Robustness of networks with topologies of dependency links

TL;DR

This paper investigates how the topology of dependency links affects the robustness of complex networks, revealing that different dependency structures lead to varying vulnerability and phase transition behaviors.

Contribution

It introduces a realistic network model incorporating dependency link topologies and analyzes their impact on network robustness through theoretical and numerical methods.

Findings

RR dependency links increase vulnerability compared to ER dependency links.

RR-RR networks disintegrate abruptly under failures.

Interaction between connectivity and dependency topologies determines phase transition types.

Abstract

The robustness of complex networks with dependencies has been studied in recent years. However, previous studies focused on the robustness of networks composed of dependency links without network topology. In this study, we will analyze the percolation properties of a realistic network model where dependency links follow certain network topology. We perform the theoretical analysis and numerical simulations to show the critical effects of topology of dependency links on robustness of complex networks. For Erd\"os-R\'enyi (ER) connectivity network, we find that the system with dependency of RR topology is more vulnerable than system with dependency of ER topology. And RR-RR (i.e. random-regular (RR) network with dependency of RR topology) disintegrates in an abrupt transition. In particular, we find that the system of RR-ER shows different types of phase transitions. For system of different combinations, the type of percolation depends on the interaction between connectivity topology and dependency topology.