Kim P, Lee D-S, Kahng B
Department of Physics and Astronomy, Seoul National University, Seoul 151-747, Korea.
Phys Rev E Stat Nonlin Soft Matter Phys. 2013 Feb;87(2):022804. doi: 10.1103/PhysRevE.87.022804. Epub 2013 Feb 7.
In information-transport and biological systems, sometimes there is more than one pathway between two nodes, so that there is a backup in case one pathway becomes defective. The size of such biconnected nodes can be an important measure of the robustness of a system. The giant biconnected components of diverse real-world networks suggest the importance of scale-free topology in biconnectivity. Thus, here, we consider the critical behavior of the largest biconnected component (BC) as links are added and form a random scale-free network. The critical exponents β((BC)) and β((SC)) associated with the order parameter of the percolation transition of the biconnected component and the single-connected component (SC), respectively, are compared. We obtain a ratio β((BC))/β((SC))=λ-1 for 2<λ<3 and 2 for λ>3, where λ is the exponent of the degree distribution in scale-free networks. We also determine the finite-size scaling behavior of the order parameter analytically and numerically.
在信息传输和生物系统中，有时两个节点之间存在多条路径，这样在一条路径出现故障时就有了备份。这种双连通节点的规模可以作为衡量系统鲁棒性的一个重要指标。各种现实世界网络中的巨型双连通分量表明无标度拓扑在双连通性方面的重要性。因此，在这里，我们考虑在添加链接并形成随机无标度网络时最大双连通分量（BC）的临界行为。分别比较了与双连通分量和单连通分量（SC）渗流转变的序参量相关的临界指数β((BC))和β((SC))。对于2<λ<3，我们得到β((BC))/β((SC)) = λ - 1，对于λ>3，该比值为2，其中λ是无标度网络中度分布的指数。我们还通过解析和数值方法确定了序参量的有限尺寸标度行为。
