Correlations of network trajectories

TL;DR

This paper introduces a method to analyze the collective dynamics of temporal networks by measuring correlations in network trajectories, revealing underlying patterns in empirical data across various domains.

Contribution

It extends correlation measures to network trajectories and demonstrates their effectiveness in capturing collective fluctuations in both synthetic and real-world networks.

Findings

Correlations effectively characterize collective network fluctuations.

Simple measures reveal patterns in empirical temporal networks.

The approach applies across different domains and network types.

Abstract

Temporal networks model how the interaction between elements in a complex system evolve over time. Just like complex systems display collective dynamics, here we interpret temporal networks as trajectories performing a collective motion in graph space, following a latent graph dynamical system. Under this paradigm, we propose a way to measure how the network pulsates and collectively fluctuates over time and space. To this aim, we extend the notion of linear correlations function to the case of sequences of network snapshots, i.e. a network trajectory. We construct stochastic and deterministic graph dynamical systems and show that the emergent collective correlations are well captured by simple measures, and illustrate how these patterns are revealed in empirical networks arising in different domains.