Related papers: Counting Horizontal Visibility Graphs

Let $G=(V,E)$ be a simple and connected graph. A $h$-order invariant of $G$ based on the path sequence is defined from a set of real numbers ${f(x_{0},x_{1},\cdots,x_{h})}$ as $^{h}I_f(G)=\sum\limits_{v_{0}v_{1}v_{2}\cdots…

As a powerful tool for modeling complex relationships, hypergraphs are gaining popularity from the graph learning community. However, commonly used frameworks in deep hypergraph learning focus on hypergraphs with edge-independent vertex…

In the Any-Angle Pathfinding problem, the goal is to find the shortest path between a pair of vertices on a uniform square grid, that is not constrained to any fixed number of possible directions over the grid. Visibility Graphs are a known…

Given a set D of nonnegative integers, we derive the asymptotic number of graphs with a givenvnumber of vertices, edges, and such that the degree of every vertex is in D. This generalizes existing results, such as the enumeration of graphs…

For $n\geq 3$ and $r=r(n) \geq 3$, let $\boldsymbol{k} =\boldsymbol{k}(n)=(k_1, \ldots, k_n)$ be a sequence of non-negative integers with sum $M(\boldsymbol{k})=\sum_{j=1}^{n} k_j$. We assume that $M(\boldsymbol{k})$ is divisible by $r$ for…

Graph-based recommendation systems use higher-order user and item embeddings for next-item predictions. Dynamically adding collaborative signals from neighbors helps to use similar users' preferences during learning. While item-item…

A strict orthogonal drawing of a graph $G=(V, E)$ in $\mathbb{R}^2$ is a drawing of $G$ such that each vertex is mapped to a distinct point and each edge is mapped to a horizontal or vertical line segment. A graph $G$ is $HV$-restricted if…

For a positive integer \( k \), let \( [k] = \{1, 2, \ldots, k\} \). Let \( h \) be a non-negative integer, and let \( n \) be a multiple of \( h + 1 \). Define \( H \) as the disjoint union of \( n/(h+1) \) cliques (each of size \( h + 1…

Undirected graphs are often used to describe high dimensional distributions. Under sparsity conditions, the graph can be estimated using $\ell_1$ penalization methods. However, current methods assume that the data are independent and…

The simple connected graphs may be classified by their cycle composition (number and lengths of cycles). This work derives the counting series of the simple connected graphs that have cycles of unrestricted number and length, but no…

The limited penetrable horizontal visibility graph algorithm was recently introduced to map time series in complex networks. We extend this visibility graph and create a directed limited penetrable horizontal visibility graph and an image…

A subgraph $H$ of a graph $G$ is isometric if the distances between vertices in $H$ coincide with the distances between the corresponding vertices in $G$. We show that for any integer $n\ge 1$, there is a graph on $3^{n+O(\log^2 n)}$…

Progress in deep learning has spawned great successes in many engineering applications. As a prime example, convolutional neural networks, a type of feedforward neural networks, are now approaching -- and sometimes even surpassing -- human…

Nonlinear time series analysis is an active field of research that studies the structure of complex signals in order to derive information of the process that generated those series, for understanding, modeling and forecasting purposes. In…

Monitoring complex systems results in massive multivariate time series data, and anomaly detection of these data is very important to maintain the normal operation of the systems. Despite the recent emergence of a large number of anomaly…

This paper studies observability for non-uniform hypergraphs with inputs and outputs. To capture higher-order interactions, we define a canonical non-homogeneous dynamical system with nonlinear outputs on hypergraphs. We then construct…

Subgraph and homomorphism counting are fundamental algorithmic problems. Given a constant-sized pattern graph $H$ and a large input graph $G$, we wish to count the number of $H$-homomorphisms/subgraphs in $G$. Given the massive sizes of…

This paper introduces a novel Graph Neural Network (GNN) architecture for time series classification, based on visibility graph representations. Traditional time series classification methods often struggle with high computational…

Hypergraphs that can depict interactions beyond pairwise edges have emerged as an appropriate representation for modeling polyadic relations in complex systems. With the recent surge of interest in researching hypergraphs, the centrality…

Multivariate time series analysis is a vital but challenging task, with multidisciplinary applicability, tackling the characterization of multiple interconnected variables over time and their dependencies. Traditional methodologies often…