Strauss传递网络模型的自由能量密度泛函
Free-energy density functional for Strauss's model of transitive networks
摘要：
图的包围模型是研究复杂网络的重要理论工具之一。其中，指数随机图（ERG）已被证明是非常有用的分析社交网络。在本文中，我们开发了一种技术，借用统计力学的晶格气体，解决施特劳斯模型的过渡网络。这个模型很久以前就被引入作为高聚类网络的ERG集成，并在三角形相互作用参数的临界值以上表现出一阶相变，其中两种不同类型的网络具有不同的链接密度（或者，不同的聚类）共存。与以前的平均场方法相比，我们的方法准确地描述了即使是小网络，并可以扩展到施特劳斯的经典模型之外-例如，具有不同类型的节点的网络。例如，这允许我们处理具有节点同质性的模型。我们为后者提供了结果，并表明，他们准确地再现了蒙特卡罗模拟的结果。
英文摘要：
Ensemble models of graphs are one of the most important theoretical tools to study complex networks. Among them, exponential random graphs (ERGs) have proven to be very useful in the analysis of social networks. In this paper we develop a technique, borrowed from the statistical mechanics of lattice gases, to solve Strauss's model of transitive networks. This model was introduced long ago as an ERG ensemble for networks with high clustering and exhibits a first-order phase transition above a critical value of the triangle interaction parameter, where two different kinds of networks with different densities of links (or, alternatively, different clustering) coexist. Compared to previous mean-field approaches, our method describes accurately even small networks and can be extended beyond Strauss's classical model -- e.g. to networks with different types of nodes. This allows us to tackle, for instance, models with node homophily. We provide results for the latter and show that they accurately reproduce the outcome of Monte Carlo simulations.
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