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Multilayer networks generalize single-layered connectivity data in several directions. These generalizations include, among others, settings where multiple types of edges are observed among the same set of nodes (edge-colored networks) or…

The proliferation of models for networks raises challenging problems of model selection: the data are sparse and globally dependent, and models are typically high-dimensional and have large numbers of latent variables. Together, these…

Relationship between agents can be conveniently represented by graphs. When these relationships have different modalities, they are better modelled by multilayer graphs where each layer is associated with one modality. Such graphs arise…

Compound graphs are networks in which vertices can be grouped into larger subsets, with these subsets capable of further grouping, resulting in a nesting that can be many levels deep. In several applications, including biological workflows,…

Many real-world complex networks are best modeled as bipartite (or 2-mode) graphs, where nodes are divided into two sets with links connecting one side to the other. However, there is currently a lack of methods to analyze properly such…

A graph covering projection, also referred to as a locally bijective homomorphism, is a mapping between the vertices and edges of two graphs that preserves incidences and is a local bijection. This concept originates in topological graph…

Structural changes in a network representation of a system (e.g.,different experimental conditions, time evolution), can provide insight on its organization, function and on how it responds to external perturbations. The deeper…

We introduce propagation kernels, a general graph-kernel framework for efficiently measuring the similarity of structured data. Propagation kernels are based on monitoring how information spreads through a set of given graphs. They leverage…

Biological and technological networks contain patterns, termed network motifs, which occur far more often than in randomized networks. Network motifs were suggested to be elementary building blocks that carry out key functions in the…

This paper presents a general framework for linear circuit analysis based on elementary aspects of projective geometry. We use a flexible approach in which no a priori assignment of an electrical nature to the circuit branches is necessary.…

Complex networks possess a rich, multi-scale structure reflecting the dynamical and functional organization of the systems they model. Often there is a need to analyze multiple networks simultaneously, to model a system by more than one…

In a previous paper, the authors developed a method for computing normal forms of dynamical systems with a coupled cell network structure. We now apply this theory to one-parameter families of homogeneous feed-forward chains with…

Clustering by projection has been proposed as a way to preserve network structure in linear multi-agent systems. Here, we extend this approach to a class of nonlinear network systems. Additionally, we generalize our clustering method which…

The ability to control a complex network towards a desired behavior relies on our understanding of the complex nature of these social and technological networks. The existence of numerous control schemes in a network promotes us to wonder:…

The representation of complex systems as networks is inappropriate for the study of certain problems. We show several examples of social, biological, ecological and technological systems where the use of complex networks gives very limited…

Given a set of points in the plane, we want to establish a connection network between these points that consists of several disjoint layers. Motivated by sensor networks, we want that each layer is spanning and plane, and that no edge is…

Bipartite networks are a well known strategy to study a variety of phenomena. The commonly used method to deal with this type of network is to project the bipartite data into a unipartite weighted graph and then using a backboning technique…

This paper presents a model architecture for encoding the representations of part-whole hierarchies in images in form of a graph. The idea is to divide the image into patches of different levels and then treat all of these patches as nodes…

We define a novel type of ensemble Graph Convolutional Network (GCN) model. Using optimized linear projection operators to map between spatial scales of graph, this ensemble model learns to aggregate information from each scale for its…

We propose a method for characterizing large complex networks by introducing a new matrix structure, unique for a given network, which encodes structural information; provides useful visualization, even for very large networks; and allows…