网络中最短路径和爆发分布的最大熵模型
Maximum Entropy Models of Shortest Path and Outbreak Distributions in Networks
摘要：
网络的性质通常用节点度分布、平均路径长度、直径或聚类系数等特征来表征。在这里，我们研究最短路径长度分布。一方面，平均距离和最大距离可以由此确定;另一方面，它们与网络扩展过程的动态密切相关。由于网络的组合性质，我们应用最大熵参数来导出一个通用的，物理上合理的模型。特别是，我们建立了广义伽玛分布作为网络或任意拓扑结构的最短路径长度直方图的连续表征。实验评价证实了我们的理论结果。
英文摘要：
Properties of networks are often characterized in terms of features such as node degree distributions, average path lengths, diameters, or clustering coefficients. Here, we study shortest path length distributions. On the one hand, average as well as maximum distances can be determined therefrom; on the other hand, they are closely related to the dynamics of network spreading processes. Because of the combinatorial nature of networks, we apply maximum entropy arguments to derive a general, physically plausible model. In particular, we establish the generalized Gamma distribution as a continuous characterization of shortest path length histograms of networks or arbitrary topology. Experimental evaluations corroborate our theoretical results.
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