Systematic evaluation of a new combinatorial curvature for complex networks. (August 2017)

• Record Type: Journal Article
• Authors: Sreejith, R.P.; Jost, Jürgen; Saucan, Emil; Samal, Areejit
• Is Part Of: Chaos, solitons and fractals. Volume 101(2017)
• Page Start: 50
• Page End: 67
• Publication Date: 2017-08
• Subjects: Complex networks -- Edge-based measures -- Forman curvature; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2017.05.021
• Languages: English
• ISSNs: 0960-0779

Abstract

Highlights: Forman curvature is an edge-based measure of characterization of complex weighted networks. Comparison of Forman curvature with other edge-based measures for complex networks. Evaluation of the two possible choices of node weights in the definition of the Forman curvature of edges. Evaluation of the two possible definitions of the Forman curvature of nodes. Abstract: We have recently introduced Forman's discretization of Ricci curvature to the realm of complex networks. Forman curvature is an edge-based measure whose mathematical definition elegantly encapsulates the weights of nodes and edges in a complex network. In this contribution, we perform a comparative analysis of Forman curvature with other edge-based measures such as edge betweenness, embeddedness and dispersion in diverse model and real networks. We find that Forman curvature in comparison to embeddedness or dispersion is a better indicator of the importance of an edge for the large-scale connectivity of complex networks. Based on the definition of the Forman curvature of edges, there are two natural ways to define the Forman curvature of nodes in a network. In this contribution, we also examine these two possible definitions of Forman curvature of nodes in diverse model and real networks. Based on our empirical analysis, we find that in practice the unnormalized definition of the Forman curvature of nodes with the choice of combinatorial node weights is a better indicator of the importance of nodes in complex networks.