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Coalescing involves gluing one or more rooted graphs onto another graph. Under specific conditions, it is possible to start with cospectral graphs that are coalesced in similar ways that will result in new cospectral graphs. We present a…

Communities in directed networks have often been characterized as regions with a high density of links, or as sets of nodes with certain patterns of connection. Our approach for community detection combines the optimization of a quality…

Because of the significant increase in size and complexity of the networks, the distributed computation of eigenvalues and eigenvectors of graph matrices has become very challenging and yet it remains as important as before. In this paper…

This paper proposes a multilayer graph model for the community detection from multiple observations. This is a very frequent situation, when different estimators are applied to infer graph edges from signals at its nodes, or when different…

Many real-world network are multilayer, with nontrivial correlations across layers. Here we show that these correlations amplify geometry in networks. We focus on mutual clustering--a measure of the amount of triangles that are present in…

The Laplacian matrix and its pseudo-inverse for a strongly connected directed graph is fundamental in computing many properties of a directed graph. Examples include random-walk centrality and betweenness measures, average hitting and…

Graph connection Laplacian (GCL) is a modern data analysis technique that is starting to be applied for the analysis of high dimensional and massive datasets. Motivated by this technique, we study matrices that are akin to the ones…

This paper aims to establish theoretical foundations of graph product multilayer networks (GPMNs), a family of multilayer networks that can be obtained as a graph product of two or more factor networks. Cartesian, direct (tensor), and…

Large graphs are natural mathematical models for describing the structure of the data in a wide variety of fields, such as web mining, social networks, information retrieval, biological networks, etc. For all these applications, automatic…

Problems from graph drawing, spectral clustering, network flow and graph partitioning can all be expressed in terms of graph Laplacian matrices. There are a variety of practical approaches to solving these problems in serial. However, as…

Spectral clustering (SC) is a popular clustering technique to find strongly connected communities on a graph. SC can be used in Graph Neural Networks (GNNs) to implement pooling operations that aggregate nodes belonging to the same cluster.…

In this paper we investigated the possibility to use the magnetic Laplacian to characterize directed graphs (a.k.a. networks). Many interesting results are obtained, including the finding that community structure is related to rotational…

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…

Modern network analysis often involves multi-layer network data in which the nodes are aligned, and the edges on each layer represent one of the multiple relations among the nodes. Current literature on multi-layer network data is mostly…

We study the time scales associated to diffusion processes that take place on multiplex networks, i.e. on a set of networks linked through interconnected layers. To this end, we propose the construction of a supra-Laplacian matrix, which…

This paper introduces a graph Laplacian regularization in the hyperspectral unmixing formulation. The proposed regularization relies upon the construction of a graph representation of the hyperspectral image. Each node in the graph…

The construction of a meaningful graph plays a crucial role in the success of many graph-based representations and algorithms for handling structured data, especially in the emerging field of graph signal processing. However, a meaningful…

In the interdisciplinary field of network science, a complex-valued network, with edges assigned complex weights, provides a more nuanced representation of relationships by capturing both the magnitude and phase of interactions.…

Diffusing a graph signal at multiple scales requires computing the action of the exponential of several multiples of the Laplacian matrix. We tighten a bound on the approximation error of truncated Chebyshev polynomial approximations of the…

Multilayer network analysis has become a vital tool for understanding different relationships and their interactions in a complex system, where each layer in a multilayer network depicts the topological structure of a group of nodes…