Inferring Network Evolutionary History via Structure-State Coupled Learning

TL;DR

Inferring an edge formation history from a single final network snapshot is challenging when temporal annotations are scarce. The authors introduce CS$^2$, a structure--state coupling framework that combines topology-derived features with steady-state node dynamics to learn pairwise edge precedence and reconstruct a global sequence via Borda aggregation. Across six real temporal networks and three dynamical processes, CS$^2 consistently outperforms topology-only baselines in both local (pairwise precedence) and global (Spearman$\rho$) metrics, and it more faithfully recovers macroscopic evolution trajectories such as clustering and hub growth. Additionally, a steady-state-only variant demonstrates that steady-state signals can provide discriminative cues even when topology is incomplete, highlighting practical applicability in structure-limited settings.

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-$ρ$) 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.

Figures (16)

• Figure 1: Problem illustration. A temporal network evolves through sequential edge formation, but is often observed only as a final snapshot with scarce temporal annotations. The goal is to recover the edge formation order from the snapshot, optionally augmented with steady-state node observations.
• Figure 2: Theoretical link between pairwise precedence accuracy and the expected error of the recovered global ordering (Eq. \ref{['eq:equivalence']}).
• Figure 3: Overview of CS$^2$. Given the final snapshot $G_T$ and its steady state $\mathbf{x}_T$, the framework extracts structural and steady-state features, learns coupled representations via graph propagation, predicts pairwise edge precedence with CPNN, and aggregates comparisons to recover a global edge formation order.
• Figure 4: Global ordering consistency under SIS dynamics. Each panel shows the relationship between the true normalized edge rank and the predicted normalized edge rank on one dataset.
• Figure 5: Evolution of degree Gini across datasets under SIS dynamics.