Holme Petter
Department of Theoretical Physics, Umeå University, Sweden.
Phys Rev E Stat Nonlin Soft Matter Phys. 2002 Sep;66(3 Pt 2A):036119. doi: 10.1103/PhysRevE.66.036119. Epub 2002 Sep 19.
We investigate growing networks based on Barabási and Albert's algorithm for generating scale-free networks, but with edges sensitive to overload breakdown. The load is defined through edge betweenness centrality. We focus on the situation where the average number of connections per vertex is, like the number of vertices, linearly increasing in time. After an initial stage of growth, the network undergoes avalanching breakdowns to a fragmented state from which it never recovers. This breakdown is much less violent if the growth is by random rather than by preferential attachment (as defines the Barabási and Albert model). We briefly discuss the case where the average number of connections per vertex is constant. In this case no breakdown avalanches occur. Implications to the growth of real-world communication networks are discussed.
我们基于巴拉巴西和阿尔伯特生成无标度网络的算法来研究增长型网络，但边对过载故障敏感。负载通过边介数中心性来定义。我们关注每个顶点的平均连接数与顶点数一样随时间线性增加的情况。在初始增长阶段之后，网络会经历雪崩式故障，进入碎片化状态且无法恢复。如果增长是随机的而非通过优先连接（如巴拉巴西和阿尔伯特模型所定义），这种故障就没那么剧烈。我们简要讨论了每个顶点的平均连接数为常数的情况。在这种情况下不会发生故障雪崩。文中还讨论了对现实世界通信网络增长的影响。
