35 citations · 175 across the 14 of their papers we have counts for
4 papers · 1 filter
Effective resistance is more than distance: Laplacians, Simplices and the Schur complement
Karel Devriendt
This article discusses a geometric perspective on the well-known fact in graph theory that the effective resistance is a metric on the nodes of a graph. The classical proofs of thi…
Nonlinear consensus on networks: equilibria, effective resistance and trees of motifs
Marc Homs-Dones, Karel Devriendt, Renaud Lambiotte
We study a generic family of nonlinear dynamics on undirected networks generalising linear consensus. We find a compact expression for its equilibrium points in terms of the topolo…
Variance and covariance of distributions on graphs
Karel Devriendt, Samuel Martin-Gutierrez, Renaud Lambiotte
We develop a theory to measure the variance and covariance of probability distributions defined on the nodes of a graph, which takes into account the distance between nodes. Our ap…
Non-linear network dynamics with consensus-dissensus bifurcation
Karel Devriendt, Renaud Lambiotte
We study a non-linear dynamical system on networks inspired by the pitchfork bifurcation normal form. The system has several interesting interpretations: as an interconnection of s…