Measuring similarity- and complementarity-driven relations in networks

Szymon Talaga, Andrzej Nowak

Structure of real-world networks is often shaped by similarity, meaning that two nodes are more likely to be linked if they are alike. However, some processes such as division of labor are driven rather by complementarity or differences and synergies. While it is well-known that similarity is associated with high abundance of triangles (3-cycles), there is no such result for complementarity. We argue that quadrangles (4-cycles) are the characteristic motif of complementarity-driven relations. Starting from very general geometric arguments we introduce two families of coefficients measuring the extent to which relations are shaped by similarity or complementarity. We study their main properties and show, through several case studies, that they can be used to distinguish between different kinds of social relations or networks from different domains as well as detect groups of similar or complementary nodes. Our results suggest that both similarity and complementarity are important processes shaping real-world networks.

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