Graph Theory and Its Applications in Computing

A special issue of Computation (ISSN 2079-3197). This special issue belongs to the section "Computational Engineering".

Deadline for manuscript submissions: 31 December 2024 | Viewed by 18886

Special Issue Editors

Department of Mathematics, Faculty of Science, University of Hail, Hail, Saudi Arabia
Interests: discrete mathematics; combinatorics; mathematical chemistry, particularly chemical graph theory

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Guest Editor
Research Center for Mathematics and Interdisciplinary Sciences, Shandong University, Qingdao 266237, China
Interests: graph theory; combinatorial optimization; bioinformatics

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Guest Editor
School of Software Technology and Key Laboratory for Ubiquitous Network and Service Software, Dalian University of Technology, Dalian 116620, China
Interests: information security; security game; cooperative game theory; graph theory

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Guest Editor
Department of mathematical sciences, University of South Carolina Aiken, Aiken, SC 29801, USA
Interests: graph theory and its applications

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Guest Editor
Supply Chain Solutions, UPS of America, Inc. 12380 Morris Rd., Alpharetta, GA, USA
Interests: data science; machine learning; graph databases

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Guest Editor
Department of Applied Mathematics, Vidyasagar University, Midnapore 721102, India
Interests: graph algorithms; computational graph theory; graph labeling; intersection graph

Special Issue Information

Dear Colleagues,

Since the birth of graph theory, it has been used to advance research and solve both theoretical and practical problems in many scientific, engineering, and social disciplines. Graphs are among the most efficient and visually appealing mathematical models for dealing with a wide range of real-world situations. Although applications of graph theory have played important roles in scientific research and discoveries for a long time, the developments of applications of graph theory in the last decades have been much more significant. It is observed that graph theory has been substantially employed in the areas of computing. The primary goal of this Special Issue is to gather the articles utilizing graph-theoretical concepts, methodologies, and advantages while solving problems to demonstrate the state-of-the-art applications of graph theory. Both the original research articles and review articles within the scope of the Special Issue are welcomed.

Research involving (but not limited to) applications of graph theory in the following fields will be considered in this Special Issue.

  • data structures
  • algorithms
  • software engineering
  • databases
  • data mining
  • information retrieval
  • image processing
  • computer networks
  • web graphs
  • edge computing
  • network sciences
  • social networks
  • machine learning, graph machine learning, and deep learning
  • recommendation systems
  • natural language processing
  • knowledge graphs
  • cryptography
  • cyber security
  • security game theory
  • blockchain
  • bioinformatics
  • chemistry and physics
  • operations research and engineering

Dr. Akbar Ali
Prof. Dr. Guojun Li
Prof. Dr. Mingchu Li
Prof. Dr. Rao Li
Dr. Colton Magnant
Prof. Dr. Madhumangal Pal
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Computation is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1800 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Published Papers (11 papers)

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Research

Jump to: Review

19 pages, 3010 KiB  
Article
Graph-Theoretical Analysis of Biological Networks: A Survey
by Kayhan Erciyes
Computation 2023, 11(10), 188; https://doi.org/10.3390/computation11100188 - 30 Sep 2023
Cited by 2 | Viewed by 1957
Abstract
Biological networks such as protein interaction networks, gene regulation networks, and metabolic pathways are examples of complex networks that are large graphs with small-world and scale-free properties. An analysis of these networks has a profound effect on our understanding the origins of life, [...] Read more.
Biological networks such as protein interaction networks, gene regulation networks, and metabolic pathways are examples of complex networks that are large graphs with small-world and scale-free properties. An analysis of these networks has a profound effect on our understanding the origins of life, health, and the disease states of organisms, and it allows for the diagnosis of diseases to aid in the search for remedial processes. In this review, we describe the main analysis methods of biological networks using graph theory, by first defining the main parameters, such as clustering coefficient, modularity, and centrality. We then survey fundamental graph clustering methods and algorithms, followed by the network motif search algorithms, with the aim of finding repeating subgraphs in a biological network graph. A frequently appearing subgraph usually conveys a basic function that is carried out by that small network, and discovering such a function provides an insight into the overall function of the organism. Lastly, we review network alignment algorithms that find similarities between two or more graphs representing biological networks. A conserved subgraph between the biological networks of organisms may mean a common ancestor, and finding such a relationship may help researchers to derive ancestral relationships and to predict the future evolution of organisms to enable the design of new drugs. We provide a review of the research studies in all of these methods, and conclude using the current challenging areas of biological network analysis, and by using graph theory and parallel processing for high performance analysis. Full article
(This article belongs to the Special Issue Graph Theory and Its Applications in Computing)
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25 pages, 1116 KiB  
Article
The Multi-Maximum and Quasi-Maximum Common Subgraph Problem
by Lorenzo Cardone and Stefano Quer
Computation 2023, 11(4), 69; https://doi.org/10.3390/computation11040069 - 27 Mar 2023
Cited by 1 | Viewed by 1607
Abstract
The Maximum Common Subgraph problem has been long proven NP-hard. Nevertheless, it has countless practical applications, and researchers are still searching for exact solutions and scalable heuristic approaches. Driven by applications in molecular science and cyber-security, we concentrate on the Maximum Common Subgraph [...] Read more.
The Maximum Common Subgraph problem has been long proven NP-hard. Nevertheless, it has countless practical applications, and researchers are still searching for exact solutions and scalable heuristic approaches. Driven by applications in molecular science and cyber-security, we concentrate on the Maximum Common Subgraph among an indefinite number of graphs. We first extend a state-of-the-art branch-and-bound procedure working on two graphs to N graphs. Then, given the high computational cost of this approach, we trade off complexity for accuracy, and we propose a set of heuristics to approximate the exact solution for N graphs. We analyze sequential, parallel multi-core, and parallel-many core (GPU-based) approaches, exploiting several leveraging techniques to decrease the contention among threads, improve the workload balance of the different tasks, reduce the computation time, and increase the final result size. We also present several sorting heuristics to order the vertices of the graphs and the graphs themselves. We compare our algorithms with a state-of-the-art method on publicly available benchmark sets. On graph pairs, we are able to speed up the exact computation by a 2× factor, pruning the search space by more than 60%. On sets of more than two graphs, all exact solutions are extremely time-consuming and of a complex application in many real cases. On the contrary, our heuristics are far less expensive (as they show a lower-bound for the speed up of 10×), have a far better asymptotic complexity (with speed ups up to several orders of magnitude in our experiments), and obtain excellent approximations of the maximal solution with 98.5% of the nodes on average. Full article
(This article belongs to the Special Issue Graph Theory and Its Applications in Computing)
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17 pages, 353 KiB  
Article
Solutions of the Yang–Baxter Equation and Automaticity Related to Kronecker Modules
by Agustín Moreno Cañadas, Pedro Fernando Fernández Espinosa and Adolfo Ballester-Bolinches
Computation 2023, 11(3), 43; https://doi.org/10.3390/computation11030043 - 21 Feb 2023
Viewed by 1083
Abstract
The Kronecker algebra K is the path algebra induced by the quiver with two parallel arrows, one source and one sink (i.e., a quiver with two vertices and two arrows going in the same direction). Modules over K are said to be Kronecker [...] Read more.
The Kronecker algebra K is the path algebra induced by the quiver with two parallel arrows, one source and one sink (i.e., a quiver with two vertices and two arrows going in the same direction). Modules over K are said to be Kronecker modules. The classification of these modules can be obtained by solving a well-known tame matrix problem. Such a classification deals with solving systems of differential equations of the form Ax=Bx, where A and B are m×n, F-matrices with F an algebraically closed field. On the other hand, researching the Yang–Baxter equation (YBE) is a topic of great interest in several science fields. It has allowed advances in physics, knot theory, quantum computing, cryptography, quantum groups, non-associative algebras, Hopf algebras, etc. It is worth noting that giving a complete classification of the YBE solutions is still an open problem. This paper proves that some indecomposable modules over K called pre-injective Kronecker modules give rise to some algebraic structures called skew braces which allow the solutions of the YBE. Since preprojective Kronecker modules categorize some integer sequences via some appropriated snake graphs, we prove that such modules are automatic and that they induce the automatic sequences of continued fractions. Full article
(This article belongs to the Special Issue Graph Theory and Its Applications in Computing)
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17 pages, 345 KiB  
Article
Solutions of the Yang–Baxter Equation Arising from Brauer Configuration Algebras
by Agustín Moreno Cañadas, Adolfo Ballester-Bolinches and Isaías David Marín Gaviria
Computation 2023, 11(1), 2; https://doi.org/10.3390/computation11010002 - 23 Dec 2022
Cited by 3 | Viewed by 1266
Abstract
Currently, researching the Yang–Baxter equation (YBE) is a subject of great interest among scientists of diverse areas in mathematics and other sciences. One of the fundamental open problems is to find all of its solutions. The investigation deals with developing theories such as [...] Read more.
Currently, researching the Yang–Baxter equation (YBE) is a subject of great interest among scientists of diverse areas in mathematics and other sciences. One of the fundamental open problems is to find all of its solutions. The investigation deals with developing theories such as knot theory, Hopf algebras, quandles, Lie and Jordan (super) algebras, and quantum computing. One of the most successful techniques to obtain solutions of the YBE was given by Rump, who introduced an algebraic structure called the brace, which allows giving non-degenerate involutive set-theoretical solutions. This paper introduces Brauer configuration algebras, which, after appropriate specializations, give rise to braces associated with Thompson’s group F. The dimensions of these algebras and their centers are also given. Full article
(This article belongs to the Special Issue Graph Theory and Its Applications in Computing)
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7 pages, 252 KiB  
Article
Characteristic Sequence of Strongly Minimal Directed Single Graphs of 1-Arity
by Abeer M. Albalahi
Computation 2022, 10(12), 220; https://doi.org/10.3390/computation10120220 - 15 Dec 2022
Viewed by 1072
Abstract
In this paper, we will classify the strongly minimal directed single graphs of 1-arity by axiomatizing the theory of characteristic sequence of such a graph. Then we will show this theory is complete by using Łos-Vaught test. Complete theory is important to capture [...] Read more.
In this paper, we will classify the strongly minimal directed single graphs of 1-arity by axiomatizing the theory of characteristic sequence of such a graph. Then we will show this theory is complete by using Łos-Vaught test. Complete theory is important to capture all the models of the theory and hence can be applied on mathematical structures which meet such a theory. The theory of algebraically closed fields with a given characteristic is complete. Thus, in this paper we will classify the strongly minimal directed single graphs of 1-arity with given characteristic sequence which can be applied on many mathematical structures not only algebraically closed fields. Full article
(This article belongs to the Special Issue Graph Theory and Its Applications in Computing)
10 pages, 241 KiB  
Article
Online Bottleneck Matching Problem with Two Heterogeneous Sensors in a Metric Space
by Man Xiao, Yaru Yang and Weidong Li
Computation 2022, 10(12), 217; https://doi.org/10.3390/computation10120217 - 9 Dec 2022
Cited by 1 | Viewed by 1140
Abstract
In this paper, we consider the online matching problem with two heterogeneous sensors s1 and s2 in a metric space (X,d). If a request r is assigned to sensor s1, the service cost of [...] Read more.
In this paper, we consider the online matching problem with two heterogeneous sensors s1 and s2 in a metric space (X,d). If a request r is assigned to sensor s1, the service cost of r is the distance d(r,s1). Otherwise, r is assigned to sensor s2, and the service cost of r is d(r,s2)w, where w1 is the weight of sensor s2. The goal is to minimize the maximum matching cost, we design an optimal online algorithm with a competitive ratio of 1+w+1w for 1w1.839, and an optimal online algorithm with a competitive ratio of w+1+w2+6w+12 for w>1.839. Full article
(This article belongs to the Special Issue Graph Theory and Its Applications in Computing)
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9 pages, 367 KiB  
Article
An Improved Approximation Algorithm for the Minimum Power Cover Problem with Submodular Penalty
by Han Dai
Computation 2022, 10(10), 189; https://doi.org/10.3390/computation10100189 - 19 Oct 2022
Cited by 1 | Viewed by 1319
Abstract
In this paper, we consider the minimum power cover problem with submodular penalty (SPMPC). Given a set U of n users, a set S of m sensors and a penalty function π:2UR+ on the plane, the relationship [...] Read more.
In this paper, we consider the minimum power cover problem with submodular penalty (SPMPC). Given a set U of n users, a set S of m sensors and a penalty function π:2UR+ on the plane, the relationship that adjusts the power p(s) of each sensor s and its corresponding radius r(s) is: p(s)=c·r(s)α, where c>0 and α1. The SPMPC problem is to determine the power assignment on each sensor such that each user uU is either covered by the sensor or penalized and the sum of the total power consumed by sensors in S plus the penalty of all uncovered users is minimized, the penalty here is determined by the submodular function. Based on the primal dual technique, we design an O(α)-approximation algorithm. Full article
(This article belongs to the Special Issue Graph Theory and Its Applications in Computing)
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7 pages, 328 KiB  
Article
On the Inverse Symmetric Division Deg Index of Unicyclic Graphs
by Abeer M. Albalahi and Akbar Ali
Computation 2022, 10(10), 181; https://doi.org/10.3390/computation10100181 - 11 Oct 2022
Cited by 1 | Viewed by 1426
Abstract
The symmetric division deg (SDD) index is among the 148 discrete Adriatic indices that were developed about a decade ago. Motivated by the success of the SDD index, Ghorbani et al. in a recent paper proposed the inverse version of this index and [...] Read more.
The symmetric division deg (SDD) index is among the 148 discrete Adriatic indices that were developed about a decade ago. Motivated by the success of the SDD index, Ghorbani et al. in a recent paper proposed the inverse version of this index and called it the inverse symmetric division deg (ISDD) index. In the aforementioned paper, the graphs possessing the maximum and minimum ISDD index over the set of all tree graphs having the given order were found. The present paper addresses the problem of finding the graphs having the largest and smallest ISDD index from the set of all connected unicyclic graphs having the specified order. Full article
(This article belongs to the Special Issue Graph Theory and Its Applications in Computing)
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31 pages, 1203 KiB  
Article
Cayley Hash Values of Brauer Messages and Some of Their Applications in the Solutions of Systems of Differential Equations
by María Alejandra Osorio Angarita, Agustín Moreno Cañadas, Cristian Camilo Fúneme, Odette M. Mendez and Robinson-Julian Serna
Computation 2022, 10(9), 164; https://doi.org/10.3390/computation10090164 - 17 Sep 2022
Viewed by 1447
Abstract
Cayley hash values are defined by paths of some oriented graphs (quivers) called Cayley graphs, whose vertices and arrows are given by elements of a group H. On the other hand, Brauer messages are obtained by concatenating words associated with multisets constituting [...] Read more.
Cayley hash values are defined by paths of some oriented graphs (quivers) called Cayley graphs, whose vertices and arrows are given by elements of a group H. On the other hand, Brauer messages are obtained by concatenating words associated with multisets constituting some configurations called Brauer configurations. These configurations define some oriented graphs named Brauer quivers which induce a particular class of bound quiver algebras named Brauer configuration algebras. Elements of multisets in Brauer configurations can be seen as letters of the Brauer messages. This paper proves that each point (x,y)V=R\{0}×R\{0} has an associated Brauer configuration algebra ΛB(x,y) induced by a Brauer configuration B(x,y). Additionally, the Brauer configuration algebras associated with points in a subset of the form ((x),(x)]×((y),(y)]V have the same dimension. We give an analysis of Cayley hash values associated with Brauer messages M(B(x,y)) defined by a semigroup generated by some appropriated matrices A0,A1,A2GL(2,R) over a commutative ring R. As an application, we use Brauer messages M(B(x,y)) to construct explicit solutions for systems of linear and nonlinear differential equations of the form X(t)+MX(t)=0 and X(t)X2(t)N(t)=N(t) for some suitable square matrices, M and N(t). Python routines to compute Cayley hash values of Brauer messages are also included. Full article
(This article belongs to the Special Issue Graph Theory and Its Applications in Computing)
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17 pages, 582 KiB  
Article
Snake Graphs Arising from Groves with an Application in Coding Theory
by Agustín Moreno Cañadas, Gabriel Bravo Rios and Robinson-Julian Serna
Computation 2022, 10(7), 124; https://doi.org/10.3390/computation10070124 - 19 Jul 2022
Cited by 4 | Viewed by 1695
Abstract
Snake graphs are connected planar graphs consisting of a finite sequence of adjacent tiles (squares) T1,T2,,Tn. In this case, for 1jn1, two consecutive tiles Tj [...] Read more.
Snake graphs are connected planar graphs consisting of a finite sequence of adjacent tiles (squares) T1,T2,,Tn. In this case, for 1jn1, two consecutive tiles Tj and Tj+1 share exactly one edge, either the edge at the east (west) of Tj (Tj+1) or the edge at the north (south) of Tj (Tj+1). Finding the number of perfect matchings associated with a given snake graph is one of the most remarkable problems regarding these graphs. It is worth noting that such a number of perfect matchings allows a bijection between the set of snake graphs and the positive continued fractions. Furthermore, perfect matchings of snake graphs have also been used to find closed formulas for cluster variables of some cluster algebras and solutions of the Markov equation, which is a well-known Diophantine equation. Recent results prove that snake graphs give rise to some string modules over some path algebras, connecting snake graph research with the theory of representation of algebras. This paper uses this interaction to define Brauer configuration algebras induced by schemes associated with some multisets called polygons. Such schemes are named Brauer configurations. In this work, polygons are given by some admissible words, which, after appropriate transformations, permit us to define sets of binary trees called groves. Admissible words generate codes whose energy values are given by snake graphs. Such energy values can be estimated by using Catalan numbers. We include in this paper Python routines to compute admissible words (i.e., codewords), energy values of the generated codes, Catalan numbers and dimensions of the obtained Brauer configuration algebras. Full article
(This article belongs to the Special Issue Graph Theory and Its Applications in Computing)
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Review

Jump to: Research

16 pages, 268 KiB  
Review
Unraveling Arrhythmias with Graph-Based Analysis: A Survey of the MIT-BIH Database
by Sadiq Alinsaif
Computation 2024, 12(2), 21; https://doi.org/10.3390/computation12020021 - 25 Jan 2024
Cited by 1 | Viewed by 2119
Abstract
Cardiac arrhythmias, characterized by deviations from the normal rhythmic contractions of the heart, pose a formidable diagnostic challenge. Early and accurate detection remains an integral component of effective diagnosis, informing critical decisions made by cardiologists. This review paper surveys diverse computational intelligence methodologies [...] Read more.
Cardiac arrhythmias, characterized by deviations from the normal rhythmic contractions of the heart, pose a formidable diagnostic challenge. Early and accurate detection remains an integral component of effective diagnosis, informing critical decisions made by cardiologists. This review paper surveys diverse computational intelligence methodologies employed for arrhythmia analysis within the context of the widely utilized MIT-BIH dataset. The paucity of adequately annotated medical datasets significantly impedes advancements in various healthcare domains. Publicly accessible resources such as the MIT-BIH Arrhythmia Database serve as invaluable tools for evaluating and refining computer-assisted diagnosis (CAD) techniques specifically targeted toward arrhythmia detection. However, even this established dataset grapples with the challenge of class imbalance, further complicating its effective analysis. This review explores the current research landscape surrounding the application of graph-based approaches for both anomaly detection and classification within the MIT-BIH database. By analyzing diverse methodologies and their respective accuracies, this investigation aims to empower researchers and practitioners in the field of ECG signal analysis. The ultimate objective is to refine and optimize CAD algorithms, ultimately culminating in improved patient care outcomes. Full article
(This article belongs to the Special Issue Graph Theory and Its Applications in Computing)

Planned Papers

The below list represents only planned manuscripts. Some of these manuscripts have not been received by the Editorial Office yet. Papers submitted to MDPI journals are subject to peer-review.

Title: Graph-Theoretic Analysis of Biological Networks
Authors: Kayhan Erciyeş
Affiliation: Yaşar University
Abstract: Biological networks such as protein interaction networks, gene regulation networks and metabolic pathways are examples of complex networks which are large graphs with small-world and scale-free properties. Analysis of these networks has a profound effect on our understanding the origins of life, health and disease states of organisms, and diagnose diseases to aid the search for remedial processes. In this review, we describe main analysis methods of biological networks using graph theory by first defining main parameters such as clustering coefficient, modularity and centrality. We then survey fundamental graph clustering methods and algorithms followed by the network motif search algorithms with the aim of finding repeating subgraphs in a biological network graph. A frequently appearing subgraph usually conveys a basic function carried out by that small network and discovering such a function provides an insight to the overall function of the organism. Lastly, we review network alignment algorithms that achieve to find similarities between two or more graphs representing biological networks. A conserved subgraph between the biological networks of organisms may mean a common ancestor and finding such relationship may help researchers derive ancestral relationships and predict the future evolution of organisms to enable designing new drugs. We conclude by the current challenging areas of biological network analysis and using algebraic graph theory and parallel processing for high performance analysis.

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