- Types of Graphs. Though, there are a lot of different types of graphs depending upon the number of vertices, number of edges, interconnectivity, and their overall structure, some of such common types of graphs are as follows: 1. Null Graph. A null graph is a graph in which there are no edges between its vertices. A null graph is also called empty graph
- Types of Graph. The graphs are basically of two types, directed and undirected. It is best understood by the figure given below. The arrow in the figure indicates the direction. Directed Graph. In graph theory, a directed graph is a graph made up of a set of vertices connected by edges, in which the edges have a direction associated with them
- A cycle graph is a graph consisting of a single cycle. The cycle graph with n vertices is denoted by Cn. The following are the examples of cyclic graphs. Note that C n is regular of degree 2, and has n edges. Path Graphs A path graph is a graph consisting of a single path. The path graph with n vertices is denoted by Pn. The following are the examples of path graphs
- Types of Graphs in Graph Theory 1. Null Graph-. A graph whose edge set is empty is called as a null graph. In other words, a null graph does not contain... 2. Trivial Graph-. A graph having only one vertex in it is called as a trivial graph. It is the smallest possible graph. 3. Non-Directed Graph-..
- A directed graph with three vertices and four directed edges (the double arrow represents an edge in each direction). A directed graph or digraph is a graph in which edges have orientations. In one restricted but very common sense of the term, a directed graph is an ordered pair. G = ( V , E ) {\displaystyle G= (V,E)

Prerequisite: Graph Theory Basics - Set 1, Graph Theory Basics - Set 2 A graph G = (V, E) consists of a set of vertices V = { V1, V2,... } and set of edges E = { E1, E2,.. A graph is a diagram of points and lines connected to the points. It has at least one line joining a set of two vertices with no vertex connecting itself. The concept of graphs in graph theory stands up on some basic terms such as point, line, vertex, edge, degree of vertices, properties of graphs, etc

Electrical Engineering − The concepts of graph theory is used extensively in designing circuit connections. The types or organization of connections are named as topologies. Some examples for topologies are star, bridge, series, and parallel topologies. Computer Science − Graph theory is used for the study of algorithms Extremal graph theory. Critical graph; Turán's theorem; Frequency partition; Frucht's theorem; Girth; Graph drawing; Graph homomorphism; Graph labeling. Graceful labeling; Graph partition; Graph pebbling; Graph property; Graph reduction; Graph-structured stack; Graphical model. Bayesian network; D-separation; Markov random field; Tree decomposition (Junction tree) and treewidt

Graph theory provides an approach to systematically testing the structure of and exploring connections in various types of biological networks. In particular, interval graph properties such as the ordering of maximal cliques via a transitive ordering along a Hamiltonian path are useful in detecting patterns in complex networks Methods in phonology (e.g. theory of optimality, which uses lattice graphs) and morphology (e.g. morphology of finite - state, using finite-state transducers) are common in the analysis of language as a graph. 4 A directed graph or digraph D is a finite collection of elements, which are called vertices, and a collection of ordered pairs of this vertices, which are called arcs. Thus, a digraph is similar to a graph except that each arc in a digraph has a direction, while an edge in a graph does not

44 Types of Graphs Perfect for Every Top Industry. Written by: Samantha Lile. Popular graph types include line graphs, bar graphs, pie charts, scatter plots and histograms. Graphs are a great way to visualize data and display statistics. For example, a bar graph or chart is used to display numerical data that is independent of one another Graph Connections: Relationships Between Graph Theory and Other Areas of Mathematics. Oxford, England: Oxford University Press, 1997. Berge, C. Graphs and Hypergraphs Types of Graphs. There are different types of graphs, which we will learn in the following section. Null Graph. A null graph has no edges. The null graph of $n$ vertices is denoted by $N_n$ Simple Graph. A graph is called simple graph/strict graph if the graph is undirected and does not contain any loops or multiple edges. Multi-Graph remains NP-complete even when restricted to certain classes of graphs such as bipartite graphs and chordal graphs. However, there are interesting classes of graphs such as trees, interval graphs, an

**Graph** **Theory** **Graphs** are discrete structures consisting of vertices and edges that connects these vertices. There are several **types** **of** **graphs** that differ with respect to the kind and number of edges that can connect a pair of vertices. A simple **graph** G = (V, E) consists of V, a nonempty set of vertices, and E, a set of unordered pairs of. Chapter : Graph Theory. Different types of a graph & Examples. Directed Graph : A graph G is called the directed graph, the set of vertices are V and the set of edges is E, consists the order pairs of elements of V. In general, we can say that each pair of vertices are connected by a straight line a direction between both the vertices are give They may involve arithmetic, algebra, geometry, theory of numbers, graph theory, topology, matrices, group theory, combinatorics (dealing combinatorics: Combinatorics during the 20th century of interest in combinatorics is graph theory, the importance of which lies in the fact that graphs can serve as abstract models for many different kinds of schemes of relations among sets of objects 10 GRAPH THEORY { LECTURE 4: TREES Tree Isomorphisms and Automorphisms Example 1.1. The two graphs in Fig 1.4 have the same degree sequence, but they can be readily seen to be non-isom in several ways. For instance, the center of the left graph is a single vertex, but the center of the right graph is a single edge Classes of Graph :- Regular graph , planar graph , connected graph , strongly connected graph , complete graph , Tree , Bipartite graph , Cycle Graph

In graph theory, a tree is an undirected graph in which any two vertices are connected by exactly one path, or equivalently a connected acyclic undirected graph. A forest is an undirected graph in which any two vertices are connected by at most one path, or equivalently an acyclic undirected graph, or equivalently a disjoint union of trees. A polytree is a directed acyclic graph whose underlying undirected graph is a tree. A polyforest is a directed acyclic graph whose underlying undirected gra There are many different types of graphs, such as connected and disconnected graphs, bipartite graphs, weighted graphs, directed and undirected graphs, and simple graphs Mathematics | Graph Theory Basics - Set 1. Difficulty Level : Easy. Last Updated : 13 Dec, 2019. A graph is a data structure that is defined by two components : A node or a vertex. An edge E or ordered pair is a connection between two nodes u,v that is identified by unique pair (u,v). The pair (u,v) is ordered because (u,v) is not same as (v. In the mathematical discipline of graph theory, a graph labelling is the assignment of labels, traditionally represented by integers, to edges and/or vertices of a graph. Formally, given a graph, a vertex labelling is a function of to a set of labels; a graph with such a function defined is called a vertex-labeled graph Introduction to graph theory. Introduction to Graphs; Directed and Undirected Graph; Basic Terminologies of Graphs; Vertices; The Handshaking Lemma; Types of Graphs; N-cube; Subgraphs; Graph Isomorphism; Operations of Graphs; The Problem of Ramsay; Connected and Disconnected Graph; Walks Paths and Circuits; Eulerial Graphs; Fluery's Algorithm.

5 Graph Theory Informally, a graph is a bunch of dots and lines where the lines connect some pairs of dots. An example is shown in Figure 5.1. The dots are called nodes (or vertices) and the lines are called edges. c h i j g e d f b Figure 5.1 An example of a graph with 9 nodes and 8 edges Definitions of **Graph** **Theory** 1.1 INTRODUCTION **Graph** **theory** is a branch of mathematics started by Euler [45] as early as 1736. It took a hundred years before the second important contribution of Kirchhoff [139] had been made for the analysis of electrical networks. Cayley [22] and Sylvester [228] discovered several properties of special **types** **of**. * Chapter 1*. Preface and Introduction to Graph Theory1 1. Some History of Graph Theory and Its Branches1 2. A Little Note on Network Science2 Chapter 2. Some De nitions and Theorems3 1. Graphs, Multi-Graphs, Simple Graphs3 2. Directed Graphs8 3. Elementary Graph Properties: Degrees and Degree Sequences9 4. Subgraphs15 5 7 ©Department of Psychology, University of Melbourne Geodesics A geodesic from a to b is a path of minimum length The geodesic distance dab between a and b is the length of the geodesic If there is no path from a to b, the geodesic distance is infinite For the graph The geodesic distances are: dAB = 1, dAC = 1, dAD = 1, dBC = 1, dBD = 2, dCD = 2 ©Department of Psychology, University of Melbourn

Graph theory is concerned with various types of networks, or really models of networks called graphs. These are not the graphs of analytic geometry, but what are often described Perhaps the most famous problem in graph theory concerns map coloring: Given a map of some countries, how many colors are required to color the map so that countrie Graph theory has abundant examples of NP-complete problems. Intuitively, a problem isin P1 if thereisan efﬁcient (practical) algorithm toﬁnd a solutiontoit.On the other hand, a problem is in NP 2, if it is ﬁrst efﬁcient to guess a solution and the * Types of Graphs provides in-depth information about charts & graphs*. Graphs are used in a variety of ways, and almost every industry, such as engineering, search engine optimization, mathematics, and education.If you cannot find the information you are looking for

2 1. Graph Theory At ﬁrst, the usefulness of Euler's ideas and of graph theory itself was found only in solving puzzles and in analyzing games and other recreations. In the mid 1800s, however, people began to realize that graphs could be used to model many things that were of interest in society. For instance, the Four Color Map. 10.2 Graph Terminology and Special Types of Graphs Undirected Graph Adjacent/Neighbors and Incident Edge Two vertices u and v in an undirected graph G are called adjacent (or neighbors) in G if u and v are endpoints of an edge e of G. Such an edge e is called incident with the vertices u and v and e is said to connect u and v. Neighborhoo 1.1 Graphs Deﬁnition1.1. Agraph GisapairG= (V;E) whereV isasetofvertices andEisa(multi)set of unordered pairs of vertices. The elements of Eare called edges. We write V(G) for the set of vertices and E(G) for the set of edges of a graph G. Also, jGj= jV(G)jdenotes the number of verticesande(G) = jE(G)jdenotesthenumberofedges. Deﬁnition1.2 #1 Line Graphs. The most common, simplest, and classic type of chart graph is the line graph. This is the perfect solution for showing multiple series of closely related series of data. Since line graphs are very lightweight (they only consist of lines, as opposed to more complex chart types, as shown below), they are great for a minimalistic look

Due to a planned power outage, our services will be reduced today (June 15) starting at 8:30am PDT until the work is complete. We apologize for the inconvenience TYPES OF GRAPHS: Some important types of graph are introduced here.. Null graph: A graph which contains only isolated node, is called a null graph. i.e., the set of edges in a null graph is empty.Null graph is denoted on n vertices by Nn. N4 is shown in Figure (13), Note that each vertex of a null graph is isolated

A computer graph is a graph in which every two distinct vertices are joined by exactly one edge. The complete graph with n vertices is denoted by Kn. The following are the examples of complete graphs. The graph Kn is regular of degree n-1, and therefore has 1/2n(n-1) edges, by consequence 3 of the handshaking lemma The graphs studied in graph theory should not be confused with the graphs of functions or other kinds of graphs. Vertex (Node). A node v is a terminal point or an intersection point of a graph Graph Theory, in essence, is the study of properties and applications of graphs or networks. As I mentioned above, this is a huge topic and the goal of this series is to gain an understanding of how to apply graph theory to solve real world problems. If we look out the premise we live, we could see a number of problems popping out which in turn. Graph data structures as we know them to be computer science actually come from math, and the study of graphs, which is referred to as graph theory. In mathematics, graphs are a way to formally. Graph Theory is a branch of mathematics that aims at studying problems related to a structure called a Graph. In this article, we will try to understand the basics of Graph Theory, and also touch upon a C programmer's perspective for representing such problems

* Types Of Labeling In Graph Theory*. {Label Gallery} Get some ideas to make labels for bottles, jars, packages, products, boxes or classroom activities for free. An easy and convenient way to make label is to generate some ideas first. You should make a label that represents your brand and creativity, at the same time you shouldn't forget the. A lot of problems we encounter every day could be paraphrased to a graph problem or a near similar subproblem. So it's required to have some familiarity with different graph variations and their applications. If you want to brush up the basics of Graph Theory - once again, you should definitely visit this.The latter will give you a brief idea about different types of Graphs and their. Any how the term Graph was introduced by Sylvester in 1878 where he drew an analogy between Quantic invariants and covariants of algebra and molecular diagrams. In 1941, Ramsey worked on colorations which lead to the identification of another branch of graph theory called extremel graph theory 4. Cyclic Graph - A graph with continuous sequence of vertices and edges is called a cyclic graph. Cyclic graph is denoted on 'n' vertices bt Cn where n >=3. 5. Wheel Graph - A graph formed by adding a vertex inside a cycle and connecting it to every other vertex is known as wheel graph. Wheel graph is denoted on 'n' vertices bt Wn where n>=3

Graph Theory - History Leonhard Euler's paper on Seven Bridges of Königsberg, published in 1736. Graph Theory - History Cycles in Polyhedra Thomas P. Kirkman William R. Hamilton Hamiltonian cycles in Platonic graphs Graph Theory - History Gustav Kirchhoff Trees in Electric Circuits Graph Theory - Histor Example. Graph Theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects.. Did you know, almost all the problems of planet Earth can be converted into problems of Roads and Cities, and solved? Graph Theory was invented many years ago, even before the invention of computer Use of graph theory is extreme when it comes to the computer science application. Many problems that are considered hard to determine or implement can easily solved use of graph theory. There are many types of graphs as a part of graph theory. Each type of graph is associated with a special property. Most applicatio

- Further information: Graph (mathematics) File:6n-graf.svg. A drawing of a graph. In mathematics and computer science, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects from a certain collection.A graph in this context is a collection of vertices or nodes and a collection of edges that connect pairs of vertices
- Definition of 'Graph Theory'. Definition: Graph is a mathematical representation of a network and it describes the relationship between lines and points. A graph consists of some points and lines between them. The length of the lines and position of the points do not matter. Each object in a graph is called a node
- Graph theory includes different types of graphs, each having basic graph properties and some 3.1 Graph: A graph-generally denoted G(V,E) or G= additional properties. These properties separate a graph (V,E) - consists of the set of vertices V unitedly with a from there type of graphs. These properties arrange set of edges E

* A graph is said to a digraph or directed graph in case the order of pair of vertices changes the meaning of the graph*. i.e. in case, G=(V, E) is the graph and Vi, Vj is a par of vertices is different from Vj, Vi. This can be seen in road maps when one of the roads is unidirectional or one-way. To denote such kind of cases directed graph is used Graph theory does not solve this problem but it can provide some interesting perspectives. mcs-ftl — 2010/9/8 — 0:40 — page 193 — #199 6.2. Tournament Graphs b d c e f Figure 6.4 A 5-node tournament graph. The results of a round-robin tournament can be represented with a tournamen

Bipartite Graph in Graph Theory- A Bipartite Graph is a special graph that consists of 2 sets of vertices X and Y where vertices only join from one set to other. Bipartite Graph Example. Bipartite Graph Properties are discussed Graphs are picture representatives for 1 or more sets of information and how these visually relate to one another. There are many types of charts and graphs of varied complexity. For almost any numerical data set, there is a graph type that is appropriate for representing it. Graphs help you present data in a meaningful way

- Different types of nodes in graph theory. Ask Question Asked 1 year, 4 months ago. Active 1 year, 4 months ago. Viewed 173 times 0. I am trying to figure out whether a path in a graph has various branches or not. For example, this path does not: But this branch does: Degree of the orange node > 2..
- Types of Line Graphs. The following are the types of the line graph. They are: Simple Line Graph: Only one line is plotted on the graph. Multiple Line Graph: More than one line is plotted on the same set of axes. A multiple line graph can effectively compare similar items over the same period of time
- e the structure of a network of connected objects is potentially a problem for graph theory
- This type of simplified picture is called a graph.. Definition of a graph. In graph theory, the term graph refers to an object built from vertices and edges in the following way.. A vertex in a graph is a node, often represented with a dot or a point. (Note that the singular form is vertex and the plural form is vertices.); The edges of a graph connect pairs of vertices

- es φ and hence deter
- Graph is a mathematical term and it represents relationships between entities. Two elements make up a graph: nodes or vertices (representing entities) and edges or links (representing relationships). The study of graphs is also known as Graph Theory in mathematics. There are different types of graphs
- Graphs: •A graph is a data structure that has two types of elements, vertices and edges. •An edge is a connection between two vetices •If the connection is symmetric (in other words A is connected to B B is connected to A), then we say the graph is undirected. •If an edge only implies one direction of connection, we say the graph is.

The body of graph theory allows mathematicians and computer scientists to apply many known principals, algorithms, and theories to their model. Fundamentally, a graph is very simple. It is composed of two kinds of elements, vertices and edges (sometimes called nodes and links in computer science) ** Graph theory deals with specific types of problems, as well as with problems of a general nature**. One type of such specific problems is the connectivity of graphs, and the study of the structure of a graph based on its connectivity (cf. Graph, connectivity of a). In the analysis of the reliability of electronic circuits or communications.

PDF version. A graph is a structure in which pairs of vertices are connected by edges.Each edge may act like an ordered pair (in a directed graph) or an unordered pair (in an undirected graph).We've already seen directed graphs as a representation for Relations; but most work in graph theory concentrates instead on undirected graphs.. Because graph theory has been studied for many centuries in. Graph Theory is an advanced topic in Mathematics. On a university level, this topic is taken by senior students majoring in Mathematics or Computer Science; however , this course will offer you the opportunity to obtain a solid foundation in Graph Theory in a very short period of time, AND without requiring you to have any advanced Mathematical. The Yield Curve is a graphical Types of Graphs Top 10 types of graphs for data presentation you must use - examples, tips, formatting, how to use them for effective communication and in presentations. representation of the interest rates on debt for a range of maturities. It shows the yield an investor is expecting to earn if he lends his money.

This mechansim can be extended to a wide variety of graphs types by slightly altering or enhancing the kind of function that represents the graph. Here are a few examples. Directed graph. type Dgraph vertex = vertex -> [vertex] The representation is the same as a undirected graph but the interpretation is different ** Definition The Cartesian product of two graphs G and H, denoted G H, is a graph defined on the pairs (g, h) ∈ V(G) × V(H)**. Two elements (g, h), (g ′, h ′) ∈ V(G H) are adjacent in G H if and only if : g = g ′ and hh ′ ∈ H; or. h = h ′ and gg ′ ∈ G. Two remarks follow : The Cartesian product is commutative. Any edge uv of a. When you begin any project that uses graph theory, you must determine what type of graph you're going to use. Using the two categories we've discussed here, we are left with 4 major types of. Graphs: basic concepts 1.1 Types of graphs. Subgraphs. Operations with graphs. The following are some important families of graphs that we will use often. Let n be a positive integer and V = fx 1;x 2;:::;x ng. The null graph of order n, denoted by N n, is the graph of order n and size 0. The graph N 1 is called the trivial graph

1.1 Speci c Types of Graphs De nition 5 (Null Graph). The graph Gwith vvertices and no edges is called the null graph on v vertices and denoted N v. For example, a diagram of the graph N 0 is displayed to the right: De nition 6 (Complete Graph). The graph Gon vvertices with one edge between each distinct pai Basic Graph Theory: Communication and Transportation Networks In this section, we will introduce some basics of graph theory with a view towards understanding some features of communication and transportation networks. 1.1 Notions of Graphs The term graph itself is deﬁned diﬀerently by diﬀerent authors, depending on what one wants to allow Introduction . The development of graph theory is very similar the development of probability theory, where much of the original work was motivated by efforts to understand games of chance.The large portions of graph theory have been motivated by the study of games and recreational mathematics. Generally speaking, we use graphs in two situations

2 M. Hauskrecht Graphs: basics Basic types of graphs: • Directed graphs • Undirected graphs CS 441 Discrete mathematics for CS a c b c d a b M. Hauskrecht Terminology an•I simple graph each edge connects two different vertices and no two edges connect the same pair of vertices pair of vertices. The graphs of figure 1.1 are not simple, whereas the graphs of figure 1.3 are. Much of graph theory is concerned with the study of simple graphs. We use the symbols v(G) and e(G) to denote the numbers of vertices and edges in graph G. Throughout the book the letter G denotes a graph Types of Graphs and Charts . There are various types of graphs and charts used in data visualization. However, in this article, we'll be covering the top 11 types that are used to visualize business data. Bar Chart/Graph. A bar chart is a graph represented by spaced rectangular bars that describe the data points in a set of data 4. Prove that a complete graph with nvertices contains n(n 1)=2 edges. 5. Prove that a nite graph is bipartite if and only if it contains no cycles of odd length. 6. Show that if every component of a graph is bipartite, then the graph is bipartite. 7. Prove that if uis a vertex of odd degree in a graph, then there exists a path from uto anothe results in graph theory, and as a result, it lends itself to many beautiful proofs. I will examine a couple of these proofs and show how they exemplify diﬀerent methods that are often used for all types of mathematics problems. 2 Basics and Deﬁnitions Not surprisingly, graph theory is the study of things called graphs. So what is a graph

Types of Charts. There are several different types of charts and graphs. The four most common are probably line graphs, bar graphs and histograms, pie charts, and Cartesian graphs. They are generally used for, and are best for, quite different things. You would use: Bar graphs to show numbers that are independent of each other. Example data. A graph H is a subgraph of a graph G if all vertices and edges in H are also in G. De nition A connected component of G is a connected subgraph H of G such that no other connected subgraph of G contains H. De nition A graph is called Eulerian if it contains an Eulerian circuit. MAT230 (Discrete Math) Graph Theory Fall 2019 7 / 7 Graph theory. A graph / network is a collection of nodes and the arcs that connect those nodes to one another. In the context of banking, each node represents a different bank and each arc represents some link between two banks. These links could represent direct or indirect links Graph theory relies on several measures and indices that assess the efficiency of transportation networks. 1. Measures at the Network Level. Transportation networks are composed of many nodes and links, and as they rise in complexity, their comparison becomes challenging

- A graph G is called connected if there is a path between every pair of vertices. When there is no concern about the direction of an edge the graph is called undirected. The graph in Figure 1 is a connected and undirected graph. Unlike most other areas in Mathematics , the theory of graphs has a definite starting point, when the Swis
- Graph theory studies combinatorial objects called graphs. These objects are a good model for many problems in mathematics, computer science, and engineering. Graph theory is not really a theory, but a collection of problems. Many of those problems have important practical applications and present intriguing intellectual challenges
- There are many types of graphs as a part of graph theory. Each type of graph is associated with a special property. Most application. makes use of one of this graph in order to fine solution to the problems. Because of the representation power of graphs and flexibility many problem can be represented as graphs and easily solved
- studied by graph theory. Social Networks: In this type of networks nodes represents person and edges represents their relationships. Pattern matching is useful method for finding positions and their locations. Facebook, Twitter are some examples of social networks [25]. Social network is a part of sociology. It is
- We employed
**graph**theoretical approach to reveal hidden properties and features of four species PCINs. Two main issues are addressed, (i) the global and local network topological properties, and (ii) the stability of the networks under 12**types****of**perturbations. According to the topological parameter classification, we identified some critical.

- Introduction to Graph Theory. Social network data consists of binary social relations. That is, it records the presence, absence or strength of relationships among pairs of persons. There are many kinds of social relations. For example: role-based. brother of, father of, sister of, etc. friend of, acquaintance of, enemy of, lover of; teacher of.
- types of labeling in graph theory 1200px tree graph.svg {Label Gallery} Get some ideas to make labels for bottles, jars, packages, products, boxes or classroom activities for free. An easy and convenient way to make label is to generate some ideas first
- Graph theory is a type of math that doesn't use a lot of numbers. A total nerd came up with it to stop his friends (not really his friends) from bugging him about getting out of the house more (he didn't). Fortunately for you, you too can use this math to avoid getting out of the house and lose your friends

- The field of Graph Theory plays vital role in various fields. One of the important areas in graph theory is Graph Labeling used in many applications like coding theory, x-ray crystallography, radar, astronomy, circuit design, communication network addressing, data base management
- A learning curve is a correlation between a learner's performance on a task and the number of attempts or time required to complete the task; this can be represented as a direct proportion on a graph. The learning curve theory proposes that a learner's efficiency in a task improves over time the more the learner performs the task. Graphical.
- This course provides a complete introduction to Graph Theory algorithms in computer science. Topics covered in these videos include: how to store and represent graphs on a computer; common graph theory problems seen in the wild; famous graph traversal algorithms (DFS & BFS); Dijkstra's shortest path algorithm (both the lazy and eager version); what a topological sort is, how to find one, and.

Students analyze dramatic works using graph theory. They gather data, record it in Microsoft Excel and use Cytoscape (a free, downloadable application) to generate graphs that visually illustrate the key characters (nodes) and connections between them (edges). The nodes in the Cytoscape graphs are color-coded and sized according to the importance of the node (in this activity nodes represent. As with many simple yet effective ideas, Euler's approach stood the test of time and yielded graph theory, a branch of mathematics that explores graph properties to this day. Graph representations attract a lot of interest because, first and foremost, they neatly visualise data and humans respond very well to data visualisations.That is exactly what Euler did - he put his thoughts in order. A graph is a way of representing connections between places. Mathematically, a graph is a collection of nodes and edges. Nodes are locations that are connected together by the edges of the graph. For instance, if you had two small towns connected by a two-way road, you could represent this as a graph with two nodes, each node representing a.