Transitivity and degree assortativity explained: The bipartite structure of social networks

TL;DR

This paper explains why social networks exhibit high transitivity and degree assortativity by analyzing their underlying bipartite structures and how these features emerge from the degree distributions and cycle patterns within bipartite networks.

Contribution

It demonstrates that the structural features of social networks can be understood through their bipartite projections, linking degree distributions and cycle presence to transitivity and assortativity.

Findings

Bipartite networks can be projected to explain social network features.

Skewed degree distributions in bipartite networks lead to high transitivity.

Presence of small cycles influences network assortativity.

Abstract

Dynamical processes, such as the diffusion of knowledge, opinions, pathogens, "fake news", innovation, and others, are highly dependent on the structure of the social network on which they occur. However, questions on why most social networks present some particular structural features, namely high levels of transitivity and degree assortativity, when compared to other types of networks remain open. First, we argue that every one-mode network can be regarded as a projection of a bipartite network, and show that this is the case using two simple examples solved with the generating functions formalism. Second, using synthetic and empirical data, we reveal how the combination of the degree distribution of both sets of nodes of the bipartite network --- together with the presence of cycles of length four and six --- explains the observed levels of transitivity and degree assortativity in the one-mode projected network. Bipartite networks with top node degrees that display a more right-skewed distribution than the bottom nodes result in highly transitive and degree assortative projections, especially if a large number of small cycles are present in the bipartite structure.