124 citations · 548 across the 41 of their papers we have counts for
6 papers · 1 filter
Geometry of Data
Parvaneh Joharinad, Jürgen Jost
Topological data analysis asks when balls in a metric space intersect. Geometric data analysis asks how much balls have to be enlarged to intersect. We connect this princip…
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…
Topology and curvature of metric spaces
Parvaneh Joharinad, Jürgen Jost
We develop a new concept of non-positive curvature for metric spaces, based on intersection patterns of closed balls. In contrast to the synthetic approaches of Alexandrov and Bues…
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…
Harmonic nets in metric spaces
J. Jost, L. Todjihounde
We investigate harmonic maps from weighted graphs into metric spaces that locally admit unique centers of gravity, like Alexandrov spaces with upper curvature bounds. We prove an e…