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.
翻译:本文提出一组网络中心点,称为固定点中心点。 这个核心点点系通过与基本网络有关的固定移动式等同绘图点来定义。 这个中心点概念被立即扩展,以界定以图形为特征的无限图解的固定点中心点。 确定了这些中心点与基础图和图解在轻度假设下的变异的界限。 固定点中心点与不同的网络模型连接, 包括图形神经网络、网络上的静态和动态游戏以及Markov决策过程。