We show that hypernetworks can be regarded as posets which, in their turn, have a natural interpretation as simplicial complexes and, as such, are endowed with an intrinsic notion of curvature, namely the Forman Ricci curvature, that strongly correlates with the Euler characteristic of the simplicial complex. This approach, inspired by the work of E. Bloch, allows us to canonically associate a simplicial complex structure to a hypernetwork, directed or undirected. In particular, this greatly simplifying the geometric Persistent Homology method we previously proposed.

中文翻译：

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超网络：从词组到几何

我们证明超网络可以看作是姿势，而姿势本身又自然地解释为简单复形，因此具有固有的曲率概念，即Forman Ricci曲率，它与Euler的Euler特征密切相关。简单复合体。这种方法受E. Bloch的启发，使我们能够将简单复杂结构规范地关联到有向或无向的超网络。特别是，这大大简化了我们先前提出的几何持久同源性方法。