Social media allow for an unprecedented amount of interaction between people online. A fundamental aspect of human social behavior, however, is the tendency of people to associate themselves with like-minded individuals, forming homogeneous social circles both online and offline. In this work, we apply a new model that allows us to distinguish between social ties of varying strength, and to observe evidence of homophily with regards to politics, music, health, residential sector & year in college, within the online and offline social network of 74 college students. We present a multiplex network approach to social tie strength, here applied to mobile communication data - calls, text messages, and co-location, allowing us to dimensionally identify relationships by considering the number of communication channels utilized between students. We find that strong social ties are characterized by maximal use of communication channels, while weak ties by minimal use. We are able to identify 75 of close friendships, 90 of weaker ties, and 90 of Facebook friendships as compared to reported ground truth. We then show that stronger ties exhibit greater profile similarity than weaker ones. Apart from high homogeneity in social circles with respect to political and health aspects, we observe strong homophily driven by music, residential sector and year in college. Despite Facebook friendship being highly dependent on residence and year, exposure to less homogeneous content can be found in the online rather than the offline social circles of students, most notably in political and music aspects.
Multiplexity has been explored in a wide range of systems from global air-transportation @cite_22 to massive online multiplayer games @cite_10 . A comprehensive review of multiplex (multilayer) network models can be found in @cite_2 . While multiplexity in most systems creates additional complexity such as layer interdependence, in social networks multiplexity can be used to define the strength of a tie.
@cite_10 @cite_22 @cite_2
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Many real-world complex systems consist of a set of elementary units connected by relationships of different kinds. All such systems are better described in terms of multiplex networks, where the links at each layer represent a different type of interaction between the same set of nodes, rather than in terms of (single-layer) networks. In this paper we present a general framework to describe and study multiplex networks, whose links are either unweighted or weighted. In particular we propose a series of measures to characterize the multiplexicity of the systems in terms of: i) basic node and link properties such as the node degree, and the edge overlap and reinforcement, ii) local properties such as the clustering coefficient and the transitivity, iii) global properties related to the navigability of the multiplex across the different layers. The measures we introduce are validated on a genuine multiplex data set of Indonesian terrorists, where information among 78 individuals are recorded with respect to mutual trust, common operations, exchanged communications and business relationships. There is growing interest in multiplex networks where individual nodes take part in several layers of networks simultaneously. This is the case for example in social networks where each individual node has different kind of social ties or transportation systems where each location is connected to another location by different types of transport. Many of these multiplex are characterized by a significant overlap of the links in different layers. In this paper we introduce a statistical mechanics framework to describe multiplex ensembles. A multiplex is a system formed by N nodes and M layers of interactions where each node belongs to the M layers at the same time. Each layer @math is formed by a network @math . Here we introduce the concept of correlated multiplex ensembles in which the existence of a link in one layer is correlated with the existence of a link in another layer. This implies that a typical multiplex of the ensemble can have a significant overlap of the links in the different layers. Moreover we characterize microcanonical and canonical multiplex ensembles satisfying respectively hard and soft constraints and we discuss how to construct multiplex in these ensembles. Finally we provide the expression for the entropy of these ensembles that can be useful to address different inference problems involving multiplexes. We study the dynamics of the European Air Transport Network by using a multiplex network formalism. We will consider the set of flights of each airline as an interdependent network and we analyze the resilience of the system against random flight failures in the passenger’s rescheduling problem. A comparison between the single-plex approach and the corresponding multiplex one is presented illustrating that the multiplexity strongly affects the robustness of the European Air Network. Online social systems are multiplex in nature as multiple links may exist between the same two users across different social networks. In this work, we introduce a framework for studying links and interactions between users beyond the individual social network. Exploring the cross-section of two popular online platforms - Twitter and location-based social network Foursquare - we represent the two together as a composite multilayer online social network. Through this paradigm we study the interactions of pairs of users differentiating between those with links on one or both networks. We find that users with multiplex links, who are connected on both networks, interact more and have greater neighbourhood overlap on both platforms, in comparison with pairs who are connected on just one of the social networks. In particular, the most frequented locations of users are considerably closer, and similarity is considerably greater among multiplex links. We present a number of structural and interaction features, such as the multilayer Adamic Adar coefficient, which are based on the extension of the concept of the node neighbourhood beyond the single network. Our evaluation, which aims to shed light on the implications of multiplexity for the link generation process, shows that multilayer features, constructed from properties across social networks, perform better than their single network counterparts in predicting links across networks. We propose that combining information from multiple networks in a multilayer configuration can provide new insights into user interactions on online social networks, and can significantly improve link prediction overall with valuable applications to social bootstrapping and friend recommendations.