On Analyzing Networks Via Curvature Measures: Review of Methodologies and Applications

Réka Albert (), Nazanin Azarhooshang, Tanima Chatterjee, Bhaskar DasGupta (), Prithviraj Sengupta, Aishi Agarwal and Garima Kankariya
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Réka Albert: Pennsylvania State University, Department of Physics
Nazanin Azarhooshang: University of Illinois Chicago, Department of Computer Science
Tanima Chatterjee: Boston University, Center for Computing & Data Sciences
Bhaskar DasGupta: University of Illinois Chicago, Department of Computer Science
Prithviraj Sengupta: University of Illinois Chicago, Department of Computer Science
Aishi Agarwal: Vernon Hills High School
Garima Kankariya: Indian Institute of Technology, New Delhi

Chapter 1 in Convex and Variational Analysis with Applications, 2026, pp 1-25 from Springer

Abstract: Abstract Suitable notions of shapes play a critical role in investigating objects in mathematics, physics, and other research areas. Various kinds of curvatures are very natural measures of shapes of higher dimensional objects in mainstream physics and mathematics. However, any attempt to extend notions of these kinds of measures to networks needs to overcome several key challenges. In this article we review several curvature measures for networks such as (i) Gromov-hyperbolic curvature, (ii) extension of discretization of Ricci curvature for polyhedral complexes, and (iii) extension of discretization of Ricci curvature via mass transportation distances, and the corresponding flow technique. We finally review the bioinformatics applications of these measures for several biological networks such as E. coli transcriptional network, metabolic network of M. tuberculosis, protein–protein interaction networks in humans, and network of functional correlations between brain regions for attention deficit hyperactivity disorder.

Keywords: Network curvature; Gromov-hyperbolicity; Ricci curvature; Computational complexity; Bioinformatics applications; Neuroscience applications (search for similar items in EconPapers)
Date: 2026
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DOI: 10.1007/978-3-032-07860-5_1

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