The q-component static model : modeling social networks

TL;DR

This paper introduces a q-component static model for social networks, capturing key features like skewed degree distribution, small diameter, and high assortativity, aligning well with real social network properties.

Contribution

It generalizes the static model by incorporating multiple components and a mixed linking process, providing a more realistic social network modeling framework.

Findings

Degree distribution is highly skewed.

Network diameter remains small.

High positive assortativity coefficient observed.

Abstract

We generalize the static model by assigning a q-component weight on each vertex. We first choose a component $(\mu)$ among the q components at random and a pair of vertices is linked with a color $\mu$ according to their weights of the component $(\mu)$ as in the static model. A (1-f) fraction of the entire edges is connected following this way. The remaining fraction f is added with (q+1)-th color as in the static model but using the maximum weights among the q components each individual has. This model is motivated by social networks. It exhibits similar topological features to real social networks in that: (i) the degree distribution has a highly skewed form, (ii) the diameter is as small as and (iii) the assortativity coefficient r is as positive and large as those in real social networks with r reaching a maximum around $f \approx 0.2$.