Copula-based analysis of the autocorrelation function for simple temporal networks

TL;DR

This paper introduces a copula-based method to analyze autocorrelation functions in temporal networks, providing an analytical solution under certain assumptions and validating it through numerical simulations.

Contribution

It develops an analytical approach to characterize temporal correlations in networks using copulas, extending methods from single time series analysis.

Findings

Analytical solution matches numerical simulations.

Heterogeneous activity levels are effectively modeled.

Weakly correlated exponential interevent times are assumed.

Abstract

To characterize temporal correlations in temporal networks, we define an autocorrelation function (ACF) for temporal networks in terms of the similarity between two snapshot networks separated by a certain time interval. By employing a copula-based method recently developed for a single time series, we analyze the ACF for the temporal network in which activity patterns of links are independent of each other but their activity levels are heterogeneous. By assuming that exponential distributed interevent times are weakly correlated with each other in each link, we obtain an analytical solution of the ACF. The validity of the analytical solution is tested against the numerical simulations to find that the numerical results are comparable to the analytical solution.