46 citations · 133 across the 42 of their papers we have counts for
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Bakry-Émery curvature sharpness and curvature flow in finite weighted graphs. II. Implementation
David Cushing, Supanat Kamtue, Shiping Liu +3
In this second part of a sequence of two papers, we discuss the implementation of a curvature flow on weighted graphs based on the Bakry-Émery calculus. This flow can be adapted to…
Graphs with nonnegative curvature outside a finite subset, harmonic functions and number of ends
Bobo Hua, Florentin Münch
We study graphs with nonnegative Bakry-Émery curvature or Ollivier curvature outside a finite subset. For such a graph, via introducing the discrete Gromov-Hausdorff convergence we…
Ollivier curvature, betweenness centrality and average distance
Florentin Münch
We give a new upper bound for the average graph distance in terms of the average Ollivier curvature. Here, the average Ollivier curvature is weighted with the edge betweenness cent…
Mixing time and expansion of non-negatively curved Markov chains
Florentin Münch, Justin Salez
We establish three remarkable consequences of non-negative curvature for sparse Markov chains. First, their conductance decreases logarithmically with the number of states. Second,…
Reflective Graphs, Ollivier curvature, effective diameter, and rigidity
Florentin Münch
We give a discrete Bonnet Myers type theorem for the effective diameter assuming positive Ollivier curvature. We prove that this diameter bound is attained if and only if the graph…
Extremal functions for the second-order Sobolev inequality on groups of polynomial growth
Bobo Hua, Ruowei Li, Florentin Münch
In this paper, we prove the second-order Sobolev inequalities on Cayley graphs of groups of polynomial growth. We use the discrete Concentration-Compactness principle to prove the…
Bakry-Émery curvature sharpness and curvature flow in finite weighted graphs. I. Theory
David Cushing, Supanat Kamtue, Shiping Liu +3
In this sequence of two papers, we introduce a curvature flow on (mixed) weighted graphs which is based on the Bakry-Émery calculus. The flow is described via a time-continuous evo…