论文标题
边缘/并发顶点模型中的相变
Phase Transitions in the Edge/Concurrent Vertex Model
论文作者
论文摘要
尽管众所周知，某些指数族的随机图模型（ERGM）家族表现出相变（其中小参数变化会导致图形结构的质量变化），但其他模型的行为仍然很少了解。最近，克里维茨基（Krivitsky）和莫里斯（Morris）报道了边缘/并发顶点家族中先前未观察到的相变（性接触网络模型的简单起点）。在这里，我们检查了此相变，这表明与与并发顶点相关的订单参数相关的订单参数是一阶转变。这种过渡源于在招募顶点到并发阶段的合作性较弱，这在某些应用中可能不是理想的财产。
Although it is well-known that some exponential family random graph model (ERGM) families exhibit phase transitions (in which small parameter changes lead to qualitative changes in graph structure), the behavior of other models is still poorly understood. Recently, Krivitsky and Morris have reported a previously unobserved phase transition in the edge/concurrent vertex family (a simple starting point for models of sexual contact networks). Here, we examine this phase transition, showing it to be a first order transition with respect to an order parameter associated with the fraction of concurrent vertices. This transition stems from weak cooperativity in the recruitment of vertices to the concurrent phase, which may not be a desirable property in some applications.
