A Review of Two Network Curvature Measures

Tanima Chatterjee (), Bhaskar DasGupta () and Réka Albert ()
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Tanima Chatterjee: University of Illinois at Chicago
Bhaskar DasGupta: University of Illinois at Chicago
Réka Albert: Pennsylvania State University

A chapter in Nonlinear Analysis and Global Optimization, 2021, pp 51-69 from Springer

Abstract: Abstract The curvature of higher-dimensional geometric shapes and topological spaces is a natural and powerful generalization of its simpler counterpart in planes and other two-dimensional spaces. Curvature plays a fundamental role in physics, mathematics, and many other areas. However, graphs are discrete objects that do not necessarily have an associated natural geometric embedding. There are many ways in which curvature definitions of a continuous surface or other similar space can be adapted to graphs depending on what kind of local or global properties the measure is desired to reflect. In this chapter, we review two such measures, namely the Gromov-hyperbolic curvature measure and a geometric measure based on topological associations to higher-dimensional complexes.

Date: 2021
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DOI: 10.1007/978-3-030-61732-5_3

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