Forman-Ricci flow for change detection in large dynamic data sets

TL;DR

This paper introduces a novel geometric method based on Forman-Ricci flow for detecting changes in large dynamic networks, providing new insights into their topological properties.

Contribution

It adapts Ricci flow to undirected weighted networks and applies it to peer-to-peer networks for change detection and structural analysis.

Findings

Effective change detection in large dynamic networks.

Revealed topological insights into peer-to-peer network structures.

Demonstrated applicability of Ricci flow in network analysis.

Abstract

We present a viable solution to the challenging question of change detection in complex networks inferred from large dynamic data sets. Building on Forman's discretization of the classical notion of Ricci curvature, we introduce a novel geometric method to characterize different types of real-world networks with an emphasis on peer-to-peer networks. Furthermore we adapt the classical Ricci flow that already proved to be a powerful tool in image processing and graphics, to the case of undirected and weighted networks. The application of the proposed method on peer-to-peer networks yields insights into topological properties and the structure of their underlying data.