Characterizing Complex Networks with Forman-Ricci Curvature and Associated Geometric Flows

TL;DR

This paper introduces Forman-Ricci curvature and geometric flows as novel edge-based tools for analyzing complex networks, offering new insights beyond traditional node-based methods and demonstrating applications in data mining tasks.

Contribution

It presents the theoretical foundation and practical application of Forman-Ricci curvature and flows for complex network analysis, extending existing methods.

Findings

Edge-based characteristics provide complementary insights to node-based analysis.

The methods effectively distinguish static and dynamic network structures.

Applications include denoising, clustering, and predicting network evolution.

Abstract

We introduce Forman-Ricci curvature and its corresponding flow as characteristics for complex networks attempting to extend the common approach of node-based network analysis by edge-based characteristics. Following a theoretical introduction and mathematical motivation, we apply the proposed network-analytic methods to static and dynamic complex networks and compare the results with established node-based characteristics. Our work suggests a number of applications for data mining, including denoising and clustering of experimental data, as well as extrapolation of network evolution.