Assortativity and leadership emerge from anti-preferential attachment in heterogeneous networks.

I Sendiña-Nadal,S Havlin,S Boccaletti,M M Danziger,Z Wang

doi:10.1038/srep21297

I Sendiña-Nadal, S Havlin + Show 3 more

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Real-world networks have distinct topologies, with marked deviations from purely random networks. Many of them exhibit degree-assortativity, with nodes of similar degree more likely to link to one another. Though microscopic mechanisms have been suggested for the emergence of other topological features, assortativity has proven elusive. Assortativity can be artificially implanted in a network via degree-preserving link permutations, however this destroys the graph’s hierarchical clustering and does not correspond to any microscopic mechanism. Here, we propose the first generative model which creates heterogeneous networks with scale-free-like properties in degree and clustering distributions and tunable realistic assortativity. Two distinct populations of nodes are incrementally added to an initial network by selecting a subgraph to connect to at random. One population (the followers) follows preferential attachment, while the other population (the potential leaders) connects via anti-preferential attachment: they link to lower degree nodes when added to the network. By selecting the lower degree nodes, the potential leader nodes maintain high visibility during the growth process, eventually growing into hubs. The evolution of links in Facebook empirically validates the connection between the initial anti-preferential attachment and long term high degree. In this way, our work sheds new light on the structure and evolution of social networks.

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IntroductionStatic SF network models[19] have been proposed with controlled assortativity[20,21], and growing
SF networks have been studied in the context of generative models, and simple rules relating to the formation of new links have been shown to lead to power-law degree distributions with non-hierarchical[10,11] and hierarchical[12,13,14,15,16,17,18] traits
On the one hand, generating a graph with an ad-hoc imprinted SF distribution (Fig. 1c) and rewiring connections does not yield the observed pattern of local assortativity, on the other hand, even starting from a configuration model (CM) retaining the original degree distribution[19], this procedure is only able to reproduce the real assortativity pattern at the expense of destroying the other significant features, such as the hierarchical inherent structure of clustering (Fig. 1d and its bottom-right inset)

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Introduction

Static SF network models[19] have been proposed with controlled assortativity[20,21], and growing. As it reflects a basic birds of a feather flock together property, it is not surprising that it is so ubiquitous. Many RWNs have a pronounced local maximum in rk located near (but above) the average degree k. In social networks such a feature even appears to be generic, while in technological and biological networks the maximum is less pronounced or www.nature.com/scientificreports/.

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