Counting triangles in real-world networks using projections

Triangle counting is an important problem in graph mining. Two frequently used metrics in complex network analysis which require the count of triangles are the clustering coefficients and the transitivity ratio of the graph. Triangles have been used successfully in several real-world applications, such as detection of spamming activity, uncovering the hidden thematic structure of the web and link recommendation in online social networks. Furthermore, the count of triangles is a frequently used network statistic in exponential random graph models. However, counting the number of triangles in a graph is computationally expensive. In this paper, we propose the EigenTriangle and EigenTriangleLocal algorithms to estimate the number of triangles in a graph. The efficiency of our algorithms is based on the special spectral properties of real-world networks, which allow us to approximate accurately the number of triangles. We verify the efficacy of our method experimentally in almost 160 exper...

• Type: Journal
• Year: 2011
• Where: KAIS
• Authors: Charalampos E. Tsourakakis
• Keywords: Algorithm, KAIS 2011, Real-world Networks, Triangles