trends that prevail among the core users and differ-entiate them from the ordinary members of the community(i.e., influence patterns).

2.3 Twitter Data SetIn our experimental study, we considered the data set that

was employed in [13]. It contains more than 475 milliontweets that were posted by over 17 million users in a timeperiod of 7 months (from the beginning of June 2009 untilthe end of December 2009). In total, this crawl recordedaround 20%-30% of the entire Twitter activity during thatperiod, thus constituting one of the largest data collectionsever gathered from Twitter. It has captured, therefore, arepresentative part of the Twitter activity that suffices fordrawing safe conclusions about the influence patterns amongits members. This data set, however, lacks any informationabout Twitter’s social graph.

To cover the need for information about social connec-tions, we additionally consider the crawl of the Twitter graphthat was employed in [8]. It constitutes a snapshot of the en-tire social graph as of August 2009, thus coinciding with thecrawling period of the content we are considering. It lacks,however, the temporal aspect of the links (i.e., the exact timethey were formed) and, thus, their evolution throughout theperiod of time we are considering. As a result, the conclu-sions we draw with respect to the link structure of Twitterconstitute an approximation of the actual phenomena.

The original data set contains more than 49 million oftweets that are marked with at least one hashtag, corre-sponding — in total — to around 3 million distinct topics.We grouped the messages and the authors into topic com-munities, and filtered them such that each topic: (i) con-tains more than 10,000 tweets, (ii) comprises more than 500users, (iii) involves more than 500 polarized tweets, (iv) en-tails more than 500 internal mentions, and (v) conveys atleast 500 internal re-tweets. The first two criteria ensurethat the communities we consider are large enough to drawsafe conclusions, while the rest of them ensure enough ev-idence for the patterns we are investigating. Note that, inall cases, the selected threshold was set to a rounded valuethat approximates the mean one across all topics.

This pre-processing resulted in eligible 728 topics. To se-lect the most vibrant of these communities, we ranked themaccording to the average number of tweets posted by eachof their members. The higher this number is, the more ac-tive the individual members are expected to be. From thisranking, we selected the top 100 topic communities.

The technical characteristics of our corpus are presentedin Table 1. On average, each test-bed community consists of13,000 distinct members, with each individual posting morethan 9 tweets. Thus, the content of the average communitycomprises 120,000 tweets, out of which 1,000 are markedas negative and 2,000 are marked as positive. In addition,20,000 of them pertain to discussions between communitymembers, while a similar portion of them pertains to internalretweets. Note that the higher frequency of the positivetweets with respect to the negative ones does not imply thatthe balance is in favor of the former across all topics. In fact,

Min. Median Max. Total

Users 502 5,992 228,684 1,297,941Tweets 10,195 45,811 1,224,161 11,318,589Tweets per User 4.29 7.32 42.68 9.40Negative Tweets 25 316 15,084 109,503Positive Tweets 28 696 73,638 198,743Internal Mentions 555 3,416 1,254,712 2,053,805Internal Retweets 653 5,846 488,477 1,963,413

Table 1: Overview of the most important techinicalcharacteristics of the data set we employed in ourexperimental study. Note that for the number ofTweets per User, the value 9.40 of the last columncorresponds to the average value across all commu-nities, rather than their sum (i.e., total value).

the negative tweets outnumber the positive ones in 1/3 ofall communities.

3. INFLUENCE CRITERIANumerous metrics for measuring users’ influence in Twit-

ter have been proposed in the literature. None of them,though, has been originally crafted for estimating influencein the context of topic communities. Since we do not in-tend to come up with yet another influence criterion, webase our analysis on existing metrics that can be appropri-ately adapted to our settings. We are actually interested inmetrics whose value can be derived from the context of acommunity in a straightforward way; that is, metrics stem-ming from the tweets posted by community members as wellas on their interconnections on the social graph. Such met-rics facilitate the integration of our conclusions in practicalapplications. We actually decided to consider several met-rics, since each one captures a particular aspect of the com-munity’s activity. In this way, we provide a comprehensiveoverview of influence patterns in topic communities.

We examined all metrics proposed in the literature toidentify the ones that are compatible with our settings. Wehad to reject the TwitterRank approach of [12], because itis not restricted to a single community’s information, butrather requires information about all the topics a user is in-terested in. We also excluded the metric employed in [1],as it is specialized on the size of cascades that are triggeredby tweets containing URLs (independently of topics). Re-stricting this metric in the borders of a community turnsit almost identical to the Retweets Influence criterion (seebelow). Thus, the influence criteria that form the basis ofour analysis are the following:

1. Indegree Influence represents the number of commu-nity members that follow a particular person (i.e., theindegree of the corresponding node on the social graphof the community). The larger its value is, the largeris the audience that receives the tweets of the user.

2. Mentions Influence denotes how many tweets of thegiven community mention a particular user. This mea-sure is related to the user’s ability to get involved indiscussions with other members of the community. Infact, the higher its value is, the more sociable the useris.

3. Retweets Influence expresses how often the posts of aspecific user are reproduced by other members of the

Criterion1 Indegree Indegree Indegree Mentions Mentions RetweetsCriterion2 Mentions Retweets Tweets Retweets Tweets Tweets

Core@10

Minimum 0.00% 0.00% 0.00% 5.00% 0.00% 0.00%Median 0.00% 0.00% 0.00% 25.00% 10.00% 15.00%Maximum 10.00% 10.00% 10.00% 45.00% 35.00% 35.00%Mean ± SD 0.40% ± 1.69 0.35% ± 1.78 0.20% ± 1.21 26.55% ± 9.37 11.45% ± 8.51 12.95% ± 7.92

Core@20

Minimum 0.00% 0.00% 0.00% 10.00% 0.00% 0.00%Median 0.00% 0.00% 0.00% 27.50% 12.50% 12.50%Maximum 5.00% 5.00% 7.50% 45.00% 32.50% 30.00%Mean ± SD 0.45% ± 1.20 0.35% ± 1.12 0.28% ± 1.00 27.08% ± 8.16 12.20% ± 7.70 13.93% ± 7.00

Core@50

Minimum 0.00% 0.00% 0.00% 11.00% 2.00% 2.00%Median 0.00% 0.00% 0.00% 29.00% 14.00% 16.00%Maximum 6.00% 6.00% 6.00% 43.00% 32.00% 30.00%Mean ± SD 0.91% ± 1.35 0.82% ± 1.18 0.68% ± 1.12 27.65% ± 7.37 14.05% ± 6.96 15.91% ± 5.85

Core@100

Minimum 0.00% 0.00% 0.00% 11.00% 3.50% 5.00%Median 0.00% 1.00% 0.50% 29.50% 15.50% 18.00%Maximum 6.00% 7.50% 7.50% 42.00% 33.00% 29.50%Mean ± SD 0.91% ± 1.35 1.42% ± 1.57 1.25% ± 1.46 27.73% ± 6.97 15.94% ± 6.92 17.69% ± 5.50

Table 2: Jaccard similarities between the core groups that are defined by different criteria over the sametopic community for k=10, 20, 50 and 100. In each case, we provide the minimum, the median, the maximumtogether with the mean value and the corresponding standard deviation (SD) - across all 100 topics.

community. This is a measure indicative of the valueof a user’s content, with higher values denoting moreinteresting content.

4. Tweets Influence represents the volume of content thatis produced by a particular user (i.e., how many tweetson the topic she has posted). The higher its valueis, the more prolific is the corresponding user and thehigher is the likelihood that another community mem-ber will read and consider her posts, thus increasingher influence.

The first three of these criteria were also employed in [3].This allows for comparing part of our conclusions with acouple of similar experiments that were conducted in [3] overthe Twitter as a whole.

3.1 Cross-criterion Overlap PatternsThe focus of this section lies on cross-criterion over-

laps; this is the portion of users that are shared by the coregroups defined by different influence criteria on the samecommunity. In other words, we investigate whether differentmetrics consider the same users as the most influential onesin the context of individual topics. The reason for this studyis twofold: first, a high overlap between the core groups oftwo distinct criteria inevitably turns one of them superflu-ous, as they both lead to the same conclusions. Second, it isworth investigating whether the highly influential membersof a community affect its activity in multiple ways; giventhat the individual metrics capture different types of influ-ence, the overlap between them corresponds to core userswith versatile activity.

To measure how close two groups of influencers are, weemploy the Jaccard similarity coefficient. Given two coregroups of equal size k, i.e., core1@k and core2@k, their Jac-card similarity J(core1@k, core2@k) is defined as the sizeof their intersection divided by the size of their union:

J(core1@k, core2@k) =|core1@k ∩ core2@k||core1@k ∪ core2@k| · 100%.

In essence, J(core1@k, core2@k) expresses the percentageof users that are common among the input groups. Thus,it takes values in the interval [0, 100], with higher valuesdenoting higher similarity (i.e., overlap).

In the context of our analysis, we computed the overlapbetween all communities for all pairs of influence criteria— 6 in total — for all the core sizes we consider. Thisresults in 24 combinations that are presented in Table 2.In each case, we provide the minimum, the median and themaximum similarity together with their mean value and thecorresponding standard deviation. In this way, we offer acomprehensive overview of the overlap distributions.

We can notice several interesting patters in the outcomesof Table 2. First, the similarity of Indegree with all othercriteria is negligible, regardless of the size of the core group.The minimum value is 0 in all cases, and so is the median —with just two exceptions. This suggests that there is a cross-criterion overlap solely for a handful of community pairs inevery case. However, the similarity of these pairs remainsrather low, taking a maximum value of 10%. As a result,the mean values remain lower than 1.5%, and we can safelydeduce that the Indegree is completely independent from theother criteria. This implies that a user with many followersis not necessarily mentioned or retweeted at a high rate inthe context of a specific community. Such users also refrainfrom posting a large amount of messages on a specific topic.

This conclusion raises the important question of whetherthe non-zero similarities between the Indegree and the restof the criteria are random or not; that is, whether they area side-effect of the size of the corresponding communities,since the smaller a community is, the higher the probabil-ity that two metrics will consider the same user(s) as influ-encer(s). To provide an answer to this issue, we comparedthe size of the overlapping communities with the average oneand found out that the former is lower than the latter in al-most all the cases. For instance, there are 7 distinct topicsfor k = 10 that exhibit an overlap between Indegree andat least one other metric; their average size is 5,300 users,with the minimum being 2,600 and the maximum 10,500.These sizes are, apparently, much lower than the averagecommunity size of 13,000 users. Consequently, users withmany followers play an active role in multiple aspects of acommunity only if it is rather small in size.

Regarding the overlap between the other three criteria, itis remarkable that 8 out of 12 cases have a minimum valuethat is higher than 0. This means that these metrics shareat least one influencer for every individual topic, for all sizes

of the core group. Also remarkable is the fact that their me-dian values are almost identical with their mean one. Thispattern provides a strong indication for a normal distribu-tion, an evidence that is advocated by another noteworthypattern: in most of the cases, the median value is equal tothe average of the minimum and the maximum ones.

Note, though, that the degree of overlap varies signifi-cantly among the three combinations of these metrics. Be-tween the Mentions and the Retweets metrics, it remainsrelatively stable and quite high, having a mean value wellover 25% for all core sizes. This suggests that 1/4 of thepeople that immerse themselves into discussions with othercommunity members generate content of high value, whichreaches out to a wide audience, and vice versa. On the otherhand, the similarities between Tweets and Mentions and be-tween Tweets and Retweets take virtually the same valuesacross all core sizes, but remain relatively low: they rangefrom 10% to 20%, increasing with the increase of k. Thus,around 1/6 of the heavy-writers (i.e., users that produce alarge amount of content) are heavily cited or discussed; themore users we consider as influencers, the higher this portiongets.

On the whole, we can conclude that the influence metricswe consider in our study are independent from each other.None of their combinations leads to an overlap that takesextremely high values (e.g., over 2/3 or even 50%); the max-imum overlap is just 45% between Mentions and Retweetsfor k = 20 for a single community. This is in accordancewith earlier evidence that was derived after examining therelations between the first three criteria (i.e., Indegree, Men-tions and Retweets) out of context (i.e., over the entire socialgraph of Twitter and over the entire activity of its users [3]).

4. SENTIMENT PATTERNSThere is no standard method in the literature for evalu-

ating the outcomes of an influence criterion. As a result,works proposing such criteria typically examine representa-tive samples of the identified top influencers, checking theirauthority in the real world (e.g., their fame or the qualityof their content). In contrast to them, we evaluate the in-fluence of the core groups with respect to their ability toguide the aggregate sentiment of a community. Real influ-encers are expected to determine the overall opinion of acommunity in a unequivocal way.

To facilitate our analysis, we quantify the aggregate opin-ion expressed by the tweets of a group of users through thefollowing measure:

Definition 1 (Polarity Ratio). Given a set of po-larized tweets T , their polarity ratio rp(T ) is defined asfollows:

rp(T ) =

|PT |+1|NT |+1

− 1, if |NT | < |PT |

− |NT |+1|PT |+1

+ 1, if |PT | ≤ |NT |(1)

where NT ⊆ T and PT ⊆ T stand for the sets of negativetweets and positive tweets, respectively, and |NT | and |PT |represent their sizes (i.e., |NT |+ |PT | = |T |).

Polarity Ratio takes values in the interval (−|T |,+|T |),with positive values suggesting the prevalence of positivetweets, and vice versa. For instance, a positive value n �1 suggests that the positive tweets are approximately n +

core@10 core@20 core@50 core@100

Indegree 0.10 0.13 0.33 0.52Mentions 0.49 0.67 0.85 0.74Retweets 0.44 0.47 0.67 0.74Tweets 0.64 0.57 0.81 0.83Random 0.25 ± 0.11 0.28 ± 0.12 0.32 ± 0.13 0.35 ± 0.15

Table 3: Pearson correlation between the aggregatesentiment of the entire topic communities and theircore groups.

core@10 core@20 core@50 core@100

Indegree 0.43 0.45 0.51 0.55Mentions 0.60 0.60 0.60 0.59Retweets 0.59 0.60 0.59 0.59Tweets 0.55 0.55 0.56 0.57

Table 4: Area under curve (AUC) of the rate ofpolarized content production for all combinations ofinfluence criteria and core sizes. Note that the AUCfor the entire communities is equal to 0.54.

1 times more than the negative ones. Neutral sentimentsresult in rp values very close to 0, where NT ≈ PT .

We computed the polarity ratio for the core groups andthe corresponding communities as a whole, for all possibleinfluence settings. To estimate how well the former ratiopredicts the latter one, we considered an established met-ric for estimating correlation: the Pearson correlationcoefficient (ρX,Y), which expresses the linear dependencybetween two variables X and Y . It takes values in theinterval [−1, 1], and the higher its absolute value is, thestronger the correlation between X and Y is. A value of|ρX,Y | = 1 indicates a completely linear relationship of theform X = α · Y + β, where α, β ∈ R and 0 < α if ρX,Y = 1,while α < 0 if ρX,Y = −1. In our case, the X variablecomprises the values of the polarity ratio across all topiccommunities, while the Y variable encompasses the polarityratios of the corresponding core groups.

The results of our analysis are presented in Table 3. Asa baseline, we considered random groups of users. In moredetail, for each core size k, we randomly selected 100 samplesof k users and estimated the correlation of their polarityratio with that of the entire communities4.

Examining the results in Table 3, we can see that thereis a positive correlation in all cases, for both our influencecriteria and the baseline. It is also clear that this correla-tion increases proportionally with the increase of the coresize. This means that the larger the (core) groups are, themore close their aggregate sentiment is to that of the entirecommunity, probably due to the larger number of polarizedtweets they produce (see Section 5 for more details). Theonly exception to this rule is the Mentions criterion; its high-est correlation is achieved for k = 50, dropping slightly fork = 100. Its value for k = 50 is actually the highest amongall influence criteria, denoting that this particular influencesettings (i.e., Mentions criterion combined with a core groupof 50 users) exert the maximum power over topic communi-ties. Similar levels of influence are exerted by the Tweets and

4Given that each topic community of our corpus comprises13,000 users on average, the samples of k ∈ {10, 20, 50, 100}random users we consider in this study represent a negligiblesubset of their user base. Consequently, the random baselinedoes not necessarily converge to the aggregate sentiment ofa community.

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Figure 1: The rate of polarized content production across all influence settings.

the Retweets criteria, though at a lesser extent. These threecriteria actually outperform the baseline one to a significantdegree in all cases: for each core size, their correlation is atleast twice as high as that of the random groups. This isin contrast to the Indegree criterion, whose performance isvery close and even lower than the baseline.

In addition to the exhibited high correlations, real influ-ence requires that the activity of community members fol-lows that of the core users; that is, the latter are expected toguide the aggregate sentiments of the former by posting theirpolarized content before them. To investigate this aspect,we compared the evolution of influencers’ polarized contentwith that of the entire communities. In more detail, we di-vided the lifetime of all topic communities in hourly timeslots5 and estimated the overall number of polarized tweetsposted in each of them by the influencers of each core groupas well as by the topic communities as a whole. We thencalculated the cumulative content production for each timeslot, summing the portion of content posted in the currentslot and the prior ones. We plotted the resulting numbersin the 2-dimensional space defined by time (horizontal axisx) and content volume (vertical axis y) in order to visualizethe rate of polarized content production for each user group;the earlier the content of a group is produced, the faster itconverges to the line y = 100 (i.e., the line that correspondsto the total volume of content produced in the examinedperiod).

The resulting plots for the influence settings we are con-sidering are presented in Figures 1(a) to (d). We can noticethe following interesting patterns: the curves of the Men-tions and the Retweets criteria converge to the line y = 100significantly faster than the baseline curve of the entire com-munities. This applies across all core sizes, as these curvesremain relatively stable in all plots. The Tweets criterionresults in a curve that — in most of the cases — lies negligi-bly higher than the baseline one, while the Indegree criterionstarts very low and rises to higher positions only for largecore sizes. We can conclude, therefore, that the polarizedcontent of the core groups defined by the Mentions and theRetweets criteria precede that of the entire communities,regardless of the core size. The Tweets criterion merely fol-

5Note that all communities have the same lifetime, compris-ing the activity of 210 days in 2009 captured in our dataset.

lows the evolution of aggregate content, while the Indegreeexhibits significantly lower rates of convergence.

To further illustrate these differences, we quantified themthrough the area under each curve (AUC). This metric takesvalues in the interval [0, 1], with higher values indicatingfaster convergence to the line y = 100. The outcomes arepresented in Table 4. The baseline curve of entire commu-nities has an AUC equal to 0.54 and is consistently lower by10% than that of the Mentions and the Retweets criteria.The Tweets and the Indegree ones start from 0.55 and 0.43,respectively, and rise proportionally to k without exceedingthe baseline one to a significant extent.

On the whole, we can safely deduce that the core groupsthat are defined by Mentions and the Retweets criteria ex-hibit real influence over their topic communities. As notedin the following section, this is actually achieved despite thefact that their core groups produce a negligible portion ofthe communities’ polarized tweets.

5. CONTENT VOLUME PATTERNSThe scope of this section is twofold: first, we investigate

what part of a community’s overall activity stems from itscore group. Second, we examine the contribution of the coreusers to the special characteristics of Twitter that lie at thecore of our influence analysis (i.e., the polarized and the in-ternally annotated tweets). We call this study content pat-tern analysis and consider it crucial for the explanation ofthe patterns that are described in this work. For example,the finding that the sentiment of the core users determinesthe overall sentiment of their community can have multi-ple interpretations, depending on the portion of polarizedtweets that stems from the influential users; in the extremecase that it exceeds 90%, they are practically the only onesexpressing any sentiments on the matter. Thus, there is noevidence that they influence their peers to a large extent.On the other hand, if their portion is small (e.g., less than1%), it means that they can influence all other memberswith minimum effort.

The outcomes of our analysis are presented in Table 5.Due to the large number of variables we are considering,instead of analytical statistics, we present only their aggre-gate values (i.e., the sum across all communities for a specificbinding of influence criterion and core size). We can easilynotice that the influence criteria can be clustered into two

Positive Negative Mentions Retweets TotalTweets Tweets Tweets

Core@10Indegree 0.00% 0.00% 0.00% 0.00% 0.10%Mentions 0.05% 0.03% 0.03% 0.04% 4.37%Retweets 0.04% 0.03% 0.03% 0.04% 4.95%Tweets 0.08% 0.23% 0.06% 0.12% 12.62%

Core@20Indegree 0.00% 0.00% 0.00% 0.00% 0.16%Mentions 0.07% 0.05% 0.04% 0.07% 6.05%Retweets 0.06% 0.06% 0.04% 0.07% 7.09%Tweets 0.11% 0.29% 0.09% 0.17% 17.38%

Core@50Indegree 0.00% 0.00% 0.00% 0.00% 0.35%Mentions 0.10% 0.07% 0.07% 0.12% 9.57%Retweets 0.09% 0.10% 0.07% 0.13% 11.20%Tweets 0.17% 0.40% 0.14% 0.25% 25.58%

Core@100Indegree 0.01% 0.01% 0.00% 0.01% 0.71%Mentions 0.13% 0.11% 0.10% 0.17% 13.43%Retweets 0.12% 0.13% 0.09% 0.18% 14.89%Tweets 0.22% 0.46% 0.18% 0.33% 32.96%

Table 5: Percentage of the community activity ineach category that is produced - on average - by thecore group defined by each influence settings.

groups according to their patterns: one comprising solelythe Indegree criterion, and another one comprising the restof them.

Regarding the former cluster, the contribution of the coregroup in every category across all core sizes is less than 1%.In fact, the users with the most followers practically post nopolarized or internally annotated tweets for core sizes up tok=50. For k=100, they merely produce 0.01% of these spe-cial tweets, while their maximum contribution to the overallcontent is just 0.71%. As a result, we do not expect theinfluencers defined by this criterion to be actively involvedin any aspect of a community, independently of the corre-sponding core size. This means that, apart from postinga handful of messages on a topic, the core users with highIndegree do not interact with their fellow members in anyother way.

The rest of the influence metrics follow similar patternswith respect to the special categories of tweets: they startfrom very low contributions (e.g., 0.03%) for k = 10, andgradually rise to higher values as the core size increases.In every case, the Mentions and the Retweets influencershave equivalent levels of contribution, with the Tweets onescontributing twice as much (in the best case, nevertheless,they account for just 0.46% of the category). With respectto the total tweets, however, the contribution is significantlyhigher for all criteria. For the Mentions and the Retweets, itranges from around 5% (for k=10) to 15% (for k=100), whilefor the Tweets it takes - by definition - much higher values:it starts from 12.5% for k=10 and raises up to (almost) 33%for k=100.

We can deduce, therefore, that the core groups of thesethree metrics produce a considerable amount of content, butonly a small portion of it expresses explicit sentiments or in-teracts with their peers. Thus, instead of citing their fellowmembers or engaging into discussions with them, they postoriginal tweets that typically are of neutral sentiment. Thisis probably because they pertain to facts, rather than ex-pressing personal opinions.

Min. Median Max. Mean ± SD

Core@10Indegree 0.00% 0.00% 17.85% 2.22% ± 2.03Mentions 0.00% 17.78% 75.56% 41.63% ± 18.00Retweets 0.00% 17.82% 71.11% 26.67% ± 18.42Tweets 0.00% 7.14% 80.56% 21.11% ± 17.41Random 0.00% 2.22% 62.22% 6.00% ± 9.65

Core@20Indegree 0.00% 0.00% 8.09% 1.10% ± 1.21Mentions 0.00% 12.46% 66.84% 25.33% ± 14.97Retweets 0.00% 13.05% 63.68% 18.68% ± 15.57Tweets 0.00% 7.56% 64.74% 18.42% ± 14.14Random 0.00% 2.50% 58.09% 6.31% ± 9.25

Core@50Indegree 0.00% 0.13% 8.41% 0.37% ± 1.19Mentions 0.53% 8.16% 50.32% 13.24% ± 10.71Retweets 0.38% 8.73% 41.75% 12.03% ± 10.40Tweets 0.00% 5.92% 57.81% 13.91% ± 10.60Random 0.00% 3.14% 47.46% 6.15% ± 0.00

Core@100Indegree 0.00% 0.13% 9.28% 0.34% ± 1.15Mentions 0.56% 6.30% 39.76% 10.06% ± 8.39Retweets 0.42% 5.25% 33.82% 9.80% ± 8.32Tweets 0.14% 3.78% 44.17% 10.45% ± 7.59Random 0.00% 3.01% 44.17% 6.11% ± 7.77

Table 6: Percentage of reciprocal pairs of users foreach core size and influence criterion.

6. STRUCTURE PATTERNSThe aim of this section is to examine the presence and the

degree of homophily between the core users of a topic com-munity. It investigates the extent to which core users sharea common background with respect to their social statusand/or their personal opinions (i.e., their way of thinking).Of course, homophily in Twitter is hard to measure, due tothe absence of private information about the users. There-fore, we follow the approach presented by Weng et al. in [12]and use an indirect metric for estimating it, namely reci-procity. In Twitter, two users are reciprocally connected ifthey follow one another.

To verify that core users typically share higher levels ofhomophily than the rest of the community members, wecompare their reciprocity rate with that of the entire com-munity. That is, we compare the percentage of pairs of usersthat are reciprocally connected to each other. If this per-centage is significantly higher for the core groups, then ourpremise holds; otherwise, it is considered absurd.

For each core size k, we considered 100 groups of k ran-dom users per topic community. The results of our analysisare summarized in Table 6. We can notice that the Inde-gree criterion exhibits very low levels of reciprocity, whichactually lie below the baseline. This clearly indicates thatthe members of the core groups it defines share no com-mon background. It is worth noting at this point that therandom groups of users exhibit a relatively stable behavioracross all core sizes: their median reciprocity rate remainsclose to 2.5% in all cases, while their mean one sticks to 6%.

On the other hand, the remaining three criteria have reci-procity rates that are significantly higher than the baselineone; the highest values actually correspond to the Mentionscriterion, with the Retweets and the Tweets one following it.In all cases, reciprocity takes the highest value for the coregroups of 10 members, and decreases proportionally withthe increase of the core size. For the largest core groups(k = 100), its value lies very close to the baseline one for allthree criteria. We expect, therefore, members of larger coregroups to share as many background features as any random

Min. Median Max. Mean ± SD

Core@10Indegree 0.00% 0.00% 33.33% 0.35% ± 3.33Retweets 0.00% 21.58% 87.37% 24.93% ± 20.11Tweets 0.00% 7.68% 90.75% 13.20% ± 17.27Mentions 0.00% 32.08% 100.00% 36.03% ± 24.14Random 0.00% 0.00% 92.86% 0.13% ± 2.33Core@20Indegree 0.00% 0.00% 24.00% 0.65% ± 3.13Retweets 0.00% 32.23% 92.51% 34.12% ± 20.74Tweets 0.00% 14.02% 93.10% 20.35% ± 21.14Mentions 0.00% 50.43% 93.61% 49.05% ± 22.56Random 0.00% 0.00% 23.53% 0.12% ± 0.90Core@50Indegree 0.00% 0.00% 53.85% 2.49% ± 7.07Retweets 0.00% 50.62% 94.43% 47.59% ± 22.53Tweets 0.00% 27.76% 95.30% 31.64% ± 24.30Mentions 22.31% 67.40% 97.76% 65.54% ± 19.50Random 0.00% 0.00% 58.33% 0.61% ± 3.22Core@100Indegree 0.00% 0.33% 43.75% 3.42% ± 6.53Retweets 0.99% 61.97% 100.00% 58.53% ± 22.74Tweets 0.00% 37.84% 98.25% 39.65% ± 25.65Mentions 30.25% 77.28% 100.00% 75.38% ± 17.68Random 0.00% 0.00% 86.49% 1.11% ± 3.89

(a)

Min. Median Max. Mean ± SD

Core@10Indegree 0.00% 0.00% 33.33% 1.04% ± 5.08Mentions 0.00% 22.56% 100.00% 27.28% ± 19.58Retweets 0.00% 31.13% 100.00% 33.58% ± 22.34Tweets 0.00% 11.63% 95.91% 15.69% ± 17.00Random 0.00% 0.00% 66.67% 0.12% ± 1.87Core@20Indegree 0.00% 0.00% 27.78% 0.92% ± 4.38Mentions 0.00% 39.71% 96.84% 40.00% ± 21.53Retweets 0.00% 47.65% 98.18% 48.00% ± 21.35Tweets 0.00% 23.27% 89.54% 25.98% ± 19.87Random 0.00% 0.00% 100.0% 0.45% ± 3.75Core@50Indegree 0.00% 0.00% 25.16% 1.78% ± 4.75Mentions 0.00% 55.91% 91.44% 54.66% ± 19.58Retweets 9.38% 69.27% 99.22% 65.95% ± 19.10Tweets 0.00% 39.82% 93.22% 39.27% ± 22.88Random 0.00% 0.00% 58.93% 1.03% ± 3.63Core@100Indegree 0.00% 0.51% 26.23% 2.77% ± 5.08Mentions 22.40% 66.50% 96.83% 64.85% ± 17.73Retweets 20.66% 78.84% 100.00% 77.81% ± 16.08Tweets 0.00% 56.02% 94.30% 50.83% ± 23.72Random 0.00% 0.00% 73.33% 2.43 %± 5.46

(b)

Table 7: Values for the intra-core mention probability (on the left side) and for the intra-core retweetprobability (on the right side) across all topic communities, for all core sizes and influence criteria.

pair of users. For this reason, we consider the core size ofk = 100 as the critical one, above which the notion of coregroups is degenerated.

On the whole, we can justifiably conclude that the coregroups of sizes up to 100 exhibit high levels of homophily,thus forming densely connected sub-graphs — in terms ofgraph structure. This is particularly true for the Mentionsinfluence criterion, but does not apply at all to the Indegreecriterion.

7. INTRA-CORE REFERENCE PATTERNSThis section examines whether the core users of a com-

munity actually know each other and socialize extensivelybetween them, regardless of their connections on the socialgraph. As a means of interaction, we consider the referencefrom one user to a another. In the context of Twitter, thisis mainly done through the annotated tweets, i.e., the men-tions and the retweets. We can reasonably assume that themore a Twitter user “refers” to another user, the stronger istheir connection. Our goal is, therefore, to examine whethercore users are more likely to “refer” to their fellow core usersthan to other members of the same community. We callthe analysis of this behavior intra-core reference patternanalysis.

In more detail, our analysis considers the following twoprobabilities:

Definition 2 (Intra-core Mention Probability).Given a topic community tc and its core group cg, its intra-core mention probability (Pim) expresses how likely it isfor a core user to mention a fellow member of the core group.It is defined as follows:

Pim =mentionscg→cg

mentionscg→tc· 100%,

where mentionscg→cg denotes the total number of mentionsbetween all possible pairs of core users (i.e., those posted by acore user and referring to another one), and mentionscg→tc

stands for the number of all internal mentions that wereposted by members of the core group.

Definition 3 (Intra-core Retweet Probability).Given a topic community tc and its core group cg, its intra-core retweet probability (Pir) denotes how likely it is fora core user to retweet a message that was originally postedby another core user. It is defined as follows:

Pir =retweetscg→cg

retweetscg→tc· 100%,

where retweetscg→cg stands for the total number of retweetsthat involve any pair of core users (i.e., those posted by acore user and were originally written by another one), andretweetscg→tc expresses the number of all internal retweetsthat were posted by members of the core group.

Both metrics take as value a percentage in the interval[0, 100], with higher values corresponding to higher self-awareness and more interactions between the members ofthe core group. Therefore, the higher these probabilitiesare, the stronger the ties between the core users are.

We calculated these probabilities for the core groups overall topic communities for the usual core sizes (k = 10, 20,50 and 100). For each core size k, we also considered 100groups of k random users per topic community in order toprovide a baseline for Pim and Pir that validates the signif-icance of the identified patterns. Note also that there is astrong bias between Pim and the Mentions criterion and be-tween Pir and the Retweets criterion: influencers with highmention (retweet) rate are expected to be frequently men-tioned (retweeted) by their peer core users, thus leading toa tautological observation. Nevertheless, we include thesecombinations in our analysis so as to provide an indicationof the maximum possible probabilities, which contrasts thebehavior of the random groups.

The outcomes of our evaluation for Pim and to Pir arepresented in Tables 7(a) and (b), respectively. Looking at

the results, we can observe that the Indegree criterion has— once more — a behavior that is totally different fromthe other three influence metrics. Among the latter, theMentions and the Retweets criteria take similar values in allcases, while the Tweets one follows them at a lower scale.

In more detail, the Indegree metric takes very low valuesfor both probabilities across all core sizes. For instance, itsmedian value is 0 (or very close to it) in all cases, while itsmean value remains lower than 3%. This can be explainedby the negligible number of internal mentions and internalretweets that are posted by users with excessive number offollowers, as explained in Section 5. A large number of fol-lowers says, therefore, little about the user’s dedication tothe given community and provides little grounds for her tointeract with the other core users.

The other influence criteria take significantly higher valuesfor both probabilities. Their median value is almost identi-cal to the mean one (with the exception of core size k = 10),thus indicating that their values follow a normal distribu-tion over the 100 communities. For Pim, the Retweets crite-rion takes values 10% to 20% lower than the maximum ones,which correspond to the tautology of the Mentions criterion,followed by the Tweets one, which are 20% to 30% lowerthan Mentions. For Pim, the Mentions metric lies close tothe tautology of the Retweets criterion, leaving the Tweetsone in the third place. In every case, the higher the size ofthe core group is, the higher the corresponding probabilitiesare. The significance of these patterns is highlighted whentaking into account the behavior of the groups of randomusers: their median probability is 0 across all influence set-tings, while their mean one is lower than 1% in the vastmajority of cases.

It is remarkable that the first two core sizes do not demon-strate any strong ties between core users (i.e., Pim < 50%or Pir < 50%), regardless of the influence criterion. How-ever, for core sizes k ≥ 50, the top influencers refer mostlyto their fellow core users (i.e., Pim � 50% or Pir � 50%),especially for those of the Mentions and the Retweets cri-teria. This indicates a strong link between the influentialusers of these two metrics, which is not the case, however,for the top influencers of the Tweets criterion.

To understand the variations of Pim and Pir across thevarious communities under the same influence settings, weexamined their content. We observed that these proba-bilities take their lowest values for the Mentions and theRetweets criteria in the case of generic topics, such as#business, #job, and #fb (which refers to the social net-work of Facebook6). On the other hand, more targetedtopics receive high probability values even for the core sizeof k = 10. A typical example of this case is the topic#bsbthisisusoct6th, which pertains to the release of a newalbum by the music group Backstreet Boys.

On the whole, we can argue that the core users of the In-degree and the Tweets criterion do not operate as a team.Contrary to them, the most influential users for the Men-tions and the Retweets criteria form a tightly coupled sub-group with frequent references to each other. In fact, themore focused a topic community is, the stronger the tiesbetween the members of its core group are.

6See http://www.facebook.com.

8. CROSS-COMMUNITYINFLUENCE PATTERNS

The goal of this section is to examine the phenomenon ofcross-community influence; that is, the extent to whichthe same users are considered highly influential across dif-ferent communities, which do not necessarily pertain to thesame or similar topics. To this end, we consider the overlapbetween the core groups of two different topic communi-ties with respect to the same influence criterion (i.e., cross-community core overlap). This is in contrast with thegeneral overlap between two communities, i.e., the por-tion of members that they have in common, regardless oftheir individual degrees of influence.

To get a comprehensive overview of cross-community in-fluence patterns, we compare the core overlap of two com-munities with their general one. If the latter is higher thanthe former, we can infer that the given topics share somerather idle users; their common users have posted tweetsabout various topics, but have not got heavily involved inall of them, probably because their interests drifted with thepassage of time. In case these measures are roughly equal,the common users of the respective communities are evenlydistributed over the scale of influence. However, if the coreoverlap is higher than the corresponding general overlap,then a larger-than-expected part the common users affectboth communities at comparable levels (with respect to thesame aspect/criterion, of course).

To estimate the core and the general overlap between twodifferent communities, we employ the Jaccard similarity co-efficient that was introduced in Section 3.1. We also con-sider all influence criteria together with the usual sizes ofthe core group (i.e., k = 10, 20, 50, and 100). Note thatmost of the 100 topics we are considering in this study arenot related to each other content-wise; some focus on healthissues, whereas others pertain to reality shows and sportsevents. In fact, we could merely indentify five clusters ofrelated topics, that in total comprise 10 distinct topics.

The outcomes of our experimental study across all combi-nations of the 100 communities (4,950 pairs of communities,in total) are presented in Table 8. The columns 2,3 and 4- from left to right - correspond to the minimum, the me-dian, and the maximum Jaccard similarity for each bindingof influence criterion and core size; the fifth column con-tains the average overlap together with the correspondingstandard deviation, while the sixth one denotes the percent-age of pairs of communities that share at least one member.Note that the first line corresponds to the general overlapbetween pairs of topics, and the rest of them to the coreoverlap for the corresponding influence settings.

Looking at the numbers of Table 8, it is easy to notice thatthe minimum value is 0 in all cases. This means that severalpairs of communities have no users in common, regardless ofthe influence criterion and the core size. A general overlap of0, however, cannot lead to a core overlap other than 0, thusnullifying our analysis. Hopefully, as the rightmost columnof the first line suggests, this applies to less 1% of the pairsof topics, and has a negligible impact on our study.

Regarding the median values, we can see that from 0.40for the general overlap it falls to 0 for all cases of the coreoverlap. This indicates two things: first, that the majorityof the overlapping communities have a negligible portion ofmembers in common, and, second, that these topics typically

Min. Median Max. Mean ± SD Overlaps

General Ov. 0.00% 0.40% 28.43% 1.19% ± 2.64 99.21%Core@10Indegree 0.00% 0.00% 30.00% 0.67% ± 2.67 8.71%Mentions 0.00% 0.00% 35.00% 0.26% ± 1.97 2.67%Retweets 0.00% 0.00% 40.00% 0.30% ± 2.28 2.71%Tweets 0.00% 0.00% 35.00% 0.20% ± 1.71 2.00%

Core@20Indegree 0.00% 0.00% 32.50% 0.75% ± 2.40 16.02%Mentions 0.00% 0.00% 45.00% 0.30% ± 2.11 4.40%Retweets 0.00% 0.00% 35.00% 0.32% ± 2.19 4.69%Tweets 0.00% 0.00% 37.50% 0.23% ± 1.84 3.21%

Core@50Indegree 0.00% 0.00% 32.00% 0.77% ± 2.22 30.95%Mentions 0.00% 0.00% 39.00% 0.36% ± 2.19 9.54%Retweets 0.00% 0.00% 37.00% 0.40% ± 2.34 10.04%Tweets 0.00% 0.00% 40.00% 0.28% ± 1.94 6.69%

Core@100Indegree 0.00% 0.00% 28.00% 0.79% ± 2.13 46.36%Mentions 0.00% 0.00% 37.00% 0.42% ± 2.22 16.77%Retweets 0.00% 0.00% 39.00% 0.48% ± 2.51 18.40%Tweets 0.00% 0.00% 35.00% 0.36% ± 2.11 13.05%

Table 8: Cross community influence patterns for allbindings of influence criterion and core size. Thefirst line pertains to the general overlap across allcommunities - independently of any influence crite-ria -, while the rest pertain to the core overlap withrespect to the corresponding settings.

have no core overlap at all. A similar conclusion is drawnfrom the average values of the Jaccard similarity: from 1.2%when considering the communities as a whole, it drops to lessthan 0.80% when considering the core groups of the Indegreecriterion and even lower for the other criteria. We brieflyinvestigated a random sample of such topics and found outthat, as expected, they are not relevant content-wise. Thisalso explains the patterns in the rightmost column of Ta-ble 8: the probability that two random communities shareat least one member of their entire user base is 99%, butthe probability that they share an influencer drops to lessthan half of it (<< 50%) for the core groups of all influencesettings.

Note that the Indegree criterion exhibits the highest — byfar — portion of overlapping communities among all crite-ria, regardless of the size of the core group. It also achievesthe highest performance with respect to all metrics we con-sider. This discrepancy with the other criteria is caused byits nature, as it constitutes the only criterion that relies onactivity-independent evidence: instead of considering the ac-tual contribution and involvement of users in a community,it exclusively takes into account the number of followers theyhave. Thus, it considers as highly influential even users thathave posted just one message on a particular topic, and hap-pen to have an excessive number of followers. Therefore, thiscriterion is not suitable for deriving safe conclusions aboutcross-community influence patterns.

In complete contrast, two patterns provide valuable in-sights to the analysis of this phenomenon. First, we cansee that the maximum value of core overlap is higher thanthat of the general one in all cases, but one. This clearlyindicates that the common users of these communities areconcentrated in the higher influence positions. Second, boththe average value and the percentage of overlapping com-munities rise significantly with the increase of the core size.This implies that the common users are concentrated in themiddle level influence positions, rather than the very top

ones. We investigated a representative sample of the topicsthat follow this pattern and found out that they are highlyrelevant, content-wise.

We can deduce, therefore, that the vast majority of ir-relevant topics share a small part of their members, whotypically exert no significant influence over their peers. Onthe other hand, communities that are related content-wise(e.g. #iran and #iranelection) share a considerable partnot only of their entire user bases, but also of their coregroups. However, their common members are not ranked inthe top influence positions, but rather at middle-level ones.It is, thus, more likely for a middle-level influencer to bepart of multiple core groups than it is for a top influencer.

Our conclusions differ from a similar study that was pre-sented in [3]. There, the authors considered three highlypopular, but unrelated topics of the summer of 2009, theyexamined their evolution for 2 months and found out thatthe core users retain equal levels of influence across differenttopics. To quantify influence, they employed two of our cri-teria: the Mentions and the Retweets one. The discrepancywith our findings can be justified by the different settingsand scale of their experimental study; the core groups of thetopics they examined are monopolized by news sources andcontent trackers, which cannot be considered as real users.Moreover, a sample of just three topics is by no means suf-ficient for drawing conclusions about the overall activity ofTwitter users.

9. RELATED WORKIn the recent years, the issue of influence in social net-

works has raised considerable interest among researchers ofcomputer science. A recurring subject is the applicationof the prevalent influence diffusion theories on the on-linesocial networks. In [3], Cha et al. examined influence dy-namics in Twitter and discovered that the top influentialusers get disproportionately more references than the ordi-nary users. Thus, they claim that the spread of informationcan be maximized by targeting a small number of opinionleaders. Their findings are in accordance with the traditionalview on influence diffusion [7], but contradict modern the-ories that emphasize the role of interpersonal relationshipsamong ordinary users [1, 6]. These works actually claim thatmarketing campaigns should target a large number of plainusers in order to be successful.

Another issue often addressed by researchers in this fieldis the prediction and measurement of influence. The authorsin [1] employed a regression tree model for predicting indi-vidual influence and found out that the local, past influenceand the number of followers are the most reliable factors fordetermining it. In [9], the authors introduced a probabilis-tic model for mining direct and indirect influence betweenthe nodes of heterogeneous networks. They evaluated theirmodel over three social networks, and their experimentaloutcomes verified that it helps to improve the accuracy ofuser behavior prediction. In [3], the authors propose threeof the influence criteria that were employed in our study,while Weng et al. introduced in [12] a novel method thatis based on a modified version of Google’s PageRank, in-tuitively called TwitterRank. To measure the influence ofindividuals, it takes into account both the topical similaritybetween users and the link structure of the social graph.

Another important issue in this field is the estimation ofhomophily among users of social networks (i.e., their ten-

dency to associate themselves mostly with similar individu-als) [10]. This notion was generally examined in [10] in thecontext of social networks. Its relationship with the infor-mation diffusion in social media was analyzed in [4], wherethe authors presented a probabilistic model that predictsthe diffusion characteristics of different user attributes. In[12], the authors interpreted the presence of high levels ofreciprocity among Twitter users as a sign of homophily andbuilt their influence criterion (i.e., TwitterRank) on top ofthis idea.

10. CONCLUSIONSIn this paper, we looked into the dynamics of topic com-

munities and their core groups of influential users, in particu-lar. Our thorough experimental study led to a precise modelfor the most influential individuals among the members ofa community: they are users who produce original contentthat is frequently retweeted. Although they are highly men-tioned by other users, they avoid getting into discussionsor reproducing others’ opinions. When they actually do so,they mainly refer to or cite other influential members. Theirmessages are mostly factual, with just a negligible part ofthem explicitly expressing strong sentiments about the com-munity’s topic. Nevertheless, they precede their peers inexpressing their feelings towards the topic in question, thusplaying a major role in shaping the dominant opinion ineach community. This explains the extremely high levelsof correlation they exhibit with the community’s aggregatesentiment. Their high levels of influence can be attributedto their specialized activity, as they are typically focused onfew, similar topics. Our large-scale experimental analysisover real-world data verified that these patterns apply par-ticularly to core groups of size k = 50 that are defined bythe Mentions influence criterion.

In the future, we plan to develop methods that automat-ically identify the community users that exert the highestinfluence among the members of a community. However,the core group — just like any other group of people —is a dynamic entity that evolves with the passage of time;new members are added, others are removed, while the rel-ative weight of its members fluctuates. In this context, wealso intend to examine automatic methods that dynamicallyidentify changes in the composition of the core group andupdate it appropriately.

AcknowledgementThis work has been supported by the SocIoS project andhas been partly funded by the European Commission’s 7thFramework Programme through theme ICT-2009.1.2: Inter-net of Services, Software and Virtualisation under contractno.257774.

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