随机网络上的最短路径渗流
Shortest-path percolation on random networks
AI总结：
提出描述交通网络资源消耗的键渗流模型，研究均匀随机图中最短路径渗流转变，发现有限预算下转变同普通渗流，无限预算下巨连通分量突然碎裂。
摘要：
我们提出了一种键渗流模型，旨在描述交通网络中资源的消耗及其最终耗尽。如果构成连接需求起讫节点的最小长度路径的边低于某个预算，则将其移除。随着节点对被需求且边被移除，图的宏观连通分量消失，即图经历了渗流转变。在此，我们在均匀随机图中研究了这种最短路径渗流转变，其中需求起讫节点对是随机生成的，并通过有限尺寸标度分析对其进行了充分表征。如果预算有限，该转变与普通渗流的转变相同，其中随着边从图中被移除，单个巨簇逐渐缩小；对于无限预算，该转变变得比普通渗流的转变更加突变，其特征是巨连通分量突然碎裂成大量大小相似的簇。
英文摘要：
We propose a bond-percolation model intended to describe the consumption, and eventual exhaustion, of resources in transport networks. Edges forming minimum-length paths connecting demanded origin-destination nodes are removed if below a certain budget. As pairs of nodes are demanded and edges are removed, the macroscopic connected component of the graph disappears, i.e., the graph undergoes a percolation transition. Here, we study such a shortest-path-percolation transition in homogeneous random graphs where pairs of demanded origin-destination nodes are randomly generated, and fully characterize it by means of finite-size scaling analysis. If budget is finite, the transition is identical to the one of ordinary percolation, where a single giant cluster shrinks as edges are removed from the graph; for infinite budget, the transition becomes more abrupt than the one of ordinary percolation, being characterized by the sudden fragmentation of the giant connected component into a multitude of clusters of similar size.
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