Weights could indicate distance, cost, etc. Adjacency matrix. AdjacencyGraph constructs a graph from an adjacency matrix representation of an undirected or directed graph. We can have a coefficient improvement in time complexity if we only store on one half of the diagonal Adjacency List In adjacency matrix, we represent the graph in a two-dimensional array of V x V vertices. Let's create this graph using an adjacency list and then show all the edges that exist in the graph. A3 ->1->4. The space complexity of adjacency matrix is O(V 2). If it is NULL then an unweighted graph is created and the elements of the adjacency matrix gives the number of edges between the vertices. The adjacency list of the graph is as follows: A1 ->2. An Adjacency matrix is a square matrix used to represent a finite graph. 3 Replies. The details depend on the value of the mode argument: "directed" The graph will be directed and a matrix element gives the number of edges between two vertices. Glossary. At any step in the algorithm, the -entry in the adjacency matrix gives the … Say, the node is u, now traverse each node in the adjacency list of u. The adjacency matrix of a graph is a square matrix of size V x V. The V is the number of vertices of the graph G. In this matrix in each side V vertices are marked. Adjacency matrix representation. Consider a directed graph as shown above. An adjacency matrix is a sequence matrix used to represent a finite graph. Depth First Search is a graph traversal technique. A. The rows and columns of the matrix are labeled as per the graph vertices. Adjacency matrix of an undirected graph is. This syntax is used for the directed … If we have a weighted graph, we now have the problem of which edge weight to take as the new undirected graph edge weight. Suppose is a finite undirected graph. "undirected" • Dense graph: lots of edges. Suppose you have a non-directed graph, represented through its adjacency matrix. An adjacency matrix uses a square matrix to represent a graph. (1) The adjacency matrix is always symmetric. An adjacency list is efficient in terms of storage because we only need to store the values for the edges. adjacency list. It means that its adjacency matrix is symmetric. A Graph, G = (V, E), where V is the number of vertices in the graph, and E is the number of edges in the graph, can be represented in two standard ways. A weighted graph may be represented with a list of vertex/weight pairs. We usually write B instead of B(G). See also adjacency-matrix representation, sparse graph. Usually, the cost of … The diagonal entries of an adjacency matrix … For example, we have a graph below. For large graphs, the adjacency matrix contains many zeros and is typically a sparse matrix. Question 2 Explanation: Total number of values in the matrix is 4*4=16, out of which 6 entries are non zero. If nodes are connected with each other then we write 1 and if not connected then write 0 in adjacency matrix. We should always have a square matrix! We here give three examples, which are important results in graph theory, to show that adjacency and incidence matrices are very useful for studying graphs. The adjacency matrix of is defined as the matrix whose entry is: 0 if there is no edge from to ; 1 if there is an edge from to For this syntax, G must be a simple graph such that ismultigraph(G) returns false. G is simple graph or not. An Adjacency matrix is just another way of representing a graph when using a graph algorithm. Adjacency matrix. Using Adjacent Matrix and 2. Conversely, a directed graph describing a network of asymmetric or anti-symmetric ties will create an asymmetric matrix.An asymmetric graph means that the values contained in the matrix do not mirror each other. Using Adjacency List. The amount of memory to store the array for the adjacency list is O(max(V,E))=O(V+E). Fact 1: Consider a directed graph and a positive integer k. Then the number of directed walks from node i to node j of length k is the entry on row i and column j of the matrix Ak, where A is the adjacency matrix. always a symmetric matrix, i.e. Below is an example of a directed graph that depicts a flight network traveling to different places. Example: The following is a simple example of a graph with vertices . Question: Q2. • Sparse graph: very few edges. Adjacency Matrix Adjacency List; For a Directed Graph, it consumes O(|V| 2) space which is often under-utilized in the implementation. A finite graph can be represented in the form of a square matrix on a computer, where the boolean value of the matrix indicates if there is a direct path between two vertices. The idea is to take 2D array of size V * V, then mark the index as “1” if there exist an edge between those 2 vertices. Figure 5.13. Let’s Create an Adjacency Matrix: 1️⃣ Firstly, create an Empty Matrix as shown below : Empty Matrix. The adjacency matrix of the directed graphs is as follows: 2. The adjacency matrix of a weighted graph can be used to store the weights of the edges. A subset of a directed graph satisfying the following conditions is called a clique: Likewise, a matrix of 0's and 1's is interpreted as an unweighted graph unless specified otherwise. Consider the directed graph given above. Figure 5.12. Note that we only have to consider 1 + 2 + 3 + ... + n-1 entries since the resultant adjacency matrix is symmetric. The graph structure can be represented by simplying storing a boolean value at each array index. Indeed, in undirected graph, if there is an edge (2, 5) then there is also an edge (5, 2). In general, a matrix is called primitive if there is a positive integer k such that Ak is a positive matrix. 2. b. Using an Adjacency Matrix: We use the names 0 through V-1 for the vertices in a V-vertex graph. In this article, we will learn about Graph, Adjacency Matrix with linked list, Nodes and Edges. In the special case of a finite simple graph, the adjacency matrix is a -matrix with zeros on its diagonal. Note: Suppose we have a directed graph … One is space requirement, and the other is access time. See also adjacency-matrix representation, sparse graph. a) in, out b) out, in c) in, total d) total, out Answer: b Clarification: Row number of the matrix represents the tail, while Column number represents the head of the edge. Display the Adjacency … We can have a coefficient improvement in time complexity if we only store on one half of the diagonal Adjacency List Dominance-directed Graph Up: Definitions Previous: Adjacency matrix (vertex matrix) Clique . For same node, it will be 0. We define the transpose of a adjacency matrix A = (a ij) to be the adjacency matrix A T = (T a ij) given by T a ij = a ji. In the previous post, we introduced the concept of graphs. If graph G = (V, E) is a directed graph, its transpose, G T = (V, E T) is the same as graph G with all arrows reversed. For the adjacency matrix of a directed graph the row sum is the _____ degree and the column sum is the _____ degree. The graph presented by example is undirected. Directed and Edge-Weighted Graphs Directed Graphs (i.e., Digraphs) In some cases, one finds it natural to associate each connection with a direction -- such as a graph that describes traffic flow on a network of one-way roads. 1. s Fill in the matrix below. Show adjacency lists for the weighted graph in Figure 20-33 and the directed graph in Figure 20-34 . Adjacency matrix V 2 Adjacency list E + V Edge from v to w? arbitrary matrix to be the edge adjacency matrix of a graph? Graphs are two types Directed and Undirected. Below is an example of a directed graph that depicts a flight network traveling to different places. This argument specifies whether to create a weighted graph from an adjacency matrix. let A be an adjacency matrix and M be an incidence matrix of the graph G. Determine whether: 1. In this tutorial, we are going to see how to represent the graph using adjacency matrix. Incidence Matrix Representation: If a directed graph G consists of n vertices and m edges, then the incidence matrix is an n x m matrix C = [c ij] and defined by. Likewise, a matrix of 0's and 1's is interpreted as an unweighted graph unless specified otherwise. It is a 2D array of size V X V matrix where V is the vertices of the graph. This matrix is a two-dimensional array wherein the value of matrix[row][column] is the weight of the edge between the vertices at row and column. If graph G = (V, E) is a directed graph, its transpose, G T = (V, E T) is the same as graph G with all arrows reversed. An Adjacency matrix is a square matrix used to represent a finite graph. As it stores the path between 2 vertices, it is called as adjacency matrix. An undirected graph may be represented by having vertex j in the list for vertex i and vertex i in the list for vertex j. In graph theory and computer science, an adjacency matrix is a square matrix used to represent a finite graph. The sum of the lengths of the adjacency lists is 2|E| in an undirected graph, and |E| in a directed graph. Browse other questions tagged graph-theory adjacency-matrix directed-graph undirected-graph or ask your own question. Arrow between nodes number 1 and 3 pass over the node number 2 and another strange half arrow on … Submitted by Radib Kar, on July 07, 2020 . There are 2 big differences between adjacency list and matrix. This approach if very fast for look-ups. In an undirected graph, if Ai,j = 1 then Aj,i = 1. Fig 4. 11 (b) ei V1 V2 es UT ed For the adjacency matrix, the rows and columns are ordered v1 through V 4 2 0 2 0 0 0 2 0 2 1 0 2 0 0 2 0 x I imagine there are all sorts of matrices associated to weighted digraphs so that computers can be used to analyze networks. It is ignored for directed graphs. $\textbf{Clarification:}$ By "analogous to the adjacency matrix" I mean a matrix that is defined simply in terms of the graph (vertices, arcs, and weights). Consider the undirected graph given above. Browse other questions tagged graph-theory adjacency-matrix directed-graph undirected-graph or ask your own question. Directed graphs are the graphs in which the vertices are ordered and in undirected graphs the vertices are unordered. And does the edge adjacency matrix of a graph contain all the information about this graph, that is, can we determine a graph from its edge adjacency matrix? Some authors use the outgoing link definition, e.g. 4.4 The Asymmetric Adjacency Matrix. However, selecting one versus the other would appear to give very different results. Find all vertices reachable from s along a directed path. Adjacency-list … For the undirected graph shown in Figure 0.2 (A) the adjacency matrix looks like: A. The rest of the cells contains either 0 or 1 (can contain an associated weight w if it is a weighted graph). this one: In a directed graph vertex v is adjacent to u, if there is an edge leaving v and coming to u. V outdegree(v) List of edges E + V E E E is proportional to V 11 Digraph Search 12 Reachability Goal. It depends on the author. The graph to convert. In this tutorial, we’ll study the differences between directed and undirected graphs. Example 1 The adjacency matrices for the two graphs in Figure 8.1 and the two digraphs in Figure 8.2 are as follows: Let be the size of the vertex set . The cost of moving from vertex 0 to vertex 1 is 1, the cost of moving from vertex 0 to vertex 2 is 2, and so on. As you can see from the above graph, if a path of length 1 exists from one vertex to another ie. In a directed graph, if Ai,j = 1 then Aj,i may or may not be 1. 3. For a directed graph, however, I'm unclear on how to best define the normalized adjacency matrix. The adjacency matrix above represents a graph that has 3 vertices. (2) The vertices must be ordered: and the adjacency matrix depends on the order chosen. Here each cell at position M [i, j] is holding the weight from edge i to j. A2 ->4. 2. Other authors use the ingoing link definition, e.g. Adjacency List representation. Consider the same directed graph from an adjacency matrix. We can easily represent the graphs using the following ways, 1. Since graphs are symmetric, the adjacency matrix is symmetric \({\bf A} = {\bf A}^T\). Adjacency Matrix is 2-Dimensional Array which has the size VxV, where V are the number of vertices in the graph. Following Are The Key Properties of an Adjacency Matrix: The adjacency matrix can also be known as the connection matrix. Solution for i. Figure \(\PageIndex{5}\) presents a graph and its adjacency matrix. let A be an adjacency matrix and M be an incidence matrix of the graph G. Determine whether: 1. Fix a bijective correspondence . The relationship between a graph and the … But the value of the determinant / A 1 is inde- pendent of this ordering. A = adjacency(G,'weighted') returns a weighted adjacency matrix, where for each edge (i,j), the value A(i,j) contains the weight of the edge. 题目描述 Give you a directed graph G with n nodes and m edges. An adjacency matrix is a square matrix that is used to represent a graph. For this syntax, G must be a simple graph such that ismultigraph(G) returns false. If this argument is NULL then an unweighted graph is created and an element of the adjacency matrix gives the number of edges to create between the two corresponding vertices. Directed graphs are the graphs in which the vertices are ordered and in undirected graphs the vertices are unordered. • Directed graph: edges have direction –edge (A, B) means that we can go (on that edge) from A to B, but not from B to A. –will have both edge (A, B) and edge (B, A) if A and B are linked in both directions. This Demonstration uses the Floyd–Warshall algorithm to find the shortest-path adjacency matrix and graph. The diagonal entries of an adjacency matrix … Directed Graphs are used in Google’s Page Ranking Algorithm. A graph is a set of nodes or known number of vertices. 6. (a) en V3 V2 es For the adjacency matrix, the rows and columns are ordered v1 through vz. Details. vertex j. Networks have adjacency matrices \({\bf A} \in R_+^{n \times n}\). A4 ->2. Browse other questions tagged graph-theory adjacency-matrix directed-graph undirected-graph or ask your own question. An adjacency matrix is essentially a 2D array (or matrix) where each row represents a vertex (node) and column represents a destination vertex. the weather of the matrix indicates whether pairs of vertices are adjacent or not within the graph. Adjacency List. See the example below, the Adjacency matrix for the graph shown above. 4 $$\hspace{2cm}$$ // nodes A directed graph (or digraph) is a set of vertices and a collection of directed edges that each connects an ordered pair of vertices. A Graph, G = (V, E), where V is the number of vertices in the graph, and E is the number of edges in the graph, can be represented in two standard ways. The adjacency matrix of a digraph having vertices P 1,P 2,…,P n is the n × n matrix whose (i,j) entry is the number of directed edges from P i to P j. Consider the following directed graph G in which the vertices are ordered as v 1v 2v 3v 4and v 5and its equivalent adjacency matrix representation on the right:. If there exists any direction, then we have to flow with direction arrow only. Adjacency matrix of a directed graph is. Figure 2 shows the seven balanced partitions of a simple single-layer directed network, whose adjacency matrix is reported in the Supplementary Note 2. For undirected graphs, the matrix is repeated about a diagonal axis. In the Example below, a graph is implemented with the help of adjacency matrix. Transpose: Transpose of a directed graph produces another graph with same edge & node configurations but the direction of all the edges have been reversed. Directed graphs have adjacency matrices just like undirected graphs. The diagonal entries of an adjacency matrix … Find the adjacency matrices for the directed graphs in (a) and (b). 2. this one:insert a 1 if vertex j is adjacent to vertex i (that is, if there is an arc from vertex i to vertex j). A symmetric matrix is interpreted as an undirected graph unless the edge direction is stated otherwise. Please print the adjacency matrix A of G. Hints: adjacency matrix is a way to represent a graph. Glossary. never symmetric, adj [i] [j] = 1 indicates a directed edge from vertex i to. Figure 2 shows the seven balanced partitions of a simple single-layer directed network, whose adjacency matrix is reported in the Supplementary Note 2. Adjacency matrix provide a constant time access, that is, O(1) to check whether there is an edge between two nodes. Adjacency matrix. If any element of graph[i][j] is 1, this means that there is an edge connecting vertex i with vertex j. Consider the same directed graph from an adjacency matrix. Adjacency Matrix: Adjacency Matrix is a 2D array of size V x V where V is the number of vertices in a graph. let A be an adjacency matrix and M be an incidence matrix of the graph G. Determine whether: 1. On the topic of making this more naturally supported, there's two parts: weighted graphs; directed graphs; Weighted. G is simple graph or not. G is directed or undirected. The adjacency matrix, sometimes also called the connection matrix, of a simple labeled graph is a matrix with rows and columns labeled by graph vertices, with a 1 or 0 in position (v_i,v_j) according to whether v_i and v_j are adjacent or not. It’s easy to implement because removing and adding an edge takes only O (1) time. Adjacency matrix for a directed graph In a directed graph, edges form an ordered pair. The nth eigenvalue, which is the most negative in the case of the adjacency matrix and is the largest in the case of the Laplacian, corresponds to the highest frequency vibration in a graph. What is space requirement for adjacency list and adjacency matrix for directed and undirected graph? For a finite directed graph. let A be an adjacency matrix and M be an incidence matrix of the graph G. Determine whether: 1. Update matrix entry to contain the weight. The Overflow Blog Using collections to make your SQL access easier and more efficient. Unlike the case of directed graphs, the entries in the incidence matrix of a graph (undirected) are nonnegative. Example. 1 outdegree(v) Iterate over edges leaving v? Adjacency matrix. G is directed or undirected. Solution for i. Note: Suppose we have a directed graph … We use the names 0 through V-1 for the vertices in a V-vertex graph. Let be the size of the vertex set . But, the operation is useful when applied to an adjacency matrix. The Overflow Blog Using collections to make your SQL access easier and more efficient. What is space requirement for adjacency list and adjacency matrix for directed and undirected graph? • The adjacency matrix is a good way to represent a weighted graph. It seems like the most direct extension is to simply consider the diagonal matrix of in- or out-degrees, instead. 4. A = adjacency(G,'weighted') returns a weighted adjacency matrix, where for each edge (i,j), the value A(i,j) contains the weight of the edge. It is a compact way to represent the finite graph containing n vertices of a m x m matrix M. Digraphs. An adjacency matrix is defined as follows: Let G be a graph with "n" vertices that are assumed to be ordered from v 1 to v n. The n x n matrix A, in which a ij = 1 if there exists a path from v i to v j a ij … As you can see from the above graph, if a path of length 1 exists from one vertex to another ie. Adjacency Matrix is also used to represent weighted graphs. 4.2 Directed Graphs. Types of Solution for finding transpose graph Adjacency List Approach. Let's assume the list of size n as Adjlist [n] Adjlist [0] will have all the nodes which are connected to vertex 0. In Example 1.6.3, we show that if Gis a strongly connected digraph of order v and the maximum degree ∆, then For example, if A(2,1) = 10, then G contains an edge from node 2 … Creating an adjacency matrix representation of a directed graph. A directed graph (or digraph) is a set of vertices and a collection of directed edges that each connects an ordered pair of vertices. Following Are The Key Properties of an Adjacency Matrix: The adjacency matrix can also be known as the connection matrix. If the graph is undirected, the adjacency matrix is symmetric. Adjacency Matrix Adjacency Matrix – Directed Graph Direct Graph with Loop. Adjacency list. Adjacency matrix. Graphs are networks, networks are not necessarily graphs. A matrix A means the adjacency matrix. Likewise, a matrix of 0's and 1's is interpreted as an unweighted graph unless specified otherwise. On GPUs, both directed and undirected graphs represented by an adjacency matrix take O(|V | 2) memory space, because the whole matrix is stored in memory with a large continuous array.In GPU architectures, it is also important, for performance, to align the matrix with memory to improve coalescence of memory accesses. G is simple graph or not. between two vertices i and j. Instead of a list of lists, it is a 2D matrix that maps the connections to nodes as seen in figure 4. We define the transpose of a adjacency matrix A = (a ij) to be the adjacency matrix A T = (T a ij) given by T a ij = a ji. For the adjacency matrix with any other ordering is of the form PAP-' for some permutation matrix P, and I PAP-' … Fill in the matrix below. Digraphs. Let the 2D array be adj[][], a slot adj[i][j] = 1 indicates that there is an edge from vertex i to vertex j. Adjacency matrix for undirected graph is always symmetric. In a weighted graph, the edges have weights associated with them. Adjacency-list … Generate the graph using the Adjacency Matrix and also traverse all the nodes of the graph using Depth First Search (BFS) Traversal Technique 4.2 Directed Graphs. For example, from the vertex v1, we can reach vertices v2, v4, and v5. The order of the vertices are preserved, i.e. G is simple graph or not. 1. When these vertices are paired together, we call … For a sparse graph with millions of vertices and edges, this can mean a lot of saved space. Gis irce or not. I was trying to plot a 9x9 adjacency matrices which produce a useless directed graph. graph_from_adjacency_matrix operates in two main modes, depending on the weighted argument.. adjMaxtrix [i] [j] = 1 when there is edge between Vertex i and Vertex j, else 0. Q2. Where (i,j) represent an edge originating from ith vertex and terminating on jth vertex. adjacency matrix with directed graph connected nodes. To construct an undirected graph using only the upper or lower triangle of the adjacency matrix, use graph (A,'upper') or graph (A,'lower'). A directed graph as well as undirected graph can be constructed using the concept of adjacency matrices, Following is an Adjacency Matrix Example. D. 0. Question: Q2. Suppose we have a directed graph G, if there is an edge from node i to node j in G, we have A[i][j] = 1 in G’s corresponding adjacency matrix A, otherwise, A[i][j] = 0. 输入 The first line will be an integer T (1 <= T <= 50). Below is the syntax highlighted version of AdjMatrixGraph.java from §4.1 Undirected Graphs. Let us consider the below directed graph … Directed graph – It is a graph with V vertices and E edges where E edges are directed.In directed graph,if Vi and Vj nodes having an edge.than it is represented by a pair of triangular brackets Vi,Vj. Its corresponding eigenvector tries to assign as di erent as possible values to neighboring vertices. 0 2 1 2 0 0 0 0 11 X (b) es Ca V2 V3 ed V4 For the adjacency matrix, the rows and columns are ordered v, through v4 2 0 0 0 0 1 0 2 1 0 2 0 0 2 0 X. 4.4 The Asymmetric Adjacency Matrix. Question 3 [CLICK ON ANY CHOICE TO KNOW MCQ multiple objective type questions RIGHT ANSWER] Adjacency matrix of all graphs are symmetric. Will the adjacency matrix be symmetrical? This matrix is a two-dimensional array wherein the value of matrix[row][column] is the weight of the edge between the vertices at row and column. If the graph has no edge weights, then A(i,j) is set to 1. A Graph, G = (V, E), where V is the number of vertices in the graph, and E is the number of edges in the graph, can be represented in two standard ways. In this tutorial we shall see how to store a graph with the help of a matrix. The nth eigenvalue, which is the most negative in the case of the adjacency matrix and is the largest in the case of the Laplacian, corresponds to the highest frequency vibration in a graph. The vertex matrix is defined by. 28)Write a C program to read the adjacency matrix of directed graph and convert it into adjacency list. If the edge is not present, then it will be infinity. The entries in the adjacency matrix A = A(D) of digraph D clearly depend on the ordering of the points. Adjacency List representation. (3) An adjacency matrix can be defined for multigraphs by defining a ij to be the number of edges between vertices i and j. In this video we will learn about directed graph and their representation using adjacency matrix. An undirected graph G is directed or undirected. An adjacency matrix uses a square matrix to represent a graph. For the current example, we’ll have 6 rows (representing nodes 1-6) and 6 columns (again, representing nodes 1-6). An adjacency matrix uses a square matrix to represent a graph. In graph theory and computing, an adjacency matrix may be a matrix wont to represent a finite graph. In this article, we will be focusing on the representation of graphs using an adjacency … Graph Representation Adjacency Matrix. An undirected graph may be represented by having vertex j in the list for vertex i and vertex i in the list for vertex j. an edge (i, j) implies the edge (j, i). Adjacency Matrix Representation of Graph. The main purpose of a graph is to find the shortest route between two given nodes where each node represents an entity. A symmetric matrix is interpreted as an undirected graph unless the edge direction is stated otherwise. Fact 1: Consider a directed graph and a positive integer k. Then the number of directed walks from node i to node j of length k is the entry on row i and column j of the matrix Ak, where A is the adjacency matrix. In Adjacency List, we use an array of a list to represent the graph. A matrix A means the adjacency matrix. Remarks 1.2.1. For example, if w(2,5) = 5 but w(5,2) = 10, the resultant edge weight is ambiguous. Consider the following directed graph G in which the vertices are ordered as v 1v 2v 3v 4and v 5and its equivalent adjacency matrix representation on the right:. There is a path from node A to node B, but there doesn’t exist any direct path from node B to node A. For undirected graphs, the matrix is repeated about a diagonal axis. The entries in the adjacency matrix A = A(D) of digraph D clearly depend on the ordering of the points. 2. Its corresponding eigenvector tries to assign as di erent as possible values to neighboring vertices. The Adjacency Matrix of One Type of Directed Graph and the Jacobsthal Numbers and Their Determinantal Representation Fatih Yılmaz 1 and Durmuş Bozkurt 1 1 Department of Mathematics, Science Faculty, Selcuk University, 42250 Konya, Turkey I'm working on my data structures knowledge and wanted to create a graph with a small DFS driver which simply prints the nodes as it visits them. We say that a directed edge points from the first vertex in the pair and points to the second vertex in the pair. Let us consider a graph in which there are N vertices numbered from 0 to N-1 and E number of edges in the form (i,j). For a simple graph with no self-loops, the adjacency matrix must have 0s on the diagonal. Adjacency-Matrix Implementation. We say that a directed edge points from the first vertex in the pair and points to the second vertex in the pair. A graph and its equivalent adjacency list representation are shown below. The cell (i,j) is true if there is an edge from Vertex-i to Vertex-j or if Vertex-i and Vertex-j are adjacent. For an Undirected Graph also, it consumes O(|V| 2) space which is also under-utilized as the generated matrix is symmetric about diagonal and values just repeat. Adjlist [1] will have all the nodes which are connected to … A graph is represented using square matrix. In the case of a directed graph GD.V;E/, the adjacency matrix A G Dfaijgis defined so that aijD (1 if i!j2E 0 otherwise. Given the total number of vertices and edges of a directed graph. In the special case of a finite simple graph, the adjacency matrix may be a … Adjacency matrix. To store weighted graph using adjacency matrix form, we call the matrix as cost matrix. Incidence Matrix . Directed graph of friendship relations among Bob, Carol, Ted, and Alice. Give the adjacency matrix representation for the directed graph.