Related papers: Harmonic Analysis on Directed Networks: A Biorthog…
We consider the problem of designing spectral graph filters for the construction of dictionaries of atoms that can be used to efficiently represent signals residing on weighted graphs. While the filters used in previous spectral graph…
Renormalization of complex networks requires principled criteria for assessing whether a coarse-graining preserves dynamical content. We prove that discrete harmonic morphisms -- surjective maps preserving harmonic functions -- provide the…
Graph Fourier transform (GFT) is one of the fundamental tools in graph signal processing to decompose graph signals into different frequency components and to represent graph signals with strong correlation by different modes of variation…
It has been recognized for quite some time that for some matrices the spectra are not enough to tell the complete story of the dynamics of the system, even for linear ODEs. While it is true that the eigenvalues control the asymptotic…
We propose an algebraic framework for generalized graph Laplacians which unifies the study of resistor networks, the critical group, and the eigenvalues of the Laplacian and adjacency matrices. Given a graph with boundary $G$ together with…
Hypergraphs provide a natural way to represent higher-order interactions among multiple entities. While undirected hypergraphs have been extensively studied, the case of directed hypergraphs, which can model oriented group interactions,…
Representing data residing on a graph as a linear combination of building block signals can enable efficient and insightful visual or statistical analysis of the data, and such representations prove useful as regularizers in signal…
Learning the graph Laplacian from observed data is one of the most investigated and fundamental tasks in Graph Signal Processing (GSP). Different variants of the Laplacian, such as the combinatorial, signless or signed Laplacians have been…
This work presents a new method for symmetrization of directed graphs that constructs an undirected graph with equivalent pairwise effective resistances as a given directed graph. Consequently a graph metric, square root of effective…
In classic graph signal processing, given a real-valued graph signal, its graph Fourier transform is typically defined as the series of inner products between the signal and each eigenvector of the graph Laplacian. Unfortunately, this…
Graph neural networks (GNNs) have shown remarkable performance on homophilic graph data while being far less impressive when handling non-homophilic graph data due to the inherent low-pass filtering property of GNNs. In general, since…
We consider bipartite tight-binding graphs composed by $N$ nodes split into two sets of equal size: one set containing nodes with on-site loss, the other set having nodes with on-site gain. The nodes are connected randomly with probability…
In the past two decades, the field of applied finance has tremendously benefited from graph theory. As a result, novel methods ranging from asset network estimation to hierarchical asset selection and portfolio allocation are now part of…
This paper extends the definitions of effective resistance and effective conductance to characterize the overall relation (positive coupling or antagonism) between any two disjoint sets of nodes in a signed graph. It generalizes the…
Graph fractional Fourier transform (GFRFT) is an extension of graph Fourier transform (GFT) that provides an additional fractional analysis tool for graph signal processing (GSP) by generalizing temporal-vertex domain Fourier analysis to…
We investigate connections between the symmetries (automorphisms) of a graph and its spectral properties. Whenever a graph has a symmetry, i.e. a nontrivial automorphism $\phi$, it is possible to use $\phi$ to decompose any matrix…
Diffusion over networks has recently been used to define spatiotemporal scales and extend Kadanoff block spins of Euclidean space to supernodes of networks in the Laplacian renormalization group (LRG). Yet, its ad hoc coarse-graining…
Separating multiple graph signals from a single observed mixture is an inherently ill-posed problem that traditionally relies on restrictive and handcrafted priors. This letter addresses this challenge by proposing an unsupervised learnable…
The Hermitian adjacency matrices of digraphs based on the sixth root of unity were introduced in [B. Mohar, A new kind of Hermitian matrices for digraphs, Linear Alg. Appl. (2020)]. They appear to be the most natural choice for the spectral…
The lack of anisotropic kernels in graph neural networks (GNNs) strongly limits their expressiveness, contributing to well-known issues such as over-smoothing. To overcome this limitation, we propose the first globally consistent…