Inferring Network Evolutionary History via Structure-State Coupled Learning

2026-01-05

arXiv.org

AI Summary

Existing methods for inferring the evolutionary history of networks rely solely on topological structure from a single temporal snapshot, which provides limited information and is highly susceptible to noise. This work proposes the first framework that incorporates steady-state dynamics—the convergent states of nodes under dynamical processes—as an independent and complementary signal to topology. We introduce a Coupled Structure–State learning framework (CS²) that jointly models the interaction between network topology and steady-state dynamics to refine the temporal ordering of edges. Evaluated on six real-world temporal networks, our approach improves edge-ordering accuracy by 4.0% and Spearman-ρ consistency by 7.7% on average, while more faithfully reconstructing macroscopic evolutionary patterns such as clustering dynamics, degree heterogeneity, and hub emergence. Notably, even when using only steady-state information, the method remains competitive in scenarios where topological data is unreliable.

Technology Category

• Planning, Routing, and Scheduling: Temporal Planning
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• Social Networks and Social Media: Computational social science

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.

Problem

• network evolution
• evolutionary history inference
• steady-state dynamics
• temporal networks
• structure-state coupling

Innovation

• structure-state coupling
• network evolution inference
• steady-state dynamics
• edge formation ordering
• temporal network reconstruction