Structural complementarity and similarity: linking relational principles to network motifs

Abstract

Similarity is one of the most important relational principles shaping the structure of networks. It is linked to homophily, triadic closure and the abundance of triangles as its characterstic motif. However, many important phenomena, such as collaboration and division of labor, are driven rather by complementarity, or differences and synergy. The principle of complementarity attracted much less attention and in particular has not been operationalized in network terms. Here we address this problem and show that complementarity is linked to the abundance of quadrangles and the presence of dense bipartite-like subgraphs. Starting from very general geometric arguments we define two families of coefficients: (1) similarity coefficients generalizing the notions of local clustering and closure; (2) analogous complementarity coefficients based on quadrangles instead of triangles. We study their main properties and behavior in random graph models and demonstrate their theoretical validity and practical utility on a set of real-world social networks. We show that friendship relations are linked to increased levels of structural similarity and health advice to significantly higher complementarity.