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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
67/2016

Systematic evaluation of a new combinatorial curvature for complex networks

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

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.

Received:
Oct 7, 2016
Published:
Oct 11, 2016
MSC Codes:
05C82, 05C7
Keywords:
complex networks, Edge-based measures, Forman curvature

Related publications

inJournal
2017 Repository Open Access
Remanan P. Sreejith, Jürgen Jost, Emil Saucan and Areejit Samal

Systematic evaluation of a new combinatorial curvature for complex networks

In: Chaos, solitons and fractals, 101 (2017), pp. 50-67