121 citations · 260 across the 28 of their papers we have counts for
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A Simple Differential Geometry for Complex Networks
Emil Saucan, Areejit Samal, Jürgen Jost
We introduce new definitions of sectional, Ricci and scalar curvature for networks and their higher dimensional counterparts, derived from two classical notions of curvature for cu…
A Simple Differential Geometry for Networks and its Generalizations
Emil Saucan, Areejit Samal, Jürgen Jost
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 sca…
Metric Curvatures and their Applications 2: Metric Ricci Curvature and Flow
Emil Saucan
In this second part of our overview of the different metric curvatures and their various applications, we concentrate on the Ricci curvature and flow for polyhedral surfaces and hi…
Discrete Ricci curvatures for directed networks
Emil Saucan, R. P. Sreejith, R. P. Vivek-Ananth +2
A goal in network science is the geometrical characterization of complex networks. In this direction, we have recently introduced Forman's discretization of Ricci curvature to the…