A Simple Differential Geometry for Networks and its Generalizations

@inproceedings{Saucan2019ASD,
  title={A Simple Differential Geometry for Networks and its Generalizations},
  author={Emil Saucan and Areejit Samal and Jurgen Jost},
  booktitle={COMPLEX NETWORKS},
  year={2019}
}
Based on two classical notions of curvature for curves in general metric spaces, namely the Menger and Haantjes curvatures, we introduce new definitions of sectional, Ricci and scalar curvature for networks and their higher dimensional counterparts. These new types of curvature, that apply to weighted and unweighted, directed or undirected networks, are far more intuitive and easier to compute, than other network curvatures. In particular, the proposed curvatures based on the interpretation of… 

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