Forman curvature for complex networks

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

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Submission date: 02. Mar. 2016
Pages: 20
published in: Journal of statistical mechanics, 2016 (2016), art-no. 063206 
DOI number (of the published article): 10.1088/1742-5468/2016/06/063206
Bibtex
MSC-Numbers: 51K10, 05C82
Keywords and phrases: Forman curvature, complex networks
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Abstract:
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 net- works. 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 dele- tion 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.