Inferring Network Evolutionary History via Structure-State Coupled Learning

TL;DR

This paper introduces CS$^2$, a novel method that combines network structure and steady-state dynamics to more accurately infer the evolutionary history of networks from a single snapshot, outperforming existing approaches.

Contribution

The paper proposes a structure-state coupling model, CS$^2$, that leverages steady-state dynamics alongside topology to improve network evolution inference, including edge ordering and macroscopic trajectory recovery.

Findings

CS$^2$ improves pairwise edge precedence accuracy by 4.0% on average.

CS$^2$ enhances global ordering consistency (Spearman-$ ho$) by 7.7% on average.

A steady-state-only variant remains effective with limited topology data.

Abstract

Inferring a network's evolutionary history from a single final snapshot with limited temporal annotations is fundamental yet challenging. Existing approaches predominantly rely on topology alone, which often provides insufficient and noisy cues. This paper leverages network steady-state dynamics -- converged node states under a given dynamical process -- as an additional and widely accessible observation for network evolution history inference. We propose CS$^2$, which explicitly models structure-state coupling to capture how topology modulates steady states and how the two signals jointly improve edge discrimination for formation-order recovery. Experiments on six real temporal networks, evaluated under multiple dynamical processes, show that CS$^2$ consistently outperforms strong baselines, improving pairwise edge precedence accuracy by 4.0% on average and global ordering consistency (Spearman-$\rho$) by 7.7% on average. CS$^2$ also more faithfully recovers macroscopic evolution trajectories such as clustering formation, degree heterogeneity, and hub growth. Moreover, a steady-state-only variant remains competitive when reliable topology is limited, highlighting steady states as an independent signal for evolution inference.