Related papers: A Path Algebra for Multi-Relational Graphs
The intersection graph of a collection of trapezoids with corner points lying on two parallel lines is called a trapezoid graph. These graphs and their generalizations were applied in various fields, including modeling channel routing…
Networks are a powerful tool to model complex systems, and the definition of many Graph Neural Networks (GNN), Deep Learning algorithms that can handle networks, has opened a new way to approach many real-world problems that would be hardly…
An arithmetical structure on a finite and connected graph G is a pair (d, r) of positive integer vectors such that r is primitive (the gcd of its entries is 1) and (diag(d) - A)r = 0, where A is the adjacency matrix of G. In this article,…
A network representation is useful for describing the structure of a large variety of complex systems. However, most real and engineered systems have multiple subsystems and layers of connectivity, and the data produced by such systems is…
A speculative overview of a future topic of research. The paper is a collection of ideas concerning two related areas: 1) Graph computation machines ("computing with graphs"). This is the class of models of computation in which the state of…
The class of closed graphs by a linear ordering on their sets of vertices is investigated. A recent characterization of such a class of graphs is analyzed by using tools from the proper interval graph theory.
Neural networks are often represented as graphs of connections between neurons. However, despite their wide use, there is currently little understanding of the relationship between the graph structure of the neural network and its…
Multimodal data pervades various domains, including healthcare, social media, and transportation, where multimodal graphs play a pivotal role. Machine learning on multimodal graphs, referred to as multimodal graph learning (MGL), is…
The notion of 1-planarity is among the most natural and most studied generalizations of graph planarity. A graph is 1-planar if it has an embedding where each edge is crossed by at most another edge. The study of 1-planar graphs dates back…
Many polynomial invariants are defined on graphs for encoding the combinatorial information and researching them algebraically. In this paper, we introduce the cycle polynomial and the path polynomial of directed graphs for counting cycles…
The line graph $\Gamma$ of a multi-graph $\Delta$ is the graph whose vertices are the edges of $\Delta$, where two such edges are adjacent if and only if they meet in a single vertex of $\Delta$. We provide several characterizations of such…
A matrix-weighted graph is an undirected graph with a $k\times k$ positive semidefinite matrix assigned to each edge. There are natural generalizations of the Laplacian and adjacency matrices for such graphs. These matrices can be used to…
Graph theory is a promising approach in handling the problem of estimating the connectivity probability of vehicular ad-hoc networks (VANETs). With a communication network represented as graph, graph connectivity indicators become valid for…
Consider a weighted graph G with n vertices, numbered by the set {1,...,n}. For any path p in G, we call w_G(p) the sum of the weights of the edges of the path and we define the multiset {\cal D}_{i,j} (G) = {w_G(p) | p simple path between…
We address the correspondence search problem among multiple graphs with complex properties while considering the matching consistency. We describe each pair of graphs by combining multiple attributes, then jointly match them in a unified…
Convolutional neural networks (CNNs) leverage the great power in representation learning on regular grid data such as image and video. Recently, increasing attention has been paid on generalizing CNNs to graph or network data which is…
The multidimensional, heterogeneous, and temporal nature of speech databases raises interesting challenges for representation and query. Recently, annotation graphs have been proposed as a general-purpose representational framework for…
The paper has a form of a survey and consists of three parts. It is focused on the relationship between the many-sorted theory, which leads to logical geometry and one-sorted theory, which is based on the important model-theoretic concepts.…
The era of data deluge has sparked the interest in graph-based learning methods in a number of disciplines such as sociology, biology, neuroscience, or engineering. In this paper, we introduce a graph recurrent neural network (GRNN) for…
We develop a purely set-theoretic formalism for binary trees and binary graphs. We define a category of binary automata, and display it as a fibred category over the category of binary graphs. We also relate the notion of binary graphs to…