Articulation points in complex networks

Liang Tian,Yang-Yu Liu,Amir Bashan,Da-Ning Shi

doi:10.1038/ncomms14223

Abstract

An articulation point in a network is a node whose removal disconnects the network. Those nodes play key roles in ensuring connectivity of many real-world networks, from infrastructure networks to protein interaction networks and terrorist communication networks. Despite their fundamental importance, a general framework of studying articulation points in complex networks is lacking. Here we develop analytical tools to study key issues pertinent to articulation points, such as the expected number of them and the network vulnerability against their removal, in an arbitrary complex network. We find that a greedy articulation point removal process provides us a different perspective on the organizational principles of complex networks. Moreover, this process results in a rich phase diagram with two fundamentally different types of percolation transitions. Our results shed light on the design of more resilient infrastructure networks and the effective destruction of terrorist communication networks.

Highlights

An articulation point in a network is a node whose removal disconnects the network
Can we design an articulation point (AP)-based attack strategy to more efficiently destroy malicious networks? Can we develop an AP-based network decomposition method to better reveal the organizing principles of complex networks? What happens if we keep removing APs from a random graph or a real network? Will there be a core left? If yes, what’s the implication of such a core in terms of structural integrity and functionality of the network? How to quantify if a real network has overrepresented or underrepresented APs comparing to its randomized counterparts? In this article we offer an analytical framework to study those fundamental issues pertinent to APs in both real networks and random graphs, harvesting a series of interesting results
Given a limited ‘budget’, this APTA strategy is very efficient in reducing the giant connected component (GCC), compared with strategies based on other node centrality measures, such as degree[10,11] and collective influence[12]

Summary

Introduction

An articulation point in a network is a node whose removal disconnects the network Those nodes play key roles in ensuring connectivity of many real-world networks, from infrastructure networks to protein interaction networks and terrorist communication networks. Despite their fundamental importance, a general framework of studying articulation points in complex networks is lacking. A fundamental challenge in studying complex networked systems is to reveal the interplay between network structure and function[1,2] We tackle this challenge by investigating a classical notion in graph theory, that is, articulation points. Can we design an AP-based attack strategy to more efficiently destroy malicious networks? Can we develop an AP-based network decomposition method to better reveal the organizing principles of complex networks? What happens if we keep removing APs from a random graph or a real network? Will there be a core left? If yes, what’s the implication of such a core in terms of structural integrity and functionality of the network? How to quantify if a real network has overrepresented or underrepresented APs comparing to its randomized counterparts? In this article we offer an analytical framework to study those fundamental issues pertinent to APs in both real networks and random graphs, harvesting a series of interesting results

Methods

Results

Conclusion