论文标题
网络的定点中心性
Fixed-Point Centrality for Networks
论文作者
论文摘要
本文提出了一个称为定点中心的网络中心家庭。这种中心性家族是通过与基础网络相关的置换置换量映射的固定点来定义的。这种中心概念立即扩展到定义以图形为特征的无限图的定点中心。在轻度假设下，这种中心基础图和图形的变化的变化界限已建立。定点中心与网络上的各种不同模型连接，包括图形神经网络，网络上的静态和动态游戏以及马尔可夫决策过程。
This paper proposes a family of network centralities called fixed-point centralities. This centrality family is defined via the fixed point of permutation equivariant mappings related to the underlying network. Such a centrality notion is immediately extended to define fixed-point centralities for infinite graphs characterized by graphons. Variation bounds of such centralities with respect to the variations of the underlying graphs and graphons under mild assumptions are established. Fixed-point centralities connect with a variety of different models on networks including graph neural networks, static and dynamic games on networks, and Markov decision processes.
