2016/03/01 by R. P. Sreejith, Karthikeyan Mohanraj, Jürgen Jost +2 · 3 citations
Biochemistry, Genetics and Molecular Biology · Physics and Astronomy · #q-bio.MN #cond-mat.dis-nn #physics.soc-ph
paper · pdf · doi:10.1088/1742-5468/2016/06/063206
published as J. Stat. Mech. (2016) 063206 · 18 pages, 15 figures. Supplementary material available upon request from authors
arxiv created 2016/03/01 · arxiv updated 2016/06/23
We adapt Forman's discretization of Ricci curvature to the case of undirected networks, both weighted and unweighted, and investigate the measure in a variety of model and real-world networks. We find that most nodes and edges in model and real networks have a negative curvature. Furthermore, the distribution of Forman curvature of nodes and edges is narrow in random and small-world networks, while the distribution is broad in scale-free and real-world networks. In most networks, Forman curvature is found to display significant negative correlation with degree and centrality measures. However, Forman curvature is uncorrelated with clustering coefficient in most networks. Importantly, we find that both model and real networks are vulnerable to targeted deletion of nodes with highly negative Forman curvature. Our results suggest that Forman curvature can be employed to gain novel insights on the organization of complex networks.