An Optimization-based Approach To Node Role Discovery in Networks: Approximating Equitable Partitions

Michael Scholkemper, Michael T Schaub

Keywords: Role Extraction, Graph Learning, Node Embeddings, Weisfeiler Lehman, Equitable Partition

TL;DR: We propose a novel perspective on role extraction grounded in the theory concerning graph isomorphism and present a cost function that is to be optimized in order to extract the roles.

Abstract: Similar to community detection, partitioning the nodes of a complex network according to their structural roles aims to identify fundamental building blocks of a network, which can be used, e.g., to find simplified descriptions of the network connectivity, to derive reduced order models for dynamical processes unfolding on processes, or as ingredients for various network analysis and 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 and two associated optimization problems (cost functions) grounded in ideas related to graph-isomorphism tests, the Weisfeiler-Leman algorithm and equitable partitions. We present theoretical guarantees and 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.

Submission Number: 7411