论文标题
施特劳斯的传递网络模型的自由能密度功能
Free-energy density functional for Strauss's model of transitive networks
论文作者
论文摘要
图形集合模型是研究复杂网络的最重要的理论工具之一。其中，已证明指数随机图（ERG）在社交网络的分析中非常有用。在本文中，我们开发了一种从晶格气体的统计力学借用的技术，以解决Strauss的传递网络模型。该模型很久以前是作为具有高聚类的网络的ERG集合而引入的，并在三角形相互作用参数的临界值高于临界值之上表现出一阶相变，其中两种具有不同链路密度的不同类型的网络（或者，或者，或者，或者，不同的是不同的聚类）。与以前的平均场方法相比，我们的方法甚至可以准确地描述了小型网络，并且可以扩展到Strauss的经典模型之外 - 例如到具有不同类型节点的网络。这使我们能够以均匀的节点进行处理。我们为后者提供结果，并表明它们准确地重现了蒙特卡洛模拟的结果。
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.
