2002/04/05 by Petter Holme, Beom Jun Kim · 236 citations
Computer Science · Mathematics · Physics and Astronomy · #Betweenness centrality #Centrality #Combinatorics #Complex Network Analysis Techniques #Complex network #Computer network #Computer science #Giant component #Graph #Mathematics #Neural Networks Stability and Synchronization #Opinion Dynamics and Social Influence #Preferential attachment #Telecommunications network #Theoretical computer science #Topology (electrical circuits) #Vertex (graph theory) #cond-mat.dis-nn
paper · pdf · doi:10.1103/physreve.65.066109
published in Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics 65(6), 066109 (American Physical Society) · To appear in Phys. Rev. E
arxiv created 2002/04/05 · openalex publication_date 2002/06/18 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study evolving networks based on the Barabási-Albert scale-free network model with vertices sensitive to overload breakdown. The load of a vertex is defined as the betweenness centrality of the vertex. Two cases of load limitation are considered, corresponding to the fact that the average number of connections per vertex is increasing with the network's size ("extrinsic communication activity"), or that it is constant ("intrinsic communication activity"). Avalanchelike breakdowns for both load limitations are observed. In order to avoid such avalanches we argue that the capacity of the vertices has to grow with the size of the system. An interesting irregular dynamics of the formation of the giant component (for the intrinsic communication activity case) is also studied. Implications on the growth of the Internet are discussed.