论文标题
复杂网络中的关键现象：从无标度到随机网络
Critical Phenomena in Complex Networks: from Scale-free to Random Networks
论文作者
论文摘要
在传统的统计物理框架内，我们研究了一类配置网络模型中具有隐藏变量的临界现象，该变量控制了节点对之间的联系。我们发现平均节点程度，预期边缘数量以及Landau和Helmholtz自由能的分析表达式是温度和节点数量的函数。我们表明，网络的温度是一个控制整个网络中平均节点度的参数，以及从无连接的图表到幂法度（无标度）和随机图的过渡。随着温度的升高，程度分布从较低温度的幂律度分布变为高温的泊松样分布。我们还表明，所谓的A型网络中的相变会导致网络拓扑的根本结构变化。在临界温度以下，该图完全断开。在临界温度上方，图形连接，并出现巨大组件。
Within the conventional statistical physics framework, we study critical phenomena in a class of configuration network models with hidden variables controlling links between pairs of nodes. We find analytical expressions for the average node degree, the expected number of edges, and the Landau and Helmholtz free energies, as a function of the temperature and number of nodes. We show that the network's temperature is a parameter that controls the average node degree in the whole network and the transition from unconnected graphs to a power-law degree (scale-free) and random graphs. With increasing temperature, the degree distribution is changed from power-law degree distribution, for lower temperatures, to a Poisson-like distribution for high temperatures. We also show that phase transition in the so-called Type A networks leads to fundamental structural changes in the network topology. Below the critical temperature, the graph is completely disconnected. Above the critical temperature, the graph becomes connected, and a giant component appears.
