Graph Theory Application

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Graph Theory Application

Graph Theory Application

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Application Of Graph Theory Based Multimodal Network Analysis On…

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Abdul Majid Abdul Majid Scilit Preprints.org Google Scholar View Publications 1, * and Ibtisam Rauf Ibtisam Rauf Scilit Preprints.org Google Scholar View Publications 2

Submission received: 5/12/2019 / Revised: 29/01/2020 / Approved: 13/02/2020 / Published: 20/02/2020

Graphs And Real Life Applications

Graph theory (GT) concepts can be applied in computer science (CS) for many purposes. Unique applications of CS from GT, such as online document clustering, encryption, and algorithm performance analysis, are among other promising applications. In addition, GT concepts can be used to simplify and analyze electronic circuits. Recently, graphs have been widely used in social networks (SN) for many purposes related to modeling and analyzing SN structures, modeling SN activity, analyzing SN users, and many other related aspects. Given the wide application of GT in SN, this paper provides a comprehensive summary of the use of GT in SN. The purpose of this study is twofold. First, we briefly discuss possible applications of GT in computer science along with practical examples. Second, we explain the use of GT in SN with enough concepts and examples to demonstrate the importance of graphs in SN modeling and analysis.

The concept/origin of graph theory (GT) arose from the Coinsbury bridge problem in 1735 for the first time in history [1]. The Coinsbury bridge problem was used to derive the concept of Euler’s count. After that, Euler explored the concept of the Coinsbury bridge problem and developed a new structure called the Euler graph. Later, AF Möbius in 1840 gave the concept of two graphs, that is, a complete graph and a bipartite graph [2]. Kurotovsky used these two graphs in some relaxation problems and showed that both graphs are flat in the domain of relaxation problems [3]. Gustav Kirchhoff gave the idea of ​​a cycleless tree-like structure in 1845 [4] . In addition, the authors explained the use of GT concepts in the calculation of current in electrical circuits. In 1852, Thomas Guthrie introduced four color problems that are very useful in modern computer programs [5]. Then in 1856 Thomas invented Hamilton’s number. P. Kirkman and Hamiltonian, and this type of graph was widely used in the literature [6, 7, 8, 9]. G. Daddini introduced the puzzle problem in 1913, using earlier GT concepts [10]. In 1878, James Joseph Sylvester introduced the word “Graphics” [11]. He used two algebraic concepts, namely covariants and quantum invariants, and drew an analogy between them. Ramsey developed the concept of exterior graph theory in 1941 while working on coloring pages [12]. Until then, most researchers adopted GT concepts in their work. Recently, graphs have been widely used in many disciplines, including social network (SN) modeling, big data analysis, natural language processing (NLP), complex network analysis, and pattern recognition applications.

Several studies report applications of graph theory in unique parts of computer science and social networks. Unique aspects related to both fields using GT are cryptography [13], quantum cryptography [14], coding theory [15], construction of asymptotically shortest k-radiation sequences [16], publication of privacy-preserving graphs for informative analysis [ 17]. , human brain anatomical network research using diagrams [18], landscape connectivity and conservation planning [19], image processing [20], information retrieval [21], social network analysis [22], signal processing diagrams [23] [23 ] , information detection in social networks [24] , robotics [25], [26], network analysis of global metro systems [27], semi-quantitative programming [28, 29], image segmentation [30], clustering [31, 32, 33 ] , 34, 35], data science [36, 37, 38] and pattern recognition [39]. These are, among others, well-known exclusive applications of graph theory. The seven most important work-related studies are: (1) Riaz et al. [40], (2) Shirinivas et al. [41], (3) DurgaPrasad et al. [42], (4) Liu et al. [43], (5) Qingbao Yu et al. [44], (6) Sporns et al. [45] and (7) Goyal et al. [46]. These studies have explained the application of GT in computer science (CS). However, these studies have not comprehensively reported the practical application of GT. Furthermore, there is no single study that covers all the practical applications of GT in CS and SN fields.

Graph Theory Application

Graph theory methods [47] are widely used in various disciplines, including chemistry, biology, physics, and computer science [48, 49, 50]. GT is a fundamentally mathematical concept with broad applications in all areas of modeling and analysis. In this paper, we will briefly discuss the use of GT in the field of CS and SN [51, 52, 53, 54, 55]. We present various applications of graph theory in both fields. Recently, efforts have been made to develop sophisticated software/environments/packages that can generate complex graphs containing excessive amounts of data in a single window or user interface [ 56 , 57 , 58 ]. A comprehensive overview of GT applications in CS is shown in Figure 1 .

A Beautiful Graph Theory Prüf 😉. For The Number Of Trees On N Vertices

A graph is a set of nodes and edges. Nodes are called vertices/points and edges are lines or arcs that connect any two/more nodes in a graph. A graph can be represented mathematically by G. For example, in SN, a user graph is G(U, V), where U is a list of users and V is a set of faces showing relationships between users or objects. There are two types of graphs: directed and undirected. Undirected edges of a graph have no direction. An example of an undirected graph is shown in Figure 2a. For example, in Figure 2a below, there is a relationship between L and M, which is the same as saying that there is a relationship between M and L. We can call the line between M and L as (L)

L) because it makes no difference in interpretation/understanding. Possible examples of an undirected graph are people and SN membership or academics and co-authored articles in a collaborative network. In contrast, in directed graphs, edges have a specific direction (that is, they can be considered inputs or outputs). In these cases, the graphs are drawn along the edges of the arrowhead. Directed graphs are commonly known as digraphs. An example of a directed graph is shown in Figure 2b. This can fix the social relations of “who likes whom” in SN. Persons A, B, and D say they like person C. Notice that person C does not say they like A, B, or D. B and A like each other. No one says they like G. An example of a directed graph is shown in Figure 2b. Possible applications of a directed graph include web page connections and hyperlinks, Twitter follower graphs, interactions between users in SNs, and the influence of one use on another user in SNs.

In addition, graphs can be classified into two additional categories: graded and ungraded. A score graph has values ​​(ie, as numbers) attached to lines that represent the intensity or strength or number of connections or frequencies between two nodes. The latter represent only the connection/relationship between us without numbers. In SN, lines can represent the relationship between two users (eg, relative, friend, lover) or the number of interactions between user X and user Y. An example value graph is shown in Figure 3, where a line represents the trade volume in trillions of dollars between five different countries. A possible example of a graph without values ​​would be the borders of some countries that are close to each other without specifying the length of the borders.

There are several types of charts that can be classified into several categories. Gartner

Graph Theory: Exploring Graph Theory Through Ioi Challenges

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