Ollivier-Ricci curvature in cycle overlap mode

Abstract: Ollivier-Ricci curvature of an edge (x,y) is defined by comparing the distance taken to transport from neighbors of x to neighbors of y. It is a structural measure that has been studied in many fields such as community detection and deep neural networks. However, high computational complexity or error limits its application in large scale-free graphs. This paper proposes an optimal transport principle to minimize the distance by 3,4,5-cycles that include the edge (x,y), and designs a curvature calculation approach named Curvature in Cycle Overlap Mode (CCOM). In this approach, a greedy and pruning algorithm is proposed to approximate the optimal transport principle. We theoretically and experimentally verified that our approach CCOM can significantly improve the accuracy of the curvature on real-world networks with low time consumption. In addition, we compared CCOM with baseline approximation approaches in community detection tasks using the same curvature-based framework, and experimentally confirmed the effectiveness of CCOM on large scale-free graphs.