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A Review of Two Network Curvature Measures

In: Nonlinear Analysis and Global Optimization

Author

Listed:
  • Tanima Chatterjee

    (University of Illinois at Chicago)

  • Bhaskar DasGupta

    (University of Illinois at Chicago)

  • Réka Albert

    (Pennsylvania State University)

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.

Suggested Citation

  • Tanima Chatterjee & Bhaskar DasGupta & Réka Albert, 2021. "A Review of Two Network Curvature Measures," Springer Optimization and Its Applications, in: Themistocles M. Rassias & Panos M. Pardalos (ed.), Nonlinear Analysis and Global Optimization, pages 51-69, Springer.
    • Handle: RePEc:spr:spochp:978-3-030-61732-5_3
    DOI: 10.1007/978-3-030-61732-5_3
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