Paper: CCSS-09-001

Title: How to make a fragile network robust and vice versa

Authors: Andre A. Moreira*, Jose S. Andrade Jr., Hans J. Herrmann, Joseph O. Indekeu

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.

Keywords: Network, Robustness, Topology, Control

Manuscript status: Published

Reference: Physical Review Letters. Volume 102, Article 018701 (2009)

JEL codes:
PACS numbers: 64.60.aq, 89.75.Hc, 64.60.ah

Local copy of the paper: CCSS-09-001.pdf

Submission date: 21-04-2009