Geodesics of Dynamic Graphs for Regime Change Detection

2026-06-05

AI Summary

This study addresses a key limitation in existing dynamic network change-point detection methods, which typically assume abrupt and stationary regime shifts, thereby failing to capture the continuous nature of real-world mechanistic transitions. The authors conceptualize a “mechanism” as a coherent evolutionary trajectory along a geodesic in graph space and propose detecting changes by measuring the cumulative deviation of an observed graph sequence from an ideal geodesic path. This approach is the first to model and identify transitions between continuously evolving mechanisms in graph space, moving beyond conventional assumptions of abrupt stationarity. By integrating graph regression with geodesic modeling and embedding it within a change-point detection framework, the method significantly outperforms existing approaches on both synthetic data and real-world mobility networks during the COVID-19 pandemic, yielding change points that align more closely with major external events.

Abstract

Traditional change point detection in dynamic networks assumes abrupt transitions between stationary states, overlooking scenarios of continuous evolution which arise in most real-world applications, such as social networks or physical systems. We address this gap by formally defining regimes as periods of coherent dynamics in temporal graphs, which we characterize as trajectories along geodesics in a suitably defined graph space. This original perspective allows us to define regime changes as significant drifts in dynamics, either toward new trajectories or with pace changes. We leverage graph regression methods to measure the cumulative distance of sequences of observed graphs from the estimated geodesics between their endpoints, in the relevant graph space, which we can combine with change point detection algorithms. We present experiments on dynamic networks, with changing trajectories and varying speeds, in which we outperform state of the art change point detection models. Then, we analyse mobility data during the Covid-19 pandemic, and show that our assumptions on regular network evolution lead to change points that are more aligned to external events compared to the outcomes of baseline methods. Our work is the first to model and detect changes between evolving regimes in graph space, providing a realistic and powerful tool for analyzing complex temporal graph data.

Problem

• dynamic graphs
• regime change detection
• temporal networks
• change point detection
• graph evolution

Innovation

• geodesics
• dynamic graphs
• regime change detection
• graph space
• temporal network evolution