A new form of assortativity in online social networks,☆☆

https://doi.org/10.1016/j.ijhcs.2015.03.006Get rights and content

Highlights

  • Introduction of two measures of membership overlap assortativity (MOA, for short).

  • Experimental observation in Facebook and Twitter of membership overlap assortativity.

  • MOA is source of privacy loss, helping the disclosure of implicit membership overlap.

  • MOA opens a future issue on how information flow crossing OSNs is structured.

Abstract

The term assortativity indicates the tendency, for a network node, to be directly connected to other nodes that are someway similar. In more technical terms, a given feature is assortative in a network if the probability that an arc exists between two nodes having this feature is greater than the probability that an arc exists between two generic nodes. The role of assortativity in real-world and online social networks has been largely investigated in the literature, in which, starting from degree assortativity, several forms of assortativity have been analyzed. When moving from a single-social-network to a multiple-social-network perspective, new specific traits can be studied, also under the assortativity magnifying glass. This is the case of membership overlap among networks (i.e., the fact that people belong to more online social networks) as expression of different traits of users׳ personality. In this paper, we deal with the above issue, by defining two different measures of membership overlap assortativity, called Loose and Constrained Inter-social-network Assortativity, respectively and by observing that in two of the most representative online social networks, namely Facebook and Twitter, membership overlap is assortative.

Introduction

In real-world social interactions, individuals tend to associate with similar ones, having common (social or demographic) characteristics, thus favoring homophilic relationships (Lazarsfeld and Merton, 1954, McPherson et al., 2001). Moreover, it may happen that individuals act similar to their social ties due to some form of mutual influence, often referred as contagion. Homophily and contagion, together with opportunity structures influencing social tie formation (e.g., spatial proximity, working in the same organization) and sociality mechanisms (unlike homophily, independent of the attributes of actors in the dyad) are the main reasons why a real-world social network exhibits assortative mixing (Ackland, 2013). Assortative mixing (often called assortativity) (Newman, 2002) is an empirical measure describing a positive correlation in the traits and personal attributes of people socially connected with each other, such as age, education, socio-economic status, physical appearance, and religion. In other words, considering for example socio-economic status, we say that it is assortative in a community if the probability that two people with similar socio-economic status belonging to this community are friends is higher than the probability that randomly selecting two people, they are friends.

While assortativity can be in general empirically observed and there are a number of reasonable ways to measure its level in social networks, it is more difficult, sometimes impossible by means of pure observational studies, to understand why people in a social network are assortatively mixing w.r.t. a given dimension (Shalizi and Thomas, 2011). Indeed, both opportunity structures and sociality mechanisms can mask the real level of homophily. Moreover, when assortativity is detected with respect to a changeable attribute or cultural preference, it becomes very hard to understand whether this characteristic is influencing friendship formation (following the homophilic rule encoded into the old adage “birds of a feather flock together”) or, vice versa, it is friendship that influences attitudes and preferences (as effect of social contagion, possibly restricted to the case of imitation).

Despite the difficulty of explaining the exact underlying process, the empirical observation of assortative mixing of a social network has been considered of remarkable importance since many years, with strong interest by sociologists, as it represents the fundamental initial step to understand the phenomenon of friendship formation and social influence in a community. In recent years, the rapid growth of online social networks has reinforced interest in assortativity, moving the center of gravity towards computer science, still keeping the role of sociological aspects always crucial. Moreover, online social networks, with the abundance of embedded information about people, even related to their sentimental state and physical health (Shirazi et al., 2013), are huge living laboratories for studying assortativity. On the other hand, it is not obvious whether assortative mixing, especially that of psychological states (Bollen et al., 2011), takes place also in situations where social ties are not mediated by physical contacts but only by online networking services. Finally, online social networks introduce new specific characteristics (e.g., Likes and reciprocity) which can be analyzed under the assortativity magnifying glass, to improve our knowledge about how people interpret and metabolize social network tools and the psycho-sociological implications.

For all these reasons, studying for which properties online social networks exhibit assortative mixing is an important issue in social network analysis. As a matter of fact, degree–degree (Newman, 2002), BC–BC (where BC stands for betweenness centrality) (Goh et al., 2003), and happiness assortativity (Bliss et al., 2012, Bollen et al., 2011) are types of assortativity already studied in the context of online social networks. Data extracted from an online social network, such as Facebook, Twitter, and LiveJournal, are typically used to characterize it in terms of degree of assortativity (even negative, talking in this case about disassortativity) with respect to a given trait, but also to infer general rules concerning social influence in online social networks.

However, to the best of our knowledge, no observation aimed at studying assortative mixing with respect to multi-social-network traits has been provided so far. Indeed, a single user can join multiple social networks, leading to have membership overlap among different social networks. Thus, membership overlap occurs whenever a user belongs to different online social networks. This feature plays an important role in online communities, as it allows the expression of different traits of users׳ personality (sometimes almost different identities), also enabling, as side effect, the passage of information from one social network to another. Moreover, a recent study has shown that higher levels of membership overlap are positively associated with higher survival rates of online communities (Zhu et al., 2014).

From all the above observations, it clearly follows that studying whether online social networks exhibit assortative mixing with respect to membership overlap is a new, challenging, and important problem. In more technical words, the problem to address is to understand whether two users of a given online social network S are friends in S with higher probability than the generic case if they both belong to other online social networks.

In the present work, we study this issue, concerning explicit membership overlap. Explicit membership overlap occurs when a user shows in the home page of his account in a social network the link to his account in another social network. We introduce two different definitions of assortativity (called Loose and Constrained Inter-social-network Assortativity) and measure their value in Facebook and Twitter, two of the most representative online social networks (Gjoka et al., 2010, Patriquin, 2007, Vasalou et al., 2010). The results obtained in this paper show that both real-life social networks exhibit assortativity according to the Loose and Constrained notions.

A relationship between explicit membership overlap assortativity and implicit membership overlap (i.e., when membership overlap is not declared by the user) is also studied, showing that our assortativity can be related to a form of social behavior which, as side effect, may reduce privacy consisting in keeping separated two accounts in case of implicit membership overlap.

The plan of this paper is as follows: Section 2 presents related literature about assortativity. The reference scenario is illustrated in Section 3. Section 4 presents our assortativity measures. Section 5 describes the experimental campaign carried out on real social networks both to validate the new assortativity measures and to compute the assortativity/disassortativity degree of social networks. Moreover, the interpretation of the results is also discussed. Section 6 illustrates an important implication of membership overlap assortativity in the context of privacy. Finally, in Section 7, we draw our conclusions.

Section snippets

Related work

The concepts of assortativity and degree assortativity have been introduced in the renowned paper of Newman (Newman, 2002). Here, the author defines a measure of connection assortativity for networks and shows that real social networks are often assortative. A further important study concerning social network assortativity has been proposed in Newman and Park (2003), in which the relation between clustering and assortativity in the communities composing a social network is investigated. In the

Reference scenario

We refer to a (real-life) scenario in which users operate in a multi-social-network environment (Okada et al., 2005, Buccafurri et al., 2014a, Zhu et al., 2014), thus joining multiple social networks. As usual in social network analysis, we model social networks as graphs. To capture the interaction among nodes belonging to different social networks, a special type of edge, namely me edge, which interconnects different social networks, is introduced. A me edge from a to b indicates that a and b

Membership overlap assortativity

In this section, we define how to measure explicit membership overlap assortativity. Recall that explicit membership overlap occurs when a user belonging to a social network S1 declares to have an account also on a second social network S2. To do this, the user first creates an HTML link to the URL of the account on S2, and publishes this link in the home page of his account in S1. According to the model introduced in the previous section, a user with explicit membership overlap is an i-bridge

Experiments

The aim of this section is to test the proposed assortativity measures on real-life datasets. We studied membership overlap assortativity on Facebook and Twitter, which are the online social networks with the highest number of users and have attracted the attention of many researchers (see, for instance, Gjoka et al., 2010, Patriquin, 2007, Kwak et al., 2010). According to our theoretical framework, we consider Facebook and Twitter as part of a Multi-Social-Network System (MSNS) composed of 9

A privacy threat related to membership overlap assortativity

In this section, we show that membership overlap assortativity can be used as a form of correlation to improve, as done in statistical attacks, the effectiveness of those techniques able to discover that two accounts belonging to different social networks are associated with the same user. Indeed, for disparate reasons (often related to privacy concerns Lee et al., 2013), users do not always make their role of i-bridge explicit by specifying their me edges. In this case, we talk about implicit

Conclusion

In this paper, we have observed that online social networks exhibit assortativity with respect to explicit membership overlap. To do this, we have provided two measures of assortativity, which captures two different traits with respect to which assortative mixing is studied. According to the approach commonly used in network theory, based on the usage of the null model as a term of comparison, we have verified that both Facebook and Twitter are assortative w.r.t. these two measures. This result

Acknowledgments

This work has been partially supported by the Program “Programma Operativo Nazionale Ricerca e Competitività” 2007–2013, Distretto Tecnologico CyberSecurity and project BA2Know (Business Analytics to Know) PON03PE_00001_1, in “Laboratorio in Rete di Service Innovation”, both funded by the Italian Ministry of Education, University and Research.

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    ☆☆

    A preliminary version of this paper appears in the Proceedings of the International Conference on Social Computing and Its Applications (SCA 2013), Karlsruhe, Germany, 2013, IEEE, under the title “Internetworking Assortativity in Facebook” (Buccafurri et al., 2013b).

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