An Empirical Investigation on Important Subgraphs in Cooperation-Competition networks

Abstract

Subgraphs are very important for understanding structure and function of complex networks. Dyad and triad are the elementary subgraphs. We focus on the distribution of their act degree defined as the number of activities, events or organizations they join, which indicates the importance of the subgraphs. The empirical studies show that, in a lot of real world systems, the dyad or triad act degree distributions follow "shifted power law" (SPL), where {\alpha} and {\gamma} are constants. We defined a "heterogeneity index", H, to describe how it is uneven and analytically deduced the correlation between H and {\alpha} and {\gamma}. This manuscript, which shows the details of the empirical studies, serves as an online supplement of a paper submitted to a journal.