López Eduardo, Buldyrev Sergey V, Havlin Shlomo, Stanley H Eugene
Center for Polymer Studies, Boston University, Boston, Massachusetts 02215, USA.
Phys Rev Lett. 2005 Jun 24;94(24):248701. doi: 10.1103/PhysRevLett.94.248701. Epub 2005 Jun 22.
To study transport properties of scale-free and Erdos-Rényi networks, we analyze the conductance G between two arbitrarily chosen nodes of random scale-free networks with degree distribution P(k)-k(-lambda) in which all links have unit resistance. We predict a broad range of values of G, with a power-law tail distribution phi(SF)(G)-G(-g(G)), where g(G)=2lambda-1, and confirm our predictions by simulations. The power-law tail in phi(SF)(G) leads to large values of G, signaling better transport in scale-free networks compared to Erdos-Rényi networks where the tail of the conductivity distribution decays exponentially. Based on a simple physical "transport backbone" picture we show that the conductances of scale-free and Erdos-Rényi networks are well approximated by ck(A)k(B)/(k(A)+k(B)) for any pair of nodes A and B with degrees k(A) and k(B), where c emerges as the main parameter characterizing network transport.
为了研究无标度网络和随机图网络的传输特性，我们分析了度分布为(P(k)\sim k^{-\lambda})的随机无标度网络中任意两个选定节点之间的电导(G)，其中所有链路的电阻均为单位电阻。我们预测了(G)的取值范围很广，其具有幂律尾部分布(\phi_{SF}(G)\sim G^{-g(G)})，其中(g(G)=2\lambda - 1)，并通过模拟证实了我们的预测。(\phi_{SF}(G))中的幂律尾部导致(G)出现较大值，这表明与电导分布尾部呈指数衰减的随机图网络相比，无标度网络具有更好的传输性能。基于一个简单的物理“传输主干”图景，我们表明，对于任意一对度分别为(k(A))和(k(B))的节点(A)和(B)来说，无标度网络和随机图网络的电导可以很好地近似为(ck(A)k(B)/(k(A)+k(B)))，其中(c)作为表征网络传输的主要参数出现。
