Node similarity as a basic principle behind connectivity in complex networks

TL;DR

This paper investigates how node similarity influences connectivity in social networks, revealing that dense networks deviate from power-law distributions and are better explained by similarity-based models, which describe the transition from sparse to dense connectivity.

Contribution

It demonstrates that node similarity is a key factor behind network connectivity and provides a model that captures the transition from sparse to dense social networks.

Findings

Power-law distributions are limited to sparse networks.

Dense networks show divergence from power-law behavior.

Node similarity effectively models network density transitions.

Abstract

How are people linked in a highly connected society? Since in many networks a power-law (scale-free) node-degree distribution can be observed, power-law might be seen as a universal characteristics of networks. But this study of communication in the Flickr social online network reveals that power-law node-degree distributions are restricted to only sparsely connected networks. More densely connected networks, by contrast, show an increasing divergence from power-law. This work shows that this observation is consistent with the classic idea from social sciences that similarity is the driving factor behind communication in social networks. The strong relation between communication strength and node similarity could be confirmed by analyzing the Flickr network. It also is shown that node similarity as a network formation model can reproduce the characteristics of different network densities and hence can be used as a model for describing the topological transition from weakly to strongly connected societies.