The q-component static model : modeling social networks

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 $f\approx 0.2$.

5 pages, 6 figures

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• Scale-free networks with a large- to hypersmall-world transition
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• Evolving Network With Different Edges