论文标题
路径同源性和时间网络
Path homology and temporal networks
论文作者
论文摘要
我们提出了一种算法来计算简单挖掘的路径同源性，并使用它来拓泊论分析各种小型挖掘，以分析复杂的时间网络，这些分析表现出诸如基础基序之类的图形。分析的挖掘物包括所有挖掘物，有向的无环图和无向图，直至某些数量的顶点以及一些特殊构造的情况。使用此分析中的信息，我们确定了三个时间网络中有助于路径同源性$ 2 $的小图形图像，并将这些挖掘物与网络行为联系起来。我们得出的结论是，路径同源性可以洞悉时间网络结构，反之亦然。
We present an algorithm to compute path homology for simple digraphs, and use it to topologically analyze various small digraphs en route to an analysis of complex temporal networks which exhibit such digraphs as underlying motifs. The digraphs analyzed include all digraphs, directed acyclic graphs, and undirected graphs up to certain numbers of vertices, as well as some specially constructed cases. Using information from this analysis, we identify small digraphs contributing to path homology in dimension $2$ for three temporal networks, and relate these digraphs to network behavior. We conclude that path homology can provide insight into temporal network structure and vice versa.
