Assortativity and leadership emergence from anti-preferential attachment in heterogeneous networks

TL;DR

This paper introduces a novel generative model for heterogeneous networks that incorporates realistic assortativity by combining preferential and anti-preferential attachment, explaining the emergence of hubs in social networks.

Contribution

It presents the first model that generates networks with scale-free properties and tunable assortativity, capturing the evolution of social networks more accurately.

Findings

Empirical validation using Facebook data supports the model.

Anti-preferential attachment leads to the formation of high-degree hubs.

The model reproduces the degree-assortativity peak observed in real social networks.

Abstract

Many real-world networks exhibit degree-assortativity, with nodes of similar degree more likely to link to one another. Particularly in social networks, the contribution to the total assortativity varies with degree, featuring a distinctive peak slightly past the average degree. The way traditional models imprint assortativity on top of pre-defined topologies is via degree-preserving link permutations, which however destroy the particular graph's hierarchical traits of clustering. Here, we propose the first generative model which creates heterogeneous networks with scale-free-like properties and tunable realistic assortativity. In our approach, two distinct populations of nodes are added to an initial network seed: one (the followers) that abides by usual preferential rules, and one (the potential leaders) connecting via anti-preferential attachments, i.e. selecting lower degree nodes for their initial links. The latter nodes come to develop a higher average degree, and convert eventually into the final hubs. Examining the evolution of links in Facebook, we present empirical validation for the connection between the initial anti-preferential attachment and long term high degree. Thus, our work sheds new light on the structure and evolution of social networks.