Truly Scalable K-Truss and Max-Truss Algorithms for Community Detection in Graphs

The notion of k -truss has been introduced a decade ago in social network analysis and security for community detection, as a form of cohesive subgraphs less stringent than a clique (set of pairwise linked nodes), and more selective than a k-core (induced subgraph with minimum degree k ). A k -truss is an inclusion-maximal subgraph H in which each edge belongs to at least k-2 triangles inside H . The truss decomposition establishes, for each edge e , the maximum k for which e belongs to a k -truss. Analogously to the largest clique and to the maximum k -core, the strongest community for k -truss is the max-truss, which corresponds to the k -truss having the maximum k . Even though the computation of truss decomposition and of the max-truss takes polynomial time, on a large scale, it suffers from handling a potentially cubic number of wedges. In this paper, we provide a new algorithm FMT, which advances the state of the art on different sides: lower execution time, lower memory usage, and no need for expensive hardware. We compare FMT experimentally with the most recent state-of-the-art algorithms on a set of large real-world and synthetic networks with over a billion edges. The massive improvement allows FMT to compute the max-truss of networks of tens of billions of edges on a single standard server machine.