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How can we accurately estimate local triangles for all nodes in simple andmultigraph streams? Local triangle counting in a graph stream is one of themost fundamental tasks in graph mining with important applications includinganomaly detection and social network analysis. Although there have been severallocal triangle counting methods in a graph stream, their estimation has a largevariance which results in low accuracy, and they do not consider multigraphstreams which have duplicate edges. In this paper, we propose FURL, an accuratelocal triangle counting method for simple and multigraph streams. FURL improvesthe accuracy by reducing a variance through biased estimation and handlesduplicate edges for multigraph streams. Also, FURL handles a stream of any sizeby using a fixed amount of memory. Experimental results show that FURLoutperforms the state-of-the-art method in accuracy and performs well inmultigraph streams. In addition, we report interesting patterns discovered fromreal graphs by FURL, which include unusual local structures in a usercommunication network and a core-periphery structure in the Web.

FURL: Fixed-memory and Uncertainty Reducing Local Triangle Counting for Graph Streams