Structural measures of similarity and complementarity in complex networks

TL;DR

This paper introduces new measures of structural similarity and complementarity in complex networks, linking motifs to these principles and demonstrating their effectiveness in social and biological contexts.

Contribution

It proposes two families of coefficients capturing similarity and complementarity, linking them to network motifs, and provides algorithms and a Python package for their computation.

Findings

Coefficients distinguish different social relations.

They measure structural diversity in PPI networks.

Complementarity explains some relations better than homophily.

Abstract

The principle of similarity, or homophily, is often used to explain patterns observed in complex networks such as transitivity and the abundance of triangles (3-cycles). However, many phenomena from division of labor to protein-protein interactions (PPI) are driven by complementarity (differences and synergy). Here we show that the principle of complementarity is linked to the abundance of quadrangles (4-cycles) and dense bipartite-like subgraphs. We link both principles to their characteristic motifs and introduce two families of coefficients of: (1) structural similarity, which generalize local clustering and closure coefficients and capture the full spectrum of similarity-driven structures; (2) structural complementarity, defined analogously but based on quadrangles instead of triangles. Using multiple social and biological networks, we demonstrate that the coefficients capture structural properties related to meaningful domain-specific phenomena. We show that they allow distinguishing between different kinds of social relations as well as measuring an increasing structural diversity of PPI networks across the tree of life. Our results indicate that some types of relations are better explained by complementarity than homophily, and may be useful for improving existing link prediction methods. We also introduce a Python package implementing efficient algorithms for calculating the proposed coefficients.