Robustness and assortativity for diffusion-like processes in scale-free networks

¹ ENEA - CR “Casaccia” - Via Anguillarese 301, I-00123, Roma, Italy, EU
² CNR-ISC and Department of Physics, University of Rome “Sapienza” - P.le Aldo Moro 5, I-00185, Rome, Italy, EU
³ London Institute of Mathematical Sciences - 22 South Audley St., Mayfair, London W1K 2NY, UK, EU
⁴ Theoretical Physics Division, Rudjer Bošković Institute - P.O. Box 180, HR-10002 Zagreb, Croatia
⁵ IMT Lucca Institute for Advanced Studies - Piazza S. Ponziano 6, Lucca, I-55100, Italy, EU

^a antonio.scala@phys.uniroma1.it

Received: 3 November 2011
Accepted: 21 February 2012

Abstract

By analysing the diffusive dynamics of epidemics and of distress in complex networks, we study the effect of the assortativity on the robustness of the networks. We first determine by spectral analysis the thresholds above which epidemics/failures can spread; we then calculate the slowest diffusional times. Our results shows that disassortative networks exhibit a higher epidemiological threshold and are therefore easier to immunize, while in assortative networks there is a longer time for intervention before epidemic/failure spreads. Moreover, we study by computer simulations the sandpile cascade model, a diffusive model of distress propagation (financial contagion). We show that, while assortative networks are more prone to the propagation of epidemic/failures, degree-targeted immunization policies increases their resilience to systemic risk.