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.

翻译：在网络分析中，识别起核心作用的顶点是一个基础性挑战。尽管传统的中心性度量已被广泛用于此目的，但现代网络日益增长的复杂性需要使用更精密的度量指标。Forman曲率的概念作为一类有前景的方法，近期受到了显著关注。我们定义了多重图（一类具有节点间多层连接特征的复杂网络）的Forman曲率，随后证明了该曲率在多重图背景下的关键性质，并展示了其在识别网络中处于中心位置的顶点方面的实用性。此外，通过与传统的图特征和图核进行一系列对比实验，我们证明了Forman曲率能够作为评估网络整体结构分类的有效度量指标。