2024 Euler circuit definition

24 Eyl 2021 ... An Euler circuit travels every edge in a graph exactly once: True. By definition, an Euler circuit is a closed walk that traverses each edge of .... Leaven newspaper

Feb 6, 2023 · Eulerian Path: An undirected graph has Eulerian Path if following two conditions are true. Same as condition (a) for Eulerian Cycle. If zero or two vertices have odd degree and all other vertices have even degree. Note that only one vertex with odd degree is not possible in an undirected graph (sum of all degrees is always even in an undirected ... Figure 6.5.3. 1: Euler Path Example. One Euler path for the above graph is F, A, B, C, F, E, C, D, E as shown below. Figure 6.5.3. 2: Euler Path. This Euler path travels every edge once and only once and starts and ends at different vertices. This graph cannot have an Euler circuit since no Euler path can start and end at the same vertex ...A product xy x y is even iff at least one of x, y x, y is even. A graph has an eulerian cycle iff every vertex is of even degree. So take an odd-numbered vertex, e.g. 3. It will have an even product with all the even-numbered vertices, so it has 3 edges to even vertices. It will have an odd product with the odd vertices, so it does not have any ...An Euler path is a path that uses every edge of a graph exactly once. An Euler circuit is a circuit that uses every edge of a graph exactly once. An Euler path starts and ends at di erent vertices. An Euler circuit starts and ends at the same vertex. Another Euler path: CDCBBADEBMay 16, 2023 · circuit C. 3 Check whether C is an Euler Circuit? If so, return C Generate a subgraph G ′ by removing all edges in C from G and any isolated vertices Pick a vertex w from C that is in G ′ Pick any sequence of adjacent vertices and edges starting and ending with w, call this circuit C′ Merge circuits C and C ′ into a new10.2 Trails, Paths, and Circuits. Summary. Definitions: Euler Circuit and Eulerian Graph. Let . G. be a graph. An . Euler circuit . for . G. is a circuit that contains every vertex and every edge of . G. An . Eulerian graph . is a graph that contains an Euler circuit. Theorem 10.2.2. If a graph has an Euler circuit, then every vertex of the ...What I did was I drew an Euler path, a path in a graph where each side is traversed exactly once. A graph with an Euler path in it is called semi-Eulerian. I thoroughly enjoyed the challenge and ...Jan 31, 2023 · Eulerian Circuit is an Eulerian Path which starts and ends on the same vertex. A graph is said to be eulerian if it has a eulerian cycle. We have discussed eulerian circuit for an undirected graph. In this post, the same is discussed for a directed graph. For example, the following graph has eulerian cycle as {1, 0, 3, 4, 0, 2, 1} An Euler circuit is a type of circuit that uses every edge in a graph with no repeats. Being a circuit, it must start and end at the same vertex. Example15.8.10.2 Trails, Paths, and Circuits. Summary. Definitions: Euler Circuit and Eulerian Graph. Let . G. be a graph. An . Euler circuit . for . G. is a circuit that contains every vertex and every edge of . G. An . Eulerian graph . is a graph that contains an Euler circuit. Theorem 10.2.2. If a graph has an Euler circuit, then every vertex of the ...Mar 24, 2023 · Graph Theory: Path vs. Cycle vs. Circuit. 1. Introduction. Graphs are data structures with multiple and flexible uses. In practice, they can define from people’s relationships to road routes, being employable in several scenarios. Several data structures enable us to create graphs, such as adjacency matrix or edges lists. Definition. A real-valued sinusoid with constant amplitude, frequency, and phase has the form: where only parameter is time-variant. The inclusion of an imaginary component : gives it, in accordance with Euler's formula, the factoring property described in the lead paragraph: whose real part is the original sinusoid.be an Euler Circuit and there cannot be an Euler Path. It is impossible to cross all bridges exactly once, regardless of starting and ending points. EULER'S THEOREM 1 If a graph has any vertices of odd degree, then it cannot have an Euler Circuit. If a graph is connected and every vertex has even degree, then it has at least one Euler Circuit.Other articles where Eulerian circuit is discussed: graph theory: …vertex is known as an Eulerian circuit, and the graph is called an Eulerian graph. An Eulerian graph is connected and, in addition, all its vertices have even degree.In graph theory, an Eulerian trail is a trail in a finite graph that visits every edge exactly once . Similarly, an Eulerian circuit or Eulerian cycle is an Eulerian trail that starts and ends on the same vertex. They were first discussed by Leonhard Euler while solving the famous Seven Bridges of Königsberg problem in 1736. The problem can be stated mathematically like this: All the planar representations of a graph split the plane in the same number of regions. Euler found out the number of regions in a planar graph as a function of the number of vertices and number of edges in the graph. Theorem – “Let be a connected simple planar graph with edges and vertices. Then the number of regions in the graph is …An Euler Circuit is a closed walk that covers every edge once starting and ending position is same. Chinese Postman problem is defined for connected and undirected graph. The problem is to find shortest path or circuity that visits every edge of …Nov 24, 2022 · 2. Definitions. Both Hamiltonian and Euler paths are used in graph theory for finding a path between two vertices. Let’s see how they differ. 2.1. Hamiltonian Path. A Hamiltonian path is a path that visits each vertex of the graph exactly once. A Hamiltonian path can exist both in a directed and undirected graph.In graph theory, an Eulerian trail is a trail in a finite graph that visits every edge exactly once . Similarly, an Eulerian circuit or Eulerian cycle is an Eulerian trail that starts and ends on the same vertex. They were first discussed by Leonhard Euler while solving the famous Seven Bridges of Königsberg problem in 1736. The problem can be stated mathematically like this:1. An Euler path is a path that uses every edge of a graph exactly once.and it must have exactly two odd vertices.the path starts and ends at different vertex. A Hamiltonian cycle is a cycle that contains every vertex of the graph hence you may not use all the edges of the graph. Share. Follow.Definition 5.2.1 5.2. 1: Closed Walk or a Circuit. A walk in a graph is a sequence of vertices and edges, v1,e1,v2,e2, …,vk,ek,vk+1 v 1, e 1, v 2, e 2, …, v k, e k, v k + 1. such that the endpoints of edge ei e i are vi v i and vi+1 v i + 1. In general, the edges and vertices may appear in the sequence more than once.Stanford’s success in spinning out startup founders is a well-known adage in Silicon Valley, with alumni founding companies like Google, Cisco, LinkedIn, YouTube, Snapchat, Instagram and, yes, even TechCrunch. And venture capitalists routin...An Euler Circuit is a closed walk that covers every edge once starting and ending position is same. Chinese Postman problem is defined for connected and undirected graph. The problem is to find shortest path or circuity that visits every edge of …Definition \(\PageIndex{1}\): Closed Walk or a Circuit; Theorem \(\PageIndex{1}\) Theorem \(\PageIndex{2}\): Euler Walks; The first problem in graph theory dates to 1735, and is …Feb 1, 2018 · Eulerian Circuit: An Eulerian circuit is an Eulerian trail that is a circuit. That is, it begins and ends on the same vertex. Eulerian Graph: A graph is called Eulerian when it contains an Eulerian circuit. Figure 2: An example of an Eulerian trial. The actual graph is on the left with a possible solution trail on the right - starting bottom ...Definition 5.2.1 A walk in a graph is a sequence of vertices and edges, v1,e1,v2,e2, …,vk,ek,vk+1 v 1, e 1, v 2, e 2, …, v k, e k, v k + 1. such that the endpoints of edge ei e i are vi v i and vi+1 v i + 1. In general, the edges and vertices may appear in the sequence more than once. If v1 =vk+1 v 1 = v k + 1, the walk is a closed walk or ...Definition of Euler Graph: Let G = (V, E), be a connected undirected graph (or multigraph) with no isolated vertices. Then G is Eulerian if and only if every vertex of G has an even degree. Definition of Euler Trail: Let G = (V, E), be a conned undirected graph (or multigraph) with no isolated vertices. Then G contains a Euler trail if and only ...Euler's cycle or circuit theorem shows that a connected graph will have an Euler cycle or circuit if it has zero odd vertices. Euler's sum of degrees theorem shows that however many edges a ...Euler's formula, named after Leonhard Euler, is a mathematical formula in complex analysis that establishes the fundamental relationship between the trigonometric functions and …If a graph has an Euler circuit, that will always be the best solution to a Chinese postman problem. Let’s determine if the multigraph of the course has an Euler circuit by looking at the degrees of the vertices in Figure 12.116. Since the degrees of the vertices are all even, and the graph is connected, the graph is Eulerian. A non-planar circuit is a circuit that cannot be drawn on a flat surface without any wires crossing each other. Graph theory is a branch of mathematics that studies the properties and relationships of graphs. An oriented graph is a graph with arrows on its edges indicating the direction of current flow in an electrical circuit.have an Euler walk and/or an Euler circuit. Justify your answer, i.e. if an Euler walk or circuit exists, construct it explicitly, and if not give a proof of its non-existence. Solution. The vertices of K 5 all have even degree so an Eulerian circuit exists, namely the sequence of edges 1;5;8;10;4;2;9;7;6;3 . The 6 vertices on the right side of ... Mar 22, 2022 · A sequence of vertices \((x_0,x_1,…,x_t)\) is called a circuit when it satisfies only the first two of these conditions. Note that a sequence consisting of a single vertex is a circuit. Before proceeding to Euler's elegant characterization of eulerian graphs, let's use SageMath to generate some graphs that are and are not eulerian. Aug 23, 2019 · Eulerian Graphs - Euler Graph - A connected graph G is called an Euler graph, if there is a closed trail which includes every edge of the graph G.Euler Path - An Euler path is a path that uses every edge of a graph exactly once. An Euler path starts and ends at different vertices.Euler Circuit - An Euler circuit is a A sequence of vertices \((x_0,x_1,…,x_t)\) is called a circuit when it satisfies only the first two of these conditions. Note that a sequence consisting of a single vertex is a circuit. Before proceeding to Euler's elegant characterization of eulerian graphs, let's use SageMath to generate some graphs that are and are not eulerian.Definition. An Eulerian circuit (or eulerian circuit) is a circuit that passes through every vertex of a graph and uses every edge exactly once. It follows that every Eulerian …The Criterion for Euler Circuits The inescapable conclusion (\based on reason alone"): If a graph G has an Euler circuit, then all of its vertices must be even vertices. Or, to put it another way, If the number of odd vertices in G is anything other than 0, then G cannot have an Euler circuit. Circuit boards, or printed circuit boards (PCBs), are standard components in modern electronic devices and products. Here’s more information about how PCBs work. A circuit board’s base is made of substrate.Oct 29, 2021 · An Euler path can have any starting point with a different end point. A graph with an Euler path can have either zero or two vertices that are odd. The rest must be even. An Euler circuit is a ... 8 Eyl 2014 ... Euler circuit – a circuit that travels through every edge of a graph once and only once. OR – a Euler path that begins and ends at the same ...In graph theory, an Eulerian trail is a trail in a finite graph that visits every edge exactly once . Similarly, an Eulerian circuit or Eulerian cycle is an Eulerian trail that starts and ends on the same vertex. They were first discussed by Leonhard Euler while solving the famous Seven Bridges of Königsberg problem in 1736. The problem can be stated mathematically like this: Apr 16, 2016 · A Euler circuit can exist on a bipartite graph even if m is even and n is odd and m > n. You can draw 2x edges (x>=1) from every vertex on the 'm' side to the 'n' side. Since the condition for having a Euler circuit is satisfied, the bipartite graph will have a Euler circuit. A Hamiltonian circuit will exist on a graph only if m = n.24 Eyl 2021 ... An Euler circuit travels every edge in a graph exactly once: True. By definition, an Euler circuit is a closed walk that traverses each edge of ...Find cycle in undirected Graph using DFS: Use DFS from every unvisited node. Depth First Traversal can be used to detect a cycle in a Graph. There is a cycle in a graph only if there is a back edge present in the graph. A back edge is an edge that is indirectly joining a node to itself (self-loop) or one of its ancestors in the tree produced by ...One meaning is a graph with an Euler circuit, the other is a graph in which all vertices are of even degree. These definitions match in connected graphs.Đường đi Euler (tiếng Anh: Eulerian path, Eulerian trail hoặc Euler walk) trong đồ thị vô hướng là đường đi của đồ thị đi qua mỗi cạnh của đồ thị đúng một lần (nếu là đồ thị có hướng thì đường đi phải tôn trọng hướng của cạnh).Eulerizing a Graph. The purpose of the proposed new roads is to make the town mailman-friendly. In graph theory terms, we want to change the graph so it contains an Euler circuit. This is also ...Voltage, resistance and current are the three components that must be present for a circuit to exist. A circuit will not be able to function without these three components. Voltage is the main electrical source that is present in a circuit.Euler’s (pronounced ‘oilers’) formula connects complex exponentials, polar coordinates, and sines and cosines. It turns messy trig identities into tidy rules for exponentials. We will use it a lot. The formula is the following: eiθ = cos(θ) + isin(θ). There are many ways to approach Euler’s formula.There are two parts of your proof that I would consider incorrect, leaving out important details (which I'm sure you were aware of, but didn't write down):An Euler circuit is a way of traversing a graph so that the starting and ending points are on the same vertex. The most salient difference in distinguishing an Euler path vs. a circuit is that a ...called an Euler trail in G if for every edge e of G, there is a unique i with 1 ≤ i < t so that e = x i x i+1. Definition A circuit (x 1, x 2, x 3, …, x t) in a graph G is called an Euler circuit if for every edge e in G, there is a unique i with 1 ≤ i ≤ t so that e = x i x i+1. Note that in this definition, we intend that x t x t+1 =x ...Eulerian Graphs - Euler Graph - A connected graph G is called an Euler graph, if there is a closed trail which includes every edge of the graph G.Euler Path - An Euler path is a path that uses every edge of a graph exactly once. An Euler path starts and ends at different vertices.Euler Circuit - An Euler circuit is aIf a graph has a Eulerian circuit, then that circuit also happens to be a path (which might be, but does not have to be closed). – dtldarek. Apr 10, 2018 at 13:08. If "path" is defined in such a way that a circuit can't be a path, then OP is correct, a graph with an Eulerian circuit doesn't have an Eulerian path. – Gerry Myerson.The definition of Euler path in the link is, however, wrong - the definition of Euler path is that it's a trail, not a path, which visits every edge exactly once. And in the definition of trail, we allow the vertices to repeat, so, in fact, every Euler circuit is also an Euler path.Every Euler path is an Euler circuit. The statement is false because both an Euler circuit and an Euler path are paths that travel through every edge of a graph once and only once. An Euler circuit also begins and ends on the same vertex. An Euler path does not have to begin and end on the same vertex. Study with Quizlet and memorize flashcards ...Oct 29, 2021 · An Euler circuit is the same as an Euler path except you end up where you began. Fleury's algorithm shows you how to find an Euler path or circuit. It begins with giving the requirement for the graph. Mar 22, 2022 · A sequence of vertices \((x_0,x_1,…,x_t)\) is called a circuit when it satisfies only the first two of these conditions. Note that a sequence consisting of a single vertex is a circuit. Before proceeding to Euler's elegant characterization of eulerian graphs, let's use SageMath to generate some graphs that are and are not eulerian. 10.5 Euler and Hamilton Paths Euler Circuit An Euler circuit in a graph G is a simple circuit containing every edge of G. Euler Path An Euler path in G is a simple path containing every edge of G. Theorem 1 A connected multigraph with at least two vertices has an Euler circuit if and only if each of its vertices has an even degree. Theorem 2Definition: Special Kinds of Works. A walk is closed if it begins and ends with the same vertex. A trail is a walk in which no two vertices appear consecutively (in either order) more than once. (That is, no edge is used more than once.) A tour is a closed trail. An Euler trail is a trail in which every pair of adjacent vertices appear ... Circuits can be a great way to work out without any special equipment. To build your circuit, choose 3-4 exercises from each category liste. Circuits can be a great way to work out and reduce stress without any special equipment. Alternate ...be an Euler Circuit and there cannot be an Euler Path. It is impossible to cross all bridges exactly once, regardless of starting and ending points. EULER'S THEOREM 1 If a graph has any vertices of odd degree, then it cannot have an Euler Circuit. If a graph is connected and every vertex has even degree, then it has at least one Euler Circuit.Feb 1, 2018 · Eulerian Circuit: An Eulerian circuit is an Eulerian trail that is a circuit. That is, it begins and ends on the same vertex. Eulerian Graph: A graph is called Eulerian when it contains an Eulerian circuit. Figure 2: An example of an Eulerian trial. The actual graph is on the left with a possible solution trail on the right - starting bottom ...Euler Circuit Definition. An Euler circuit can easily be found using the model of a graph. A graph is a collection of objects and a list of the relationships between pairs of those objects. When ...An Eulerian path on a graph is a traversal of the graph that passes through each edge exactly once. It is an Eulerian circuit if it starts and ends at the same vertex. _\square . The informal proof in the previous section, translated into the language of graph theory, shows immediately that: If a graph admits an Eulerian path, then there are ... However, our objective here is to obtain the above time evolution using a numerical scheme. 3.2. The forward Euler method#. The most elementary time integration scheme - we also call these ‘time advancement schemes’ - is known as the forward (explicit) Euler method - it is actually member of the Euler family of numerical methods for ordinary differential …An Eulerian path on a graph is a traversal of the graph that passes through each edge exactly once. It is an Eulerian circuit if it starts and ends at the same vertex. _\square . The informal proof in the previous section, translated into the language of graph theory, shows immediately that: If a graph admits an Eulerian path, then there are ... 20 Eki 2020 ... An Euler circuit is an Euler path which starts and stops at the same ... The Euler Characteristic χ is defined by χ := v − e + f . Question.One meaning is a graph with an Euler circuit, the other is a graph in which all vertices are of even degree. These definitions match in connected graphs.An Euler path, in a graph or multigraph, is a walk through the graph which uses every edge exactly once. An Euler circuit is an Euler path which starts and stops at the same vertex. Our goal is to find a quick way to check whether a graph (or multigraph) has an Euler path or circuit. Jul 12, 2021 · Figure 6.5.3. 1: Euler Path Example. One Euler path for the above graph is F, A, B, C, F, E, C, D, E as shown below. Figure 6.5.3. 2: Euler Path. This Euler path travels every edge once and only once and starts and ends at different vertices. This graph cannot have an Euler circuit since no Euler path can start and end at the same vertex ... Mar 24, 2023 · Eulerian: this circuit consists of a closed path that visits every edge of a graph exactly once; Hamiltonian: this circuit is a closed path that visits every node of a graph exactly once.; The following image exemplifies eulerian and hamiltonian graphs and circuits: We can note that, in the previously presented image, the first graph (with the hamiltonian …Definition of Euler's Circuit. Euler's Circuit in finite connected graph is a path that visits every single edge of the graph exactly once and ends at the same vertex where it started. Although it allows revisiting of same nodes. It is also called Eulerian Circuit. It exists in directed as well as undirected graphs.A Hamiltonian cycle, also called a Hamiltonian circuit, Hamilton cycle, or Hamilton circuit, is a graph cycle (i.e., closed loop) through a graph that visits each node exactly once (Skiena 1990, p. 196). A graph possessing a Hamiltonian cycle is said to be a Hamiltonian graph. By convention, the singleton graph K_1 is considered to be …Definition 1: An Euler path is a path that crosses each edge of the graph exactly once. If the path is closed, we have an Euler circuit. In order to proceed to ...Euler tour of a tree, with edges labeled to show the order in which they are traversed by the tour. The Euler tour technique (ETT), named after Leonhard Euler, is a method in graph theory for representing trees.The tree is viewed as a directed graph that contains two directed edges for each edge in the tree. The tree can then be represented as a …Euler path and circuit. An Euler path is a path that uses every edge of the graph exactly once. Edges cannot be repeated. This is not same as the complete graph as it needs to be a path that is an Euler path must be traversed linearly without recursion/ pending paths. This is an important concept in Graph theory that appears frequently in real ...Definition: Special Kinds of Works. A walk is closed if it begins and ends with the same vertex.; A trail is a walk in which no two vertices appear consecutively (in either order) more than once.(That is, no edge is used more than once.) A tour is a closed trail.; An Euler trail is a trail in which every pair of adjacent vertices appear consecutively. (That is, every edge is used exactly once.)Stanford’s success in spinning out startup founders is a well-known adage in Silicon Valley, with alumni founding companies like Google, Cisco, LinkedIn, YouTube, Snapchat, Instagram and, yes, even TechCrunch. And venture capitalists routin...

An Euler circuit is a circuit that uses every edge in a graph with no repeats. Being a circuit, it must start and end at the same vertex. The graph below has several possible Euler circuits. Here's a couple, starting and ending at vertex A: ADEACEFCBA and AECABCFEDA. The second is shown in arrows.. Harris scott

Learning Outcomes. Add edges to a graph to create an Euler circuit if one doesn’t exist. Find the optimal Hamiltonian circuit for a graph using the brute force algorithm, the nearest neighbor algorithm, and the sorted edges algorithm. Use Kruskal’s algorithm to form a spanning tree, and a minimum cost spanning tree. An Euler circuit is a circuit that uses every edge in a graph with no repeats. Being a circuit, it must start and end at the same vertex. The graph below has several possible Euler circuits. Here’s a couple, starting and ending at vertex A: ADEACEFCBA and AECABCFEDA. The second is shown in arrows.👉Subscribe to our new channel:https://www.youtube.com/@varunainashots Any connected graph is called as an Euler Graph if and only if all its vertices are of...Unfortunately, in contrast to Euler’s result about Euler tours and trails (given in Theorem 13.1.1 and Corollary 13.1.1), there is no known characterisation that enables us to quickly determine whether or not an arbitrary graph has a Hamilton cycle (or path). This is a hard problem in general.If a graph has an Euler circuit, that will always be the best solution to a Chinese postman problem. Let’s determine if the multigraph of the course has an Euler circuit by looking at the degrees of the vertices in Figure 12.116. Since the degrees of the vertices are all even, and the graph is connected, the graph is Eulerian.2 Nis 2017 ... ... definitions, are all distinct from one another. Euler1. An Eulerian cycle, Eulerian circuit or Euler tour in an undirected graph is a cycle ...Paths traversing all the bridges (or, in more generality, paths traversing all the edges of the underlying graph) are known as Eulerian paths, and Eulerian paths which start and end at the same place are called …Oct 29, 2021 · An Euler circuit is the same as an Euler path except you end up where you began. Fleury's algorithm shows you how to find an Euler path or circuit. It begins with giving the requirement for the graph. An Eulerian cycle, [3] also called an Eulerian circuit or Euler tour, in an undirected graph is a cycle that uses each edge exactly once. If such a cycle exists, the graph is called Eulerian or unicursal. [5] The term "Eulerian graph" is also sometimes used in a weaker sense to denote a graph where every vertex has even degree.Jul 31, 2020 · called an Euler trail in G if for every edge e of G, there is a unique i with 1 ≤ i < t so that e = x i x i+1. Definition A circuit (x 1, x 2, x 3, …, x t) in a graph G is called an Euler circuit if for every edge e in G, there is a unique i with 1 ≤ i ≤ t so that e = x i x i+1. Note that in this definition, we intend that x tx t+1=x tx 1.Mar 22, 2016 · We can use Euler’s formula to prove that non-planarity of the complete graph (or clique) on 5 vertices, K 5, illustrated below. This graph has v =5vertices Figure 21: The complete graph on ﬁve vertices, K 5. and e = 10 edges, so Euler’s formula would indicate that it should have f =7 faces. We have just seen that for any planar graph we ...Definition of Euler Graph: Let G = (V, E), be a connected undirected graph (or multigraph) with no isolated vertices. Then G is Eulerian if and only if every vertex of G has an even degree. Definition of Euler Trail: Let G = (V, E), be a conned undirected graph (or multigraph) with no isolated vertices. Then G contains a Euler trail if and only ...Other articles where Hamilton circuit is discussed: graph theory: …path, later known as a Hamiltonian circuit, along the edges of a dodecahedron (a Platonic solid consisting of 12 pentagonal faces) that begins and ends at the same corner while passing through each corner exactly once. The knight’s tour (see number game: Chessboard problems) is …What do you mean by the Eulerian path? An Eulerian trail (also known as an Eulerian path) is a finite graph trail in graph theory that reaches each edge exactly once (allowing for revisiting vertices). An analogous Eulerian trail that begins and finishes at the same vertex is known as an Eulerian circuit or cycle.Back in the section Use Euler's Formula, A2 was defined in terms of the K constants. A2 = j(K1 - K2) Then we pressed ahead and figured out A2 = 5. If you go back to the definition of A2 in terms of K's, that means the K's have to be imaginary numbers. They have to include a j term to get rid of the j in A2 = j(K1 - K2).Graph Theory: Path vs. Cycle vs. Circuit. 1. Introduction. Graphs are data structures with multiple and flexible uses. In practice, they can define from people’s relationships to road routes, being employable in several scenarios. Several data structures enable us to create graphs, such as adjacency matrix or edges lists..

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