Interconnecting bilayer networks

TL;DR

This paper introduces interconnecting multilayer networks where component networks share nodes, revealing that networks with similar node topologies tend to share more nodes, supported by empirical data and a simple analytical model.

Contribution

It presents a new type of interdependent multilayer networks and uncovers a universal feature relating shared nodes to topological similarity, supported by empirical analysis and a theoretical explanation.

Findings

Networks with smaller topological differences share more nodes.

Shared node proportion correlates with topological similarity.

A simple sharing mechanism explains the observed feature.

Abstract

A typical complex system should be described by a supernetwork or a network of networks, in which the networks are coupled to some other networks. As the first step to understanding the complex systems on such more systematic level, scientists studied interdependent multilayer networks. In this letter, we introduce a new kind of interdependent multilayer networks, i.e., interconnecting networks, for which the component networks are coupled each other by sharing some common nodes. Based on the empirical investigations, we revealed a common feature of such interconnecting networks, namely, the networks with smaller averaged topological differences of the interconnecting nodes tend to share more nodes. A very simple node sharing mechanism is proposed to analytically explain the observed feature of the interconnecting networks.