Temporal network analysis via a degree-corrected Cox model

2025-07-26

AI Summary

This paper addresses the challenge of modeling time-varying degree heterogeneity (in-degree and out-degree) and homophily effects in dynamic directed networks. We propose a degree-corrected time-varying Cox model that extends the classical Cox proportional hazards framework to dynamic network analysis. The model permits degree-specific parameters and homophily effects to evolve nonparametrically over time, thereby mitigating the curse of dimensionality associated with high-dimensional time-varying parameters. Statistical inference is achieved via locally constructed estimating equations, ensuring consistency and asymptotic normality. We further develop graphical goodness-of-fit diagnostics and hypothesis tests to detect temporal variation and degree heterogeneity. Theoretical analysis establishes consistency and asymptotic normality of estimators under high-dimensional settings. Extensive simulations and empirical studies—including applications to social network data—demonstrate the method’s finite-sample robustness and interpretability, enabling precise characterization of dynamic network structural evolution.

Technology Category

• Reasoning under Uncertainty: Graphical Models
• Machine Learning: Probabilistic Circuits and Graphical Models
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• Social Networks and Social Media: Social media analysis through the lenses of networks

Abstract

Temporal dynamics, characterised by time-varying degree heterogeneity and homophily effects, are often exhibited in many real-world networks. As observed in an MIT Social Evolution study, the in-degree and out-degree of the nodes show considerable heterogeneity that varies with time. Concurrently, homophily effects, which explain why nodes with similar characteristics are more likely to connect with each other, are also time-dependent. To facilitate the exploration and understanding of these dynamics, we propose a novel degree-corrected Cox model for directed networks, where the way for degree-heterogeneity or homophily effects to change with time is left completely unspecified. Because each node has individual-specific in- and out-degree parameters that vary over time, the number of unknown parameters grows with the number of nodes, leading to a high-dimensional estimation problem. Therefore, it is highly nontrivial to make inference. We develop a local estimating equations approach to estimate the unknown parameters and establish the consistency and asymptotic normality of the proposed estimators in the high-dimensional regime. We further propose test statistics to check whether temporal variation or degree heterogeneity is present in the network and develop a graphically diagnostic method to evaluate goodness-of-fit for dynamic network models. Simulation studies and two real data analyses are provided to assess the finite sample performance of the proposed method and illustrate its practical utility.

Problem

• Modeling time-varying degree heterogeneity in directed networks
• Estimating high-dimensional parameters for dynamic network analysis
• Testing presence of temporal variation and degree heterogeneity

Innovation

• Degree-corrected Cox model for directed networks
• Local estimating equations for high-dimensional parameters
• Test statistics for temporal variation detection