A Unified Framework to Estimate Global and Local Graphlet Counts for Streaming Graphs

Abstract

Counting small connected subgraph patterns called graphlets is emerging as a powerful tool for exploring topological structure of networks and for analysis of roles of individual nodes. Graphlets have numerous applications ranging from biology to network science. Computing graphlet counts for "dynamic graphs" is highly challenging due to the streaming nature of the input, sheer size of the graphs, and superlinear time complexity of the problem. Few practical results are known under the massive streaming graphs setting. In this work, we propose a "unified framework" to estimate the graphlet counts of the whole graph as well as the graphlet counts of individual nodes under the streaming graph setting. Our framework subsumes previous methods and provides more flexible and accurate estimation of the graphlet counts. We propose a general unbiased estimator which can be applied to any k-node graphlets. Furthermore, efficient implementation is provided for the 3, 4-node graphlets. We perform detailed empirical study on real-world graphs, and show that our framework produces estimation of graphlet count for streaming graphs with 1.7 to 170.8 times smaller error compared with other state-of-the-art methods. Our framework also achieves high accuracy on the estimation of graphlets for each individual node which previous works could not achieve.