The Resistance Perturbation Distance: A Metric for the Analysis of Dynamic Networks

TL;DR

This paper introduces a new family of graph distances called Resistance Perturbation Distance, capable of capturing multi-scale structural changes in dynamic networks, with efficient algorithms for approximation and robustness enhancement.

Contribution

It presents a novel true distance metric for dynamic networks, along with fast randomized algorithms for approximation and a method to improve network robustness by reducing the Kirchhoff index.

Findings

Effective detection of structural changes in synthetic and real networks.

The proposed algorithms operate in linear time relative to the number of edges.

Demonstrated ability to identify hidden variables influencing network evolution.

Abstract

To quantify the fundamental evolution of time-varying networks, and detect abnormal behavior, one needs a notion of temporal difference that captures significant organizational changes between two successive instants. In this work, we propose a family of distances that can be tuned to quantify structural changes occurring on a graph at different scales: from the local scale formed by the neighbors of each vertex, to the largest scale that quantifies the connections between clusters, or communities. Our approach results in the definition of a true distance, and not merely a notion of similarity. We propose fast (linear in the number of edges) randomized algorithms that can quickly compute an approximation to the graph metric. The third contribution involves a fast algorithm to increase the robustness of a network by optimally decreasing the Kirchhoff index. Finally, we conduct several experiments on synthetic graphs and real networks, and we demonstrate that we can detect configurational changes that are directly related to the hidden variables governing the evolution of dynamic networks.