%0 Generic %1 roy2019formanricci %A Roy, Indrava %A Vijayaraghavan, Sudharsan %A Ramaia, Sarath Jyotsna %A Samal, Areejit %D 2019 %K TDA network_analysis topology %T Forman-Ricci curvature and Persistent homology of unweighted complex networks %U http://arxiv.org/abs/1912.11337 %X We present the application of topological data analysis (TDA) to study unweighted complex networks via their persistent homology. By endowing appropriate weights that capture the inherent topological characteristics of such a network, we convert an unweighted network into a weighted one. Standard TDA tools are then used to compute their persistent homology. To this end, we use two main quantifiers: a local measure based on Forman's discretized version of Ricci curvature, and a global measure based on edge betweenness centrality. We have employed these methods to study various model and real-world networks. Our results show that persistent homology can be used to distinguish between model and real networks with different topological properties.

@preprint{roy2019formanricci, abstract = {We present the application of topological data analysis (TDA) to study unweighted complex networks via their persistent homology. By endowing appropriate weights that capture the inherent topological characteristics of such a network, we convert an unweighted network into a weighted one. Standard TDA tools are then used to compute their persistent homology. To this end, we use two main quantifiers: a local measure based on Forman's discretized version of Ricci curvature, and a global measure based on edge betweenness centrality. We have employed these methods to study various model and real-world networks. Our results show that persistent homology can be used to distinguish between model and real networks with different topological properties.}, added-at = {2019-12-26T06:25:24.000+0100}, author = {Roy, Indrava and Vijayaraghavan, Sudharsan and Ramaia, Sarath Jyotsna and Samal, Areejit}, biburl = {https://www.bibsonomy.org/bibtex/28befe08958994856ae73dfdc4f468751/j.c.m.janssen}, description = {Forman-Ricci curvature and Persistent homology of unweighted complex networks}, interhash = {701f0a903946faa468aa498090d7a0a2}, intrahash = {8befe08958994856ae73dfdc4f468751}, keywords = {TDA network_analysis topology}, note = {cite arxiv:1912.11337Comment: 25 pages, 6 Main figures, 10 SI figures}, timestamp = {2019-12-26T06:25:24.000+0100}, title = {Forman-Ricci curvature and Persistent homology of unweighted complex networks}, url = {http://arxiv.org/abs/1912.11337}, year = 2019 }