2005/08/29 by K. Rho, Rho, K., Sun Hong +4
Environmental Science · Physics and Astronomy · #Complex Network Analysis Techniques #Ecosystem dynamics and resilience #FOS: Physical sciences #Opinion Dynamics and Social Influence #Statistical Mechanics (cond-mat.stat-mech) #cond-mat.stat-mech
paper · pdf · doi:10.48550/arxiv.cond-mat/0508682
4 pages, 5 figures
openalex publication_date 2005/08/29 · arxiv created 2005/09/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce a toy model displaying the avalanche dynamics of failure in scale-free networks. In the model, the network growth is based on the Barabási and Albert model and each node is assigned a capacity or tolerance, which is constant irrespective of node index. The degree of each node increases over time. When the degree of a node exceeds its capacity, it fails and each link connected to it is is rewired to other unconnected nodes by following the preferential attachment rule. Such a rewiring edge may trigger another failure. This dynamic process can occur successively, and it exhibits a self-organized critical behavior in which the avalanche size distribution follows a power law. The associated exponent is τ≈ 2.6(1). The entire system breaks down when any rewired edges cannot locate target nodes: the time at which this occurs is referred to as the breaking time. We obtain the breaking time as a function of the capacity. Moreover, using extreme value statistics, we determine the distribution function of the breaking time.