Multiplex networks with heterogeneous activities of the nodes

TL;DR

This paper models multiplex networks with heterogeneous node activities, analyzing their robustness and phase transition behaviors, revealing that activity distribution and correlations significantly influence network resilience and the nature of percolation transitions.

Contribution

It introduces a percolation model for multiplex networks with heterogeneous node activities and studies how activity patterns affect robustness and phase transition types.

Findings

Networks with many nodes active in only one layer are more resilient.

Broader activity distributions lead to increased fragility.

Positive activity-degree correlations can cause discontinuous phase transitions.

Abstract

In multiplex networks with a large number of layers, the nodes can have different activities, indicating the total number of layers in which the nodes are present. Here we model multiplex networks with heterogeneous activity of the nodes and we study their robustness properties. We introduce a percolation model where nodes need to belong to the giant component only on the layers where they are active (i.e. their degree on that layer is larger than zero). We show that when there are enough nodes active only in one layer, the multiplex becomes more resilient and the transition becomes continuous. We find that multiplex networks with a power-law distribution of node activities are more fragile if the distribution of activity is broader. We also show that while positive correlations between node activity and degree can enhance the robustness of the system, the phase transition may become discontinuous, making the system highly unpredictable.