The Cactus Criterion: When Nonlinear Hodge Theory Reduces to Linear on Graphs

Sebastian Pardo-Guerra, Anil Thapa, Jonathan Washburn

Let $G$ be a finite connected simple graph with a chosen orientation of its edges. For the edge potential $\psi (t)=\cosh t-1,$ we minimize ${\sum }_{e\in E^{\to }}\psi (z_e)$ over each affine c…