Fast Graphlet Transform of Sparse Graphs

We introduce the computational problem of graphlet transform of a sparse graph. Graphlets are fundamental topology elements of all graphs/networks. They can be used as coding elements to encode graph-topological information at multiple granularity levels, for classifying vertices on the same graph/network, as well as, for making differentiation or connection across different networks. Network/graph analysis using graphlets has growing applications. We recognize the universality and increased encoding capacity in using multiple graphlets, we address the arising computational complexity issues, and we present a fast method for exact graphlet transform. The fast graphlet transform establishes a few remarkable records at once in high computational efficiency, low memory consumption, and ready translation to high-performance program and implementation. It is intended to enable and advance network/graph analysis with graphlets, and to introduce the relatively new analysis apparatus to graph theory, high-performance graph computation, and broader applications.