A systematic association of subgraph counts over a network

Abstract: We associate all small subgraph counting problems with a systematic graph encoding/representation system which makes a coherent use of graphlet structures. The system can serve as a unified foundation for studying and connecting many important graph problems in theory and practice. We describe topological relations among graphlets (graph elements) in rigorous mathematics language and from the perspective of graph encoding. We uncover, characterize and utilize algebraic and numerical relations in graphlet counts/frequencies. We present a novel algorithm for efficiently counting small subgraphs as a practical product of our theoretical findings.