Intersection Representation of Big Data Networks and Triangle Counting

Triangles are an essential part of network analysis, representing metrics such as transitivity ratio and clustering coefficient Because of its diverse applications, enumeration and counting of triangles in large networks has been extensively studied, and continues to draw much interest from many different fields. This has only increased with the introduction of approximate counting, parallel and distributed implementations, and restricted and streaming data access scenarios. We propose a compact and efficient representation of network data based on the intersection of edge labels, and use sparse matrix data structures for its computer implementation. We then present a scalable algorithm that uses this structure to count triangles. On a set of large (the largest with more that 3.6 billion edges) real-world and synthetic networks, our algorithm performs significantly better than the reference implementation miniTri [1].