Algorithms for the Truss Maintenance Problem on Edge-Weighted Graphs

The k-truss was proposed by Jonathan Cohen in 2008, and it is a widely used as index in graph analysis for cohesive subgraph mining. There are two basic problems in this area. One is the truss decomposition problem, which is to compute the truss number of every edge; the other is the truss maintenance problem, which is to update the truss numbers of the affected edges in a dynamic graph while avoiding the truss number recomputation of all edges. However, few results are known on edge-weighted graphs. In this paper, we focus on the truss maintenance problem on edge-weighted graphs. Firstly, we propose a basic algorithm for the truss decomposition problem on edge-weighted graphs. Then we propose two indices, weighted growth potential support (WGPS) and weighted remaining potential support (WRPS), to help find the edges with potential changes on their truss numbers. Finally, we propose algorithms for the truss maintenance problem on edge-weighted graphs.