Topology of Online Social Networks

Abstract

The study of complex networks is a dominant 26 trend in recent research that transcends domain 27 boundaries. The pervasiveness of networked 28 systems in biology, technology, and society has 29 led to a recent surge of interest in uncovering the 30 organizing principles that govern the topology 31 and the dynamics of various complex networks 32 (Park and Barabasi 2007). Indeed, complex 33 networks research can be conceptualized as 34 lying at the intersection between graph theory 35 and statistical mechanics, which endows it with 36 a truly multidisciplinary nature (Costa et al. 37 2007). In particular, many social systems can 38 be modelled as complex networks. These include 39 online social media, collaborations of scientists, 40 interconnected groups of corporations and banks 41 with shareholding links between them, ecological 42 systems of species, communities of people who 43 are subject to spread of infection, and operational 44 hierarchies in defense organizations, among 45 others. It has been shown that many of these 46 networks from various domains can exhibit 47 surprisingly similar underlying structures. For 48 example, most social networks are shown to 49 have the “scale-free” structure (Dorogovtsev and 50 Mendes 2003; Piraveenan et al. 2012b, 2007, 51 2008, 2010), where the topological structure 52 is largely independent of scale, and many 53 also display the “small-world” property, where 54 the average diameter of the network remains 55 largely independent of the size of the network(Albert and Barabasi 2002; Milgram 1967). 58 A number of structural properties of these 59 networks such as modularity, topological 60 robustness, mixing patterns, network diameter, 61 and clustering have been analyzed in detail. 62 Furthermore, it has been explained that many 63 of these structural features are closely related to 64 the functions the networks, or subnetworks and 65 motifs contained therein, are intended to perform 66 (Dorogovtsev and Mendes 2003). Therefore, 67 many topological and behavioral patterns of 68 social networks can be studied generically across 69 domains.