Critical load and congestion instabilities in scale-free networks

PACS. 89.75.-k – Complex systems. PACS. 89.75.Fb – Structures and organization in complex systems. PACS. 05.70.Jk – Critical point phenomena. Abstract. – We study the tolerance to congestion failures in communication networks with scale-free topology. The traffic load carried by each damaged element in the network must be partly or totally redistributed among the remaining elements. Overloaded elements might fail on their turn, triggering the occurrence of failure cascades able to isolate large parts of the network. We find a critical traffic load above which the probability of massive traffic congestions destroying the network communication capabilities is finite. Complex heterogeneous connectivity patterns have recently been identified in several nat-ural and technological networks [1–3]. The Internet and the World-Wide-Web (WWW) net-works, where nodes represent routers or web pages and edges physical connections or hyper-links, appear to have a topology characterized by the presence of “hubs ” with many connec-tions to peripherical nodes. Empirical evidence recently collected shows that this distinctive feature finds its statistical characterization in the presence of heavy tailed degree distribu-