The force-directed paradigm is one of the few generic approaches to drawing graphs. Since force-directed algorithms can be extended easily, they are used frequently. Most of these algorithms are, however, quite slow on large graphs, as they compute a...
We give a deterministic drawing algorithm to draw a graph onto a torus, which is based on the usual spectral drawing algorithm. For most of the well-known toroidal vertex-transitive graphs, the result drawings give an embedding of the graphs onto the...
In this paper, we investigate how one can modify an orthogonal graph drawing to accommodate the placement of overlap-free labels with the minimum cost (i.e., minimum increase of the area and preservation of the quality of the drawing). We investigate...
23 November 2022
Visualisation techniques have been one of the best data processing and analysis methods in recent decades, and they have assisted in data understanding efforts in various fields. Visualisation techniques for low-dimensional data are well developed an...
Graphs are often used to model data with a relational structure and graphs are usually visualised into node-link diagrams for a better understanding of the underlying data. Node-link diagrams represent not only data entries in a graph, but also the r...
The video game industry has evolved significantly, with different genres becoming popular over time, but how to visualize such information by curating data into a form that makes it easier to identify and understand the trends is quite an interesting...
The crossing number of a graph is a significant measure that indicates the complexity of the graph and the difficulty of visualizing it. In this paper, we examine the crossing numbers of join products involving the complete graph
This paper presents a new formulation and solution of a mixed-integer program for the hierarchical orthogonal hypergraph drawing problem, and the number of hyperedge crossings is minimized. The novel feature of the model is in combining several stage...
The main aim of the paper is to give the crossing number of the join product
Graphs are an excellent tool with applications in various branches of engineering. Graph layouts have emerged as a cornerstone in the visual representation and analysis of complex systems. They are indispensable in reducing complexity, optimizing des...
The crossing number of a graph G is the minimum number of edge crossings over all drawings of G in the plane. The main purpose of this paper is to determine the crossing numbers of the join products of six symmetric graphs on six vertices with paths...
Due to the wide deployment of wireless local area networks (WLAN), received signal strength (RSS)-based indoor WLAN localization has attracted considerable attention in both academia and industry. In this paper, we propose a novel page rank-based ind...
This study analyses the influence of the course of the disease of idiopathic cervical dystonia (CD) before botulinum toxin (BoNT) therapy on long-term outcomes. 74 CD-patients who were treated on a regular basis in the botulinum toxin outpatient depa...
When drawing small graphs (with up to five or six vertices) we can use their underlying symmetry to represent them in a clear and natural way. [...]
Understanding family physical activity (PA) behaviour is essential for designing effective family-based PA interventions. However, effective approaches to capture the perceptions and “lived experiences” of families are not yet well established. The a...
3 June 2020
Virus outbreaks are threats to humanity, and coronaviruses are the latest of many epidemics in the last few decades in the world. SARS-CoV (Severe Acute Respiratory Syndrome Associated Coronavirus) is a member of the coronavirus family, so its study...
Reducing the number of crossings on graph edges can be useful in various applications, including network visualization, circuit design, graph theory, cartography or social choice theory. This paper aims to determine the crossing number of the join pr...
In the paper, we extend known results concerning crossing numbers of join products of small graphs of order six with discrete graphs. The crossing number of the join product
In this article, we present a simple method for network visualization. The proposed method is based on distmesh [P.O. Persson and G. Strang, A simple mesh generator in MATLAB, SIAM Review 46 (2004) pp. 329–345], which is a simple unstructured t...
The significance of searching for edge crossings in graph theory lies inter alia in enhancing the clarity and readability of graph representations, which is essential for various applications such as network visualization, circuit design, and data re...
Compacting orthogonal drawings is a challenging task. Usually, algorithms try to compute drawings with small area or total edge length while preserving the underlying orthogonal shape. We suggest a moderate relaxation of the orthogonal compaction pro...
The main aim of the paper is to give the crossing number of the join product
The visual exploration of large and complex network structures remains a challenge for many application fields. Moreover, a growing number of real-world networks is multivariate and often interconnected with each other. Entities in a network may have...
We compare two mathematical theories that address duality between cycles and vertex-cuts of graphs in geometric settings. First, we propose a rigorous definition of a new type of graph, vector graphs. The special case of R2-vector graphs matches the...
This paper addresses the pressing environmental concern of plastic waste, particularly in the biopharmaceutical production sector, where single-use assemblies (SUAs) significantly contribute to this issue. To address and mitigate this problem, we pro...
Edge bundling is a promising graph visualization approach to simplifying the visual result of a graph drawing. Plenty of edge bundling methods have been developed to generate diverse graph layouts. However, it is difficult to defend an edge bundling...
Global warming is becoming worse owing to carbon dioxide emissions around the world, and eco-friendly energy for reducing carbon dioxide emissions is gaining importance. Wind power plants are the most representative of the environmentally friendly en...
The crossing number of a graph G,
The Single-Source Shortest Paths (SSSP) graph problem is a fundamental computation. This study attempted to characterize concretely the energy behaviors of the two primary methods to solve it, the Bellman–Ford and Dijkstra algorithms. The very...
In this paper, we present a new egocentric metaphor for graph visualization that consists in positioning a graph between two concentric spheres of different radii. It improves the expansion of nodes in space, contrary to 3D spatialization algorithms....
The crossing number
Many symmetric properties are well-explored in graph theory, especially in graph coloring, such as symmetric graphs defined by the automorphism groups, symmetric drawing of planar graphs, and symmetric functions which are used to count the number of...
The graph burning problem is an NP-hard combinatorial optimization problem that helps quantify how vulnerable a graph is to contagion. This paper introduces three mathematical formulations of the problem: an integer linear program (ILP) and two const...
In this exploratory paper, we discuss quantitative graph-theoretical measures of network aesthetics. Related work in this area has typically focused on geometrical features (e.g., line crossings or edge bendiness) of drawings or visual representation...
This paper introduces and studies the following beyond-planarity problem, which we call h-Clique2Path Planarity. Let G be a simple topological graph whose vertices are partitioned into subsets of size at most h, each inducing a clique. h-Clique2Path ...
Let k and n be two positive integers. Firefighting is a discrete dynamical process of preventing the spread of fire. Let G be a connected graph G with n vertices. Assuming a fire starts at one of the vertices of G, the firefighters choose k unburned...
Graph theory is a powerful representation and problem-solving tool, but it is not included in present curriculum at school levels. In this study we perform a didactic proposal based in graph theory, to provide students useful and motivational tools f...
We introduce a family of models, which we name matrix models associated with children’s drawings—the so-called dessin d’enfant. Dessins d’enfant are graphs of a special kind drawn on a closed connected orientable surface (in the sky). The vertices of...
In a dominance drawing
Generative algorithms for random graphs have yielded insights into the structure and evolution of real-world networks. Most networks exhibit a well-known set of properties, such as heavy-tailed degree distributions, clustering and community formation...
In this paper, we study the networks of financial institutions using textual data (i.e., news). We draw knowledge graphs after the textual data has been processed via various natural language processing and embedding methods, including use of the mos...
The notion of fuzzy graph (FG) is widely used in many problems arising from partial or incomplete descriptions of the real world and in particular from fields such as engineering, economics, computer science, social disciplines, or medical diagnostic...
Aim of the study: To compare the course of severity of cervical dystonia (CD) before and after long-term botulinum toxin (BoNT) therapy to detect indicators for a good or poor clinical outcome. Patients and Methods: A total of 74 outpatients with idi...
Sketched drawings sometimes include non-solid lines drawn as sets of consecutive strokes. They represent dashed lines, which are useful for various purposes. Recognizing such dashed lines while parsing drawings is reasonably straightforward if they a...
Currently, Chinese villages are grappling with the issue of regional value collapse within the long-standing ‘urban-rural dual system’ strategy. Characteristic villages, as integral components of the urban–rural hierarchical spatial...
We introduce the Concept→Model→Graph→View Cycle (CMGVC). The CMGVC facilitates coherent architecture analysis, reasoning, insight, and decision making based on conceptual models that are transformed into a generic, robust graph data structure (GDS)....
The automatic extraction of biomedical events from the scientific literature has drawn keen interest in the last several years, recognizing complex and semantically rich graphical interactions otherwise buried in texts. However, very few works revolv...
A topological index is a numeric quantity associated with a chemical structure that attempts to link the chemical structure to various physicochemical properties, chemical reactivity, or biological activity. Let
Hierarchy analysis of the knowledge graphs aims to discover the latent structure inherent in knowledge base data. Drawing inspiration from topic modeling, which identifies latent themes and content patterns in text corpora, our research seeks to adap...
A connected graph, G, is Crossing Free-connected (
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