复杂网络的曲率和温度
Curvature and temperature of complex networks
摘要：
我们发现，异构度分布在观察到的复杂网络的无标度拓扑结构可以出现作为隐藏的双曲空间的指数膨胀的后果。费米-狄拉克统计提供了双曲距离作为链接能量的物理解释。隐藏空间曲率影响度分布的异质性，而聚类是温度的函数。我们将互联网嵌入到双曲平面，并发现嵌入和我们的双曲模型之间的显着一致性。除了证明我们的模型是现实的，这种嵌入可以用于路由只有本地信息，这对提高互联网路由的性能具有重要的承诺。
英文摘要：
We show that heterogeneous degree distributions in observed scale-free topologies of complex networks can emerge as a consequence of the exponential expansion of hidden hyperbolic space. Fermi-Dirac statistics provides a physical interpretation of hyperbolic distances as energies of links. The hidden space curvature affects the heterogeneity of the degree distribution, while clustering is a function of temperature. We embed the Internet into the hyperbolic plane, and find a remarkable congruency between the embedding and our hyperbolic model. Besides proving our model realistic, this embedding may be used for routing with only local information, which holds significant promise for improving the performance of Internet routing.
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