On Randomness Measures for Social Networks

Social networks tend to contain some amount of randomness and some amount of non-randomness. The amount of randomness versus non-randomness affects the properties of a social network. In this paper, we theoretically analyze graph randomness and present a framework which provides a series of non-randomness measures at levels of edge, node, and the overall graph. We show that graph nonrandomness can be obtained mathematically from the spectra of the adjacency matrix of the network. We also derive the upper bound and lower bound of non-randomness value of the overall graph. We conduct both theoretical and empirical studies in spectral geometries of social networks and show our proposed non-randomness measures can better characterize and capture graph randomness than previous measures.