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Networks are a widely used and efficient paradigm to model real-world systems where basic units interact pairwise. Many body interactions are often at play, and cannot be modelled by resorting to binary exchanges. In this work, we consider…
Complex time-varying networks are prominent models for a wide variety of spatiotemporal phenomena. The functioning of networks depends crucially on their connectivity, yet reliable techniques for learning communities in time-evolving…
Reasoning about the physical world requires models that are endowed with the right inductive biases to learn the underlying dynamics. Recent works improve generalization for predicting trajectories by learning the Hamiltonian or Lagrangian…
To describe the flow of a miscible quantity on a network, we introduce the graph wave equation where the standard continuous Laplacian is replaced by the graph Laplacian. This is a natural description of an array of inductances and…
This paper deals with spectral graph theory issues related to questions of monotonicity and comparison of eigenvalues. We consider finite directed graphs with non symmetric edge weights and we introduce a special self-adjoint operator as…
In a large variety of systems (biological, physical, social etc.), synchronization occurs when different oscillating objects tune their rhythm when they interact with each other. The different underlying network defining the connectivity…
Design of filters for graph signal processing benefits from knowledge of the spectral decomposition of matrices that encode graphs, such as the adjacency matrix and the Laplacian matrix, used to define the shift operator. For shift matrices…
Starting with an isolated vertex, here we construct a threshold hypergraph by repeatedly adding an isolated vertex or a $k$-dominating vertex set. We represent a threshold hypergraph by a string of non-negative integers and find the…
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…
Let $H_n$ be the linear heptagonal networks with $2n$ heptagons. We study the structure properties and the eigenvalues of the linear heptagonal networks. According to the Laplacian polynomial of $H_n$, we utilize the decomposition theorem.…
Spectral approaches of network analysis heavily rely upon the eigendecomposition of the graph Laplacian. For instance, in graph signal processing, the Laplacian eigendecomposition is used to define the graph Fourier transform and then…
Graph generative modelling has become an essential task due to the wide range of applications in chemistry, biology, social networks, and knowledge representation. In this work, we propose a novel framework for generating graphs by adapting…
We propose a procedure to generate dynamical networks with bursty, possibly repetitive and correlated temporal behaviors. Regarding any weighted directed graph as being composed of the accumulation of paths between its nodes, our…
We propose a framework for achieving perfect synchronization in complex networks of Sakaguchi-Kuramoto oscillators in presence of higher order interactions (simplicial complexes) at a targeted point in the parameter space. It is achieved by…
This work explores the definiteness of the weighted graph Laplacian matrix with negative edge weights. The definiteness of the weighted Laplacian is studied in terms of certain matrices that are related via congruent and similarity…
Simplicial complexes are generalizations of graphs that describe higher-order network interactions among nodes in the graph. Network dynamics described by graph Laplacian flows have been widely studied in network science and control theory,…
For joint inference over multiple variables, a variety of structured prediction techniques have been developed to model correlations among variables and thereby improve predictions. However, many classical approaches suffer from one of two…
Traditionally, interaction systems have been described as networks, where links encode information on the pairwise influences among the nodes. Yet, in many systems, interactions take place in larger groups. Recent work has shown that…
We study the synchronization properties of a generic networked dynamical system, and show that, under a suitable approximation, the transition to synchronization can be predicted with the only help of eigenvalues and eigenvectors of the…
The interactions between the components of complex networks are often directed. Proper modeling of such systems frequently requires the construction of ensembles of digraphs with a given sequence of in- and out-degrees. As the number of…