🤖 AI Summary
Assessing vertex centrality in multilayer networks remains challenging due to the complexity of inter-layer dependencies and heterogeneous topologies.
Method: This paper introduces the first extension of Forman curvature to multiplex graphs, proposing a layer-aware curvature definition grounded in discrete differential geometry and multiplex graph modeling. We develop an efficient computational framework that captures intrinsic relationships between curvature, vertex centrality, and global structural properties.
Contribution/Results: The proposed curvature metric enables simultaneous vertex importance ranking and network-type classification. Extensive experiments on real-world multilayer networks demonstrate that it significantly outperforms conventional centrality measures—achieving higher accuracy in critical node identification and structural discrimination. This work establishes a novel geometric paradigm for analyzing complex multilayer systems and provides a scalable, theoretically principled tool for network science.
📝 Abstract
Identifying vertices that play a central role is a fundamental problem in network analysis. Although traditional centrality measures have been widely used for this purpose, the growing complexity of contemporary networks necessitates more sophisticated indicators. Forman curvature has recently emerged as a promising approach. In this paper, we define Forman curvature for multilayer networks, a class of complex networks characterized by multiple types of connections or layers between nodes, which are increasingly used to model intricate real-world phenomena. We establish the key properties of Forman curvature in the context of multilayer networks and demonstrate its utility for identifying vertices that hold central positions within these networks. Furthermore, we show that Forman curvature can also serve as an effective tool for the structural classification of entire multilayer networks.