Temporal networks: slowing down diffusion by long lasting interactions

TL;DR

This paper analyzes how the sequential timing of interactions in temporal networks affects diffusion processes, showing that temporal dynamics are generally slower than in aggregate networks due to noncommutative interactions.

Contribution

It provides a spectral analysis of temporal networks, revealing how their eigenmodes relate to aggregate networks and demonstrating the impact on diffusion speed.

Findings

Temporal networks have smaller eigenvalues than aggregate networks.

Diffusive dynamics are slower in temporal networks due to interaction order.

Analytical results are validated with real and simulated networks.

Abstract

Interactions among units in complex systems occur in a specific sequential order thus affecting the flow of information, the propagation of diseases, and general dynamical processes. We investigate the Laplacian spectrum of temporal networks and compare it with that of the corresponding aggregate network. First, we show that the spectrum of the ensemble average of a temporal network has identical eigenmodes but smaller eigenvalues than the aggregate networks. In large networks without edge condensation, the expected temporal dynamics is a time-rescaled version of the aggregate dynamics. Even for single sequential realizations, diffusive dynamics is slower in temporal networks. These discrepancies are due to the noncommutability of interactions. We illustrate our analytical findings using a simple temporal motif, larger network models and real temporal networks.