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Identifying vertices that play a central role is a fundamental problem innetwork analysis. Although traditional centrality measures have been widelyused for this purpose, the growing complexity of contemporary networksnecessitates more sophisticated indicators. Forman curvature has recentlyemerged as a promising approach. In this paper, we define Forman curvature formultilayer networks, a class of complex networks characterized by multipletypes of connections or layers between nodes, which are increasingly used tomodel intricate real-world phenomena. We establish the key properties of Formancurvature in the context of multilayer networks and demonstrate its utility foridentifying vertices that hold central positions within these networks.Furthermore, we show that Forman curvature can also serve as an effective toolfor the structural classification of entire multilayer networks.

Vertex evaluation of multiplex graphs using Forman Curvature