Abstract
The dynamics of social networks is a complex process, as there are many factors which contribute to the formation and evolution of social links. While certain real-world properties are captured by the degree-driven preferential attachment model, it still cannot fully explain social network dynamics. Indeed, important properties such as dynamic community formation, link weight evolution, or degree saturation cannot be completely and simultaneously described by state of the art models. In this paper, we explore the distribution of social network parameters and centralities and argue that node degree is not the main attractor of new social links. Consequently, as node betweenness proves to be paramount to attracting new links – as well as strengthening existing links –, we propose the new Weighted Betweenness Preferential Attachment (WBPA) model, which renders quantitatively robust results on realistic network metrics. Moreover, we support our WBPA model with a socio-psychological interpretation, that offers a deeper understanding of the mechanics behind social network dynamics.
Highlights
People have weighted relationships, i.e., not all ties are important: an average person knows roughly 350 persons, can actively befriend no more than 150 people (Dunbar’s number)[4], and has only a few very strong social ties[6]
We investigate the distributions of node betweenness on a variety of social network datasets: Facebook users (590 nodes), Google Plus users (638 nodes), weighted co-authorships in network science (1589 nodes), weighted online social network (1899 nodes), weighted Bitcoin web of trust (5881 nodes), unweighted Wikipedia votes (7115 nodes), weighted scientific collaboration network (7343 nodes), unweighted Condensed Matter collaborations (23 K nodes), weighted MathOverflow user interactions (25 K nodes), unweighted High-Energy Physics citation network (HEP) citations (28 K nodes), POK social network (29 K nodes), unweighted email interaction (37 K nodes), IMDB actors (48 K nodes), Brightkite Online social network (OSN) users (58 K nodes), Facebook - New Orleans (64 K nodes), respectively Epinions (76 K nodes), Slashdot (82 K nodes) and Timik (364 K nodes) on-line platforms
We propose the betweenness preferential attachment model (BPA) and conjecture that–for social networks–it is more realistic than the degree preferential attachment (DPA) model
Summary
People have weighted relationships, i.e., not all ties are important: an average person knows roughly 350 persons, can actively befriend no more than 150 people (Dunbar’s number)[4], and has only a few very strong social ties (links)[6]. E.g., static-geographic[19] and cellular[20] models All these models are still not accurate enough when compared against real-world social networks. Our empirical findings align well with previous research in some particular cases[11,21] Such empirical pieces of evidence suggest that, for social networks, the node degree is not the main driver of preferential attachment; other centralities may be better attractors of social ties. As the main theoretical contribution, we introduce the new Weighted Betweenness Preferential Attachment (WBPA) model, which is a simple yet fundamental mechanism to replicate real-world social networks topologies more accurately than other state-of-the-art models. We show that the WBPA model is the first social network model that is able to replicate community structure while it simultaneously: (i) explains how link weights evolve, and (ii) reproduces the natural saturation of degree in hub nodes
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