SNOD: a fast sampling method of exploring node orbit degrees for large graphs

Exploring small connected and induced subgraph patterns (CIS patterns, or graphlets) has recently attracted considerable attention. Despite recent efforts on computing how frequent a graphlet appears in a large graph (i.e., the total number of CISes isomorphic to the graphlet), little effort has been made to characterize a node’s graphlet orbit degree, i.e., the number of CISes isomorphic to the graphlet that touch the node at a particular orbit, which is an important fine-grained metric for analyzing complex networks such as learning functions/roles of nodes in social and biological networks. Like global graphlet counting, it is computationally intensive to compute node orbit degrees for a large graph. Furthermore, previous methods of computing global graphlet counts are not suited to solve this problem. In this paper, we propose a novel sampling method SNOD to efficiently estimate node orbit degrees for large-scale graphs and quantify the error of our estimates. To the best of our knowledge, we are the first to study this problem and give a fast scalable solution. We conduct experiments on a variety of real-world datasets and demonstrate that our method SNOD is several orders of magnitude faster than state-of-the-art enumeration methods for accurately estimating node orbit degrees for graphs with millions of edges.