Fast Graphlet Transform of Sparse Graphs

We introduce the computational problem of graphlet transform of a sparse large graph. Graphlets are fundamental topology elements of all graphs/networks. They can be used as coding elements for encoding graph-topological information at multiple granularity levels on a graph, and for making differentiation and connection across different graphs and networks. Network/graph analysis using multiple 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 facilitate or enable advanced network/graph analysis with graphlets, and to advance at the same time sparse graph theory, high-performance graph computation and broader applications.