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Multivariate graphs are prolific across many fields, including transportation and neuroscience. A key task in graph analysis is the exploration of connectivity, to, for example, analyze how signals flow through neurons, or to explore how…

The (variational) graph auto-encoder and its variants have been popularly used for representation learning on graph-structured data. While the encoder is often a powerful graph convolutional network, the decoder reconstructs the graph…

Decompositions of tensors into factor matrices, which interact through a core tensor, have found numerous applications in signal processing and machine learning. A more general tensor model which represents data as an ordered network of…

We use the k-core decomposition to visualize large scale complex networks in two dimensions. This decomposition, based on a recursive pruning of the least connected vertices, allows to disentangle the hierarchical structure of networks by…

Analyzing interconnection structures among underlying entities or objects in a dataset through the use of graph analytics has been shown to provide tremendous value in many application domains. However, graphs are not the primary…

A simple-triangle graph is the intersection graph of triangles that are defined by a point on a horizontal line and an interval on another horizontal line. The time complexity of the recognition problem for simple-triangle graphs was a…

A matching is said to be disconnected if the saturated vertices induce a disconnected subgraph and induced if the saturated vertices induce a 1-regular graph. The disconnected and induced matching numbers are defined as the maximum…

A hole in a graph is an induced cycle on at least four vertices. A graph is Berge if it has no odd hole and if its complement has no odd hole. In 2002, Chudnovsky, Robertson, Seymour and Thomas proved a decomposition theorem for Berge…

Neural networks are the pinnacle of Artificial Intelligence, as in recent years we witnessed many novel architectures, learning and optimization techniques for deep learning. Capitalizing on the fact that neural networks inherently…

Given a connected undirected graph G = [V; E] where |E| =2(|V| -1), we present two algorithms to check if G can be decomposed into two edge disjoint spanning trees, and provide such a decomposition when it exists. Unlike previous algorithms…

We study a problem of reconstruction of connected graphs where the input gives all subsets of size k that induce a connected subgraph. Originally introduced by Bastide et al. (WG 2023) for triples ($k=3$), this problem received…

This paper studies the nucleus decomposition problem, which has been shown to be useful in finding dense substructures in graphs. We present a novel parallel algorithm that is efficient both in theory and in practice. Our algorithm achieves…

(Hyper)Graph decomposition is a family of problems that aim to break down large (hyper)graphs into smaller sub(hyper)graphs for easier analysis. The importance of this lies in its ability to enable efficient computation on large and complex…

Graphlets are defined as k-node connected induced subgraph patterns. For an undirected graph, 3-node graphlets include close triangle and open triangle. When k = 4, there are six types of graphlets, e.g., tailed-triangle and clique are two…

Graph clustering or community detection constitutes an important task for investigating the internal structure of graphs, with a plethora of applications in several domains. Traditional techniques for graph clustering, such as spectral…

The K-way vertex cut problem} consists in, given a graph G, finding a subset of vertices of a given size, whose removal partitions G into the maximum number of connected components. This problem has many applications in several areas. It…

Given a graph G, of arbitrary size and unbounded vertex degree, denote by |G| the one-complex associated with $G$. The topological space |G| is n-arc connected (n-ac) if every set of no more than n points of |G| are contained in an arc (a…

Networks (or graphs) are used to model the dyadic relations between entities in a complex system. In cases where there exists multiple relations between the entities, the complex system can be represented as a multilayer network, where the…

Vertical decomposition is a widely used general technique for decomposing the cells of arrangements of semi-algebraic sets in $d$-space into constant-complexity subcells. In this paper, we settle in the affirmative a few long-standing open…

The intersection graph of a collection of trapezoids with corner points lying on two parallel lines is called a trapezoid graph. Using binary indexed tree data structure, we improve algorithms for calculating the size and the number of…