The critical effect of dependency groups on the function of networks

TL;DR

This paper introduces an analytical framework to study the robustness of networks with both connectivity and dependency links, revealing how their interaction causes cascading failures and alters traditional robustness assumptions.

Contribution

It presents the first analytical model for networks with dual link types, showing how dependency links fundamentally change network stability and failure behavior.

Findings

High dependency density causes first-order phase transition in disintegration.

Low dependency density leads to second-order phase transition.

Broader degree distributions increase vulnerability when dependency links are present.

Abstract

Current network models assume one type of links to define the relations between the network entities. However, many real networks can only be correctly described using two different types of relations. Connectivity links that enable the nodes to function cooperatively as a network and dependency links that bind the failure of one network element to the failure of other network elements. Here we present for the first time an analytical framework for studying the robustness of networks that include both connectivity and dependency links. We show that the synergy between the two types of failures leads to an iterative process of cascading failures that has a devastating effect on the network stability and completely alters the known assumptions regarding the robustness of networks. We present exact analytical results for the dramatic change in the network behavior when introducing dependency links. For a high density of dependency links the network disintegrates in a form of a first order phase transition while for a low density of dependency links the network disintegrates in a second order transition. Moreover, opposed to networks containing only connectivity links where a broader degree distribution results in a more robust network, when both types of links are present a broad degree distribution leads to higher vulnerability.