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MiS Preprint

Forman curvature for complex networks

R.P. Sreejith, Karthikeyan Mohanraj, Jürgen Jost, Emil Saucan and Areejit Samal


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.

Mar 2, 2016
Mar 3, 2016
MSC Codes:
51K10, 05C82
Forman curvature, complex networks

Related publications

2016 Repository Open Access
Remanan P. Sreejith, Karthikeyan Mohanraj, Jürgen Jost, Emil Saucan and Areejit Samal

Forman curvature for complex networks

In: Journal of statistical mechanics, 2016 (2016), p. 063206