  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.
