Vertex evaluation of multiplex graphs using Forman Curvature
Taiki Yamada
TL;DR
This work extends Forman curvature to doubly-weighted multiplex graphs by introducing compile graphs and a vertex-based curvature framework. It defines a comprehensive evaluation CE based on inter-layer curvature and develops a three-step algorithm to identify structurally important vertices across layers, demonstrating its utility for vulnerability analysis and network classification. Empirical results show that CE features provide complementary information to traditional metrics and improve classification when combined with graph kernels, with inter-layer curvature offering novel cross-layer insights. The approach offers a practical, scalable tool for analyzing complex weighted multilayer systems and suggests directions for deeper study of inter-layer curvature effects.
Abstract
The identification of vertices that play a central role in network analysis is a fundamental challenge. Although traditional centrality measures have been extensively employed for this purpose, the increasing complexity of modern networks necessitates the use of sophisticated metrics. The concept of Forman curvature has recently garnered significant attention as a promising approach. We define the Forman curvature for multiplex graphs, which are a category of complex networks characterized by multiple layers of connections between nodes. We then prove the key properties of the Forman curvature in the context of multiplex graphs and show its usefulness in identifying vertices occupying central positions within these networks. Moreover, through a series of comparative experiments with traditional graph features and graph kernels, we demonstrate that the Forman curvature can function as an effective metric for classifying the overall structure of networks.