Related papers: Data structure for representing a graph: combinati…
The representation of graphs is commonly based on the adjacency matrix concept. This formulation is the foundation of most algebraic and computational approaches to graph processing. The advent of deep learning language models offers a wide…
A graph is a data structure composed of dots (i.e. vertices) and lines (i.e. edges). The dots and lines of a graph can be organized into intricate arrangements. The ability for a graph to denote objects and their relationships to one…
The use of complex networks as a modern approach to understanding the world and its dynamics is well-established in literature. The adjacency matrix, which provides a one-to-one representation of a complex network, can also yield several…
Dynamic or temporal networks enable representation of time-varying edges between nodes. Conventional adjacency-based data structures used for storing networks such as adjacency lists were designed without incorporating time and can thus…
Current paper introduces a Hypergraph Graph model of data storage which can be represented as a hybrid data structure based on Hypergraph and Graph. The pro-posed data structure is claimed to realize complex combinatorial structures. The…
Graphs can be used to represent a wide variety of data belonging to different domains. Graphs can capture the relationship among data in an efficient way, and have been widely used. In recent times, with the advent of Big Data, there has…
The topological (or graph) structures of real-world networks are known to be predictive of multiple dynamic properties of the networks. Conventionally, a graph structure is represented using an adjacency matrix or a set of hand-crafted…
We give an overview of combinatorial methods to represent 3D data, such as graphs and meshes, from the viewpoint of their amenability to analysis using machine learning algorithms. We highlight pros and cons of various representations and…
We introduce a hypergraph matrix, named the unified matrix, and use it to represent the hypergraph as a graph. We show that the unified matrix of a hypergraph is identical to the adjacency matrix of the associated graph. This enables us to…
A graph is a structure composed of a set of vertices (i.e.nodes, dots) connected to one another by a set of edges (i.e.links, lines). The concept of a graph has been around since the late 19$^\text{th}$ century, however, only in recent…
In this paper, we introduce a matrix for a mixed graph, called the integrated adjacency matrix. This matrix uniquely determines a mixed graph, as long as the indices of the matrix are specified. Additionally, we associate an (undirected)…
Graph algorithms play an important role in many computer science areas. In order to solve problems that can be modeled using graphs, it is necessary to use a data structure that can represent those graphs in an efficient manner. On top of…
Tables are widely used in documents because of their compact and structured representation of information. In particular, in scientific papers, tables can sum up novel discoveries and summarize experimental results, making the research…
Graph representation matrices are essential tools in graph data analysis. Recently, Hermitian adjacency matrices have been proposed to investigate directed graph structures. Previous studies have demonstrated that these matrices can extract…
Data processing systems impose multiple views on data as it is processed by the system. These views include spreadsheets, databases, matrices, and graphs. Associative arrays unify and simplify these different approaches into a common…
In this work, for the given adjacency matrix of a graph, we present an algorithm which checks the connectivity of a graph and computes all of its connected components. Also, it is mathematically proved that the algorithm presents all the…
Complex systems of interacting components often can be modeled by a simple graph $\mathcal{G}$ that consists of a set of $n$ nodes and a set of $m$ edges. Such a graph can be represented by an adjacency matrix $A\in\R^{n\times n}$, whose…
Computing over compressed data combines the space saving of data compression with efficient support for queries directly on the compressed representation. Such data structures are widely applied in text indexing and have been successfully…
Linked lists have long served as a valuable teaching tool in programming. However, the question arises: Are they truly practical for everyday program use? In most cases, it appears that array-based data structures offer distinct advantages,…
Hash tables are one of the most fundamental data structures for effectively storing and accessing sparse data, with widespread usage in domains ranging from computer graphics to machine learning. This study surveys the state-of-the-art…