This paper studies learning meaningful node representations for signed graphs, where both positive and negative links exist. problem has been widely studied by meticulously designing expressive graph neural networks, as well capturing the structural information of through traditional structure decomposition methods, e.g., spectral theory. In this paper, we propose a novel representation framewo...

The toughness $t(G)$ of a graph $G=(V,E)$ is defined as $t(G)=\min\{\frac{|S|}{c(G-S)}\}$, in which the minimum taken over all $S\subset V$ such that $G-S$ disconnected, where $c(G-S)$ denotes number components $G-S$. We present two tight lower bounds for terms Laplacian eigenvalues and provide strong support conjecture better bound which, if true, implies both bounds, improves generalizes know...

Image deblurring is a relevant problem in many fields of science and engineering. To solve this problem, different approaches have been proposed, and, among the various methods, variational ones are extremely popular. These substitute original with minimization where functional composed two terms, data fidelity term regularization term. In paper we propose, classical non-negative constrained $\...

We introduce a one-parameter family of massive Laplacian operators (∆)k∈[0,1) defined on isoradial graphs, involving elliptic functions. We prove an explicit formula for minus the inverse of ∆, the massive Green function, which has the remarkable property of only depending on the local geometry of the graph, and compute its asymptotics. We study the corresponding statistical mechanics model of ...