一种基于优化的网络节点角色发现方法：近似等权划分
An Optimization-based Approach To Node Role Discovery in Networks: Approximating Equitable Partitions
AI总结：
本文提出一种基于优化的节点角色发现方法，通过图同构测试与等权划分定义角色并给出理论保证，同时构建角色注入划分基准进行验证。
摘要：
与社区检测类似，根据节点的结构角色对网络节点进行划分，旨在识别网络的基本构建块。所得到的划分可以用于简化网络连通性的描述，为在网络上展开的动力学过程推导降阶模型，或者作为各种图挖掘任务的组成部分。在本工作中，我们对角色提取问题及其与社区检测的差异提供了一个新的视角，并给出了与图同构测试、Weisfeiler-Leman算法和等权划分相关的节点角色定义。我们研究了两个基于图同构测试思想的关联优化问题（代价函数），并给出了与这些问题解相关的理论保证。最后，我们通过一种新颖的“角色注入划分基准”——一个网络模型，从中我们可以以随机方式采样节点被赋予不同角色的网络——来验证我们的方法。
英文摘要：
Similar to community detection, partitioning the nodes of a network according to their structural roles aims to identify fundamental building blocks of a network. The found partitions can be used, e.g., to simplify descriptions of the network connectivity, to derive reduced order models for dynamical processes unfolding on processes, or as ingredients for various graph mining tasks. In this work, we offer a fresh look on the problem of role extraction and its differences to community detection and present a definition of node roles related to graph-isomorphism tests, the Weisfeiler-Leman algorithm and equitable partitions. We study two associated optimization problems (cost functions) grounded in ideas from graph isomorphism testing, and present theoretical guarantees associated to the solutions of these problems. Finally, we validate our approach via a novel "role-infused partition benchmark", a network model from which we can sample networks in which nodes are endowed with different roles in a stochastic way.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
