Global synchronization beyond dense graphs: the case of threshold graphs

Hongjin Wu, Ulrik Brandes

Given a graph \(G\) with adjacency matrix \(A\), consider the homogeneous Kuramoto energy $E_G(\mathbf{\theta }):=\frac{1}{2}{\sum }_{1\le i,j\le n}{A}_{ij}(1-\cos ({\theta }_i-{\theta }_j))$. W…