Efficient Sampling of Temporal Networks with Preserved Causality Structure

TL;DR

This paper introduces an efficient method for sampling synthetic temporal networks that accurately preserve causality and neighborhood structures, improving upon existing randomization techniques.

Contribution

It extends the Color Refinement algorithm to temporal networks, enabling preservation of causal paths and neighborhood structures up to a specified length.

Findings

Preserves time-respecting paths up to length d

Retains key temporal features better than existing methods

Scales efficiently to large real-world networks

Abstract

In this paper, we extend the classical Color Refinement algorithm for static networks to temporal (undirected and directed) networks. This enables us to design an algorithm to sample synthetic networks that preserves the $d$-hop neighborhood structure of a given temporal network. The higher $d$ is chosen, the better the temporal neighborhood structure of the original network is preserved. Specifically, we provide efficient algorithms that preserve time-respecting ("causal") paths in the networks up to length $d$, and scale to real-world network sizes. We validate our approach theoretically (for Degree and Katz centrality) and experimentally (for edge persistence, causal triangles, and burstiness). An experimental comparison shows that our method retains these key temporal characteristics more effectively than existing randomization methods.