论文标题
顶点与子图中心的区别：Estrada的猜想证明和一些概括
Vertex distinction with subgraph centrality: a proof of Estrada's conjecture and some generalizations
论文作者
论文摘要
中心度度量用于网络科学中，以确定图表上信息和动态传输的最重要的顶点。这些措施之一是由埃斯特拉达（Estrada）和合作者引入的，是$β$ -subgraph的中心性，它基于矩阵$βa$的指数，其中$ a $是图形的邻接矩阵，$β$是一个真实的参数（“倒数温度”）。我们证明，对于代数$β$，两个具有相等$β$ - 纸的中心性的顶点必然是合适的。我们进一步表明，两个这样的顶点必须具有相同的程度和特征向量中心。我们的结果解决了埃斯特拉达的猜想，以及克洛斯特，克拉尔和沙利文引起的概括。我们还讨论了结果的可能扩展。
Centrality measures are used in network science to identify the most important vertices for transmission of information and dynamics on a graph. One of these measures, introduced by Estrada and collaborators, is the $β$-subgraph centrality, which is based on the exponential of the matrix $βA$, where $A$ is the adjacency matrix of the graph and $β$ is a real parameter ("inverse temperature"). We prove that for algebraic $β$, two vertices with equal $β$-subgraph centrality are necessarily cospectral. We further show that two such vertices must have the same degree and eigenvector centralities. Our results settle a conjecture of Estrada and a generalization of it due to Kloster, Král and Sullivan. We also discuss possible extensions of our results.
