How to make a fragile network robust and vice versa

TL;DR

This paper explores how biasing failure towards either highly connected or less connected nodes in scale-free networks affects their robustness, revealing a tunable transition between robustness and fragility.

Contribution

It introduces a model where failure probability depends on node degree, showing how topological bias can control network robustness or fragility.

Findings

Topological bias creates a characteristic scale in the degree distribution.

Critical percolation threshold varies with bias parameter and degree exponent.

Network robustness can be tuned by adjusting failure bias.

Abstract

We investigate topologically biased failure in scale-free networks with degree distribution $P(k) \propto k^{-\gamma}$. The probability $p$ that an edge remains intact is assumed to depend on the degree $k$ of adjacent nodes $i$ and $j$ through $p_{ij}\propto(k_{i}k_{j})^{-\alpha}$. By varying the exponent $\alpha$, we interpolate between random ($\alpha=0$) and systematic failure. For $\alpha >0 $ ($<0$) the most (least) connected nodes are depreciated first. This topological bias introduces a characteristic scale in $P(k)$ of the depreciated network, marking a crossover between two distinct power laws. The critical percolation threshold, at which global connectivity is lost, depends both on $\gamma$ and on $\alpha$. As a consequence, network robustness or fragility can be controlled through fine tuning of the topological bias in the failure process.