Hidden dependence of spreading vulnerability on topological complexity

TL;DR

This paper introduces the entropy of temporal entanglement as a novel measure to quantify how the topological complexity of temporal networks influences their vulnerability to spreading phenomena across various real-world systems.

Contribution

The study develops a new entropy-based metric for topological complexity and demonstrates its effectiveness in predicting spreading vulnerability across diverse systems.

Findings

Entropy of temporal entanglement correlates with spreading vulnerability.

The measure enables topological comparison across different systems.

It works independently of the specific dynamical processes.

Abstract

Many dynamical phenomena in complex systems concern spreading that plays out on top of networks with changing architecture over time -- commonly known as temporal networks. A complex system's proneness to facilitate spreading phenomena, which we abbreviate as its `spreading vulnerability', is often surmised to be related to the topology of the temporal network featured by the system. Yet, cleanly extracting spreading vulnerability of a complex system directly from the topological information of the temporal network remains a challenge. Here, using data from a diverse set of real-world complex systems, we develop the `entropy of temporal entanglement' as a novel and insightful quantity to measure topological complexities of temporal networks. We show that this parameter-free quantity naturally allows for topological comparisons across vastly different complex systems. Importantly, by simulating three different types of stochastic dynamical processes playing out on top of temporal networks, we demonstrate that the entropy of temporal entanglement serves as a quantitative embodiment of the systems' spreading vulnerability, irrespective of the details of the processes. In being able to do so, i.e., in being able to quantitatively extract a complex system's proneness to facilitate spreading phenomena from topology, this entropic measure opens itself for applications in a wide variety of natural, social, biological and engineered systems.