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A metrized graph is a compact singular 1-manifold endowed with a metric. A given metrized graph can be modelled by a family of weighted combinatorial graphs. If one chooses a sequence of models from this family such that the vertices become…

With the rapid development of the World Wide Web (WWW), heterogeneous graphs (HG) have explosive growth. Recently, heterogeneous graph neural network (HGNN) has shown great potential in learning on HG. Current studies of HGNN mainly focus…

The application of the network approach to the urban case poses several questions in terms of how to deal with metric distances, what kind of graph representation to use, what kind of measures to investigate, how to deepen the correlation…

Graph learning from data represents a canonical problem that has received substantial attention in the literature. However, insufficient work has been done in incorporating prior structural knowledge onto the learning of underlying…

This work builds on our recent work on a distributed optimization algorithm for graphs with directed unreliable communications. We show its linear convergence when we take either the proximal of each function or an affine minorant for when…

In many real-world networks the ability to synchronize is a key property for its performance. Examples include power-grid, sensor, and neuron networks as well as consensus formation. Recent work on undirected networks with diffusive…

Joint network topology inference represents a canonical problem of jointly learning multiple graph Laplacian matrices from heterogeneous graph signals. In such a problem, a widely employed assumption is that of a simple common component…

In this note, we study Laplacians on graphs for which connectivity within certain subgraphs tends to infinity. Our main focus are graphs sharing a common node set on which edge weights within certain clusters grow to infinity. As…

Graph Neural Networks have emerged as the most popular architecture for graph-level learning, including graph classification and regression tasks, which frequently arise in areas such as biochemistry and drug discovery. Achieving good…

We consider the class of simple graphs with large algebraic connectivity (the second-smallest eigenvalue of the Laplacian matrix). For this class of graphs we determine the asymptotic behavior of the number of Eulerian orientations. In…

In this paper, we initiate the study of the dynamic maintenance of $2$-edge-connectivity relationships in directed graphs. We present an algorithm that can update the $2$-edge-connected blocks of a directed graph with $n$ vertices through a…

Graph classification benchmarks, vital for assessing and developing graph neural networks (GNNs), have recently been scrutinized, as simple methods like MLPs have demonstrated comparable performance. This leads to an important question: Do…

In graph signal processing, data samples are associated to vertices on a graph, while edge weights represent similarities between those samples. We propose a convex optimization problem to learn sparse well connected graphs from data. We…

We present a method to extract temporal hypergraphs from sequences of 2-dimensional functions obtained as solutions to Optimal Transport problems. We investigate optimality principles exhibited by these solutions from the point of view of…

The dynamical behavior of networked complex systems is shaped not only by the direct links among the units, but also by the long-range interactions occurring through the many existing paths connecting the network nodes. In this work, we…

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…

Learning a graph with a specific structure is essential for interpretability and identification of the relationships among data. It is well known that structured graph learning from observed samples is an NP-hard combinatorial problem. In…

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…

Accurate routing network status estimation is a key component in Software Defined Networking. However, existing deep-learning-based methods for modeling network routing are not able to extrapolate towards unseen feature distributions. Nor…

Determining the effect of structural perturbations on the eigenvalue spectra of networks is an important problem because the spectra characterize not only their topological structures, but also their dynamical behavior, such as…