Structural measures of similarity and complementarity in complex networks
arXiv:2201.03664 · doi:10.1038/s41598-022-20710-w
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.
Authors' copy of the published version
References in corpus (6)
- The clustering coefficient and community structure of bipartite networks
- On network bipartivity
- Unbiased sampling of network ensembles
- Fast and scalable likelihood maximization for Exponential Random Graph Models with local constraints
- Extracting Complements and Substitutes from Sales Data: A Network Perspective
- Functional structure in production networks