CCOM algorithm dramatically improves graph curvature accuracy on large networks

Ollivier-Ricci curvature measures edge importance in graphs by comparing distances when transporting mass between neighbor sets, with applications in community detection, network analysis, and deep neural network interpretability. However, exact computation is computationally expensive and error-prone on large scale-free graphs, limiting practical use. In a new arXiv paper, Zexian Zhou and Bo Jiao introduce Curvature in Cycle Overlap Mode (CCOM), which redefines the optimal transport principle by focusing on cycles of length 3, 4, and 5 that include the target edge. This cycle-based approach minimizes transport distance more efficiently than traditional methods, and the authors pair it with a greedy pruning algorithm to further reduce computational overhead.

The authors theoretically and experimentally demonstrate that CCOM significantly improves curvature accuracy on real-world networks while keeping time consumption low. In community detection tasks using a curvature-based framework, CCOM outperforms baseline approximation approaches across multiple large scale-free graphs. The paper (26 pages, 10 figures) is available on arXiv (arXiv:2606.03317) and targets the Social and Information Networks community. This work makes curvature-based graph analysis practical for larger datasets, potentially advancing fields like social network analysis, biological network modeling, and efficient training of graph neural networks.