Correlations in complex networks under attack

TL;DR

This paper develops analytical expressions to predict topological changes in complex networks under various attack strategies, showing how to manipulate degree correlations through targeted node or edge removals.

Contribution

It introduces a general analytical framework for understanding how different attack strategies affect degree correlations in complex networks.

Findings

Analytical expressions accurately predict network evolution after attacks.

It is possible to switch between assortative and disassortative networks by fine-tuning removals.

Targeted edge removal can induce correlations in initially uncorrelated networks.

Abstract

For any initial correlated network after any kind of attack where either nodes or edges are removed, we obtain general expressions for the degree-degree probability matrix and degree distribution. We show that the proposed analytical approach predicts the correct topological changes after the attack by comparing the evolution of the assortativity coefficient for different attack strategies and intensities in theory and simulations. We find that it is possible to turn an initial assortative network into a disassortative one, and vice versa, by fine-tuning removal of either nodes or edges. For an initial uncorrelated network, on the other hand, we discover that only a targeted edge-removal attack can induce such correlations.