For the following Directed Graph, create an adjacency matrix. Then, via matrix multiplication, give me a COMPLETE list of all pairs of nodes that can reach one another in THREE moves. (Keep in mind when listing an ordered pair, the node you start from goes first, and the node you end on goes last.)
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(4) For the following Directed Graph, create an adjacency matrix. Then, via matrix multiplication, give me a COMPLETE list of all pairs of nodes that can reach one another in THREE moves. (Keep in mind when listing an ordered pair, the node you start from goes first, and the node you end on goes last.)
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- a) Illustrate the sequence of vertices of this graph visited using depth-first search traversal starting at vertex g. b) Illustrate adjacency list representation and adjacency matrix representation, respectively, for this graph. What are the advantages and disadvantages of those two representations? c) Describe an algorithm to find in the graph a path illustrated below that goes through every edge exactly once in each direction.Consider the un-directed graph shown in the Fig. The values inside the node refer to the feature value of the node. The order of the nodes is A,B,C,D when following the matrix form in below questions.(You can use python or other languages to find the eigen values and other operationfor this question):1. For the given graph, write down the degree matrix, adjacency matrix, and Laplacian matrix representation.2.Find the eigenvalues and eigenvectors of the graph Laplacian matrix. Do you see any pattern pertaining to the signs of the eigenvalues (all positive or negative or no such pattern). Will it be same for all such graph Laplacianmatrices, and why?3.(a) Assume there is an adjacency matrix A of an undirected graph G. Further assume a 1 isindicated in the element, A(ij), if there is an edge between node i and node j, and a 0 is indicatedin the element A(ij) if there is no edge between node i and node j. Explain the characteristics ofthe matrix A when(i) the graph is complete,(ii) the graph has a loop (edge connecting a vertex to itself),(iii) the graph has an isolated vertex, i.e., a vertex with no edges incident on it.(b) Repeat (a) for adjacency list representation, each row takes a linked list like structure.
- Question 9 Create a graph, if possible, with the following attributes, then find the index matrix of your graph. 6 vertices 5 edges One vertex with a degree of 3 All vertices are connected in some way, but it does not have to be a direct connection1) Find the adjacency matrix M for the following graph (see attached) 1a) Find M^2,M^3,M^4. What do the entries represent? Note that M^2,M^3,M^4 are matrix powers, not graph powers 1b) Express the transitive closure of a general graph G in terms of its adjacency matrix. That is, compute the adjacency matrix of G's transitive closure from G's adjacency matrix.In Computer Science a Graph is represented using an adjacency matrix. Ismatrix is a square matrix whose dimension is the total number of vertices.The following example shows the graphical representation of a graph with 5 vertices, its matrixof adjacency, degree of entry and exit of each vertex, that is, the total number ofarrows that enter or leave each vertex (verify in the image) and the loops of the graph, that issay the vertices that connect with themselvesTo program it, use Object Oriented Programming concepts (Classes, objects, attributes, methods), it can be in Java or in Python.-Declare a constant V with value 5-Declare a variable called Graph that is a VxV matrix of integers-Define a MENU procedure with the following textGRAPHS1. Create Graph2.Show Graph3. Adjacency between pairs4.Input degree5.Output degree6.Loops0.exit-Validate MENU so that it receives only valid options (from 0 to 6), otherwise send an error message and repeat the reading-Make the MENU call in the main…
- 5. (This question goes slightly beyond what was covered in the lectures, but you can solve it by combining algorithms that we have described.) A directed graph is said to be strongly connected if every vertex is reachable from every other vertex; i.e., for every pair of vertices u, v, there is a directed path from u to v and a directed path from v to u. A strong component of a graph is then a maximal subgraph that is strongly connected. That is all vertices in a strong component can reach each other, and any other vertex in the directed graph either cannot reach the strong component or cannot be reached from the component. (Note that we are considering directed graphs, so for a pair of vertices u and v there could be a path from u to v, but no path path from v back to u; in that case, u and v are not in the same strong component, even though they are connected by a path in one direction.) Given a vertex v in a directed graph D, design an algorithm for com- puting the strong connected…Create the matrix of the graph above and answer the following questions (If there isno arrow at the end of both sides of line, it is bidirectional).Answer the following questions by examining the matrix and its powers, show yourresults step by step clearly:(a) How many walks of length 2 are there from 2 to 4?(b) How many walks of length 2 are there from 3 to 5?(c) How many walks of length 3 are there from 0 to 5?(d) How many walks of length 3 are there from 2 to 4?Answer True or False to the following claims: a. If G is graph on at most 5 vertices and every vertex has degree 2, then G is a cycle. b. Let G be a forest. If we add an edge to G, then G is no longer a forest. c. Let G be a graph, and let u, v, and w be vertices in G. Suppose that a shortest path from u to v in G is of length 3, andsuppose that a shortest path from v to w in G is of length 4. Then a shortest path from u to w in G is of length 7.
- 2. Consider the graph given by the following adjacency list: vertex adjacent vertics 1 2, 3, 4 2 1 3 1, 4 4 1, 3 5 - (a) Draw the corresponding graph. (b) Write down the adjacency matrix A for this graph. Calculate A2. What is the meaning of the entries of matrices A and A2? (c) Starting at vertex 4, use the adjacency matrix algorithm to check for connectivity. Please no plagiarism and also i want clear hand writting. ThanksFor the undirected graph G shown in Exampleand reproduced here for convenience, undertake Breadth first search for the key 9, by refining the Breadth first traversal algorithm.Run BFS algorithm on the following graph starting with vertex s. Whenever there is a choice of vertices, choose the one that is alphabetically first. What is the order that the vertices are visited? What is the shortest path from vertex s to vertex b?