Resilience of the Internet to Random Breakdowns

Abstract

A common property of many large networks, including the Internet, is that the connectivity of the various nodes follows a scale-free power-law distribution, P(k) = ck(-alpha). We study the stability of such networks with respect to crashes, such as random removal of sites. Our approach, based on percolation theory, leads to a general condition for the critical fraction of nodes, p(c), that needs to be removed before the network disintegrates. We show analytically and numerically that for alpha</=3 the transition never takes place, unless the network is finite. In the special case of the physical structure of the Internet (alpha approximately 2.5), we find that it is impressively robust, with p(c)>0.99.

Why nestedness in mutualistic networks?

“…The assessment of the tolerance of a network through the removal of nodes bears some conceptual similarity with the studies performed by Cohen et al 2000 to determine the resilience of the Internet under the random removal of nodes. There are however important differences that render impossible the direct application of Cohen's results to the present situation.…”

Networks formed from interdependent networks

“…The discovery of scale-free networks led to a re-evaluation of the basic properties of networks, such as their robustness, which exhibit a drastically different character than those of ErdAEs-Rényi networks. For example, whereas homogeneous ErdAEs-Rényi networks are extremely vulnerable to random failures, heterogeneous scale-free networks are remarkably robust 4,5 . A great part of our current knowledge on networks is based on ideas borrowed from statistical physics, such as percolation theory, fractals and scaling analysis.…”

Évaluer le risque épidémique à partir de données lacunaires

“…Or ces données ne concernent jamais l'intégralité de la population étudiée. En effet, généralement, seule une partie de la [6]. En revanche, d'autres caractéristiques restent stables.…”