Steinerberger proposed a notion of curvature on graphs (J. Graph Theory, 2023). We show
that nonnegative curvature is almost preserved under three graph operations. We …

Abstract The resistance distance\(r_ {G}(u, v)\) between two vertices u and v of a graph G is
defined as the net effective resistance between them in the electric network constructed from …

The fields of effective resistance and optimal transport on graphs are filled with rich
connections to combinatorics, geometry, machine learning, and beyond. In this article we put …

Discrete curvatures are quantities associated to the nodes and edges of a graph that reflect
the local geometry around them. These curvatures have a rich mathematical theory and they …

Let $ G $ be a connected graph. The resistance distance between two vertices $ u $ and $ v
$ of $ G $, denoted by $ R_ {G}[u, v] $, is defined as the net effective resistance between …

In this note, we provide Steinerberger curvature formulas for block graphs, discuss curvature
relations between two graphs and the graph obtained by connecting them via a bridge, and …

In this paper, we introduce a new notion of curvature on the edges of a graph that is defined
in terms of effective resistances. We call this the Ricci--Foster curvature. We study the Ricci …

Devriendt and Lambiotte recently introduced the\emph {node resistance curvature}, a notion
of graph curvature based on the effective resistance matrix. In this paper, we begin the study …

In this paper, we study the Ricci curvature defined by Yong Lin, Linyuan Lu and Shing-Tung
Yau, and characterize several graphs with constant positive Ricci curvature. We find the …

This article introduces and studies a new class of graphs motivated by discrete curvature.
We call a graph resistance nonnegative if there exists a distribution on its spanning trees …