Consider the directed network G = (V,E) with N = 5 nodes and L = 8 links, in whichnode 1 points to nodes 2 and 3, node 2 points to node 4, node 3 points to nodes 2 and4, node 4 points to node 2, and node 5 points to nodes 3 and 4.(b) How many weakly-connected components and how many non-trivial (i.e. withmore than one node) strongly-connected components are there in the network?List all the nodes belonging to each one of these components. List all the nodesbelonging, respectively, to the in-component and the out-component of each of thenon-trivial strongly-connected components.

To analyze the directed graph 𝐺=(𝑉,𝐸) with 5 nodes and 8 links as described, we will determine…

Answered: Consider the directed network G = (V,E)…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.6: Applications And The Perron-frobenius Theorem

Problem 36EQ

See similar textbooks

Similar questions

Draw the network defined by N = {1, 2, 3, 4, 5, 6} A = {(1,2), (1,3), (1,4), (1,5), (2,3), (2,4), (2,5), (3,4), (3,6), (4,5), (4,6)}
Consider the network with adjacency matrix A given by Which type of network best represent the data Select one: a. Directed, Weighted b. Undirected C. None of the other choices 4- (1₂) A =
2. Consider the following network (G, w). V2 4 2 Vi ་ 2 1 V3 00 VA 1 2 V5 2 - 2 2 07 (b) Explain the effect each of the following changes of the length of a single edge would have on the length of a shortest v₁-7-path: an increase of w(v3v4) from 1 to 2; a decrease of w(v6v7) from 2 to 1; a decrease of w(v3v5) from 4 to 1.
Find the adjacency matrices for the directed graphs in (a) and (b).
A graph with vertices X, Y, Z has the adjacency matrix. How many walks of length 3 are there from Y to Z?
Q7. Construct an undirected network diagram using the given set of nodes and arcs: Nodes (A, B, C, D, E} Arcs (AB)=1, (AC)=3, (BC)=5, (CD)=1, (DB)=3,(DE)=1, (CE)=6}
Consider a complete network formed by 5 nodes. Does this network have an Eulerian cycle? Yes No Does this network have an Hamiltonian cycle? Yes No It is possible that an Hamiltonian cycle is also an Eulerian cycle of this network? Yes No N/A. The Hamiltonian cycle and/or the Eulerian cycle do not exist.
What is the minimum number of links L of an undirected network of N nodes? Select one: О а. 0 O b. N+1 C. N О с. O d. None of the above.
Construct a table that displays the number of directed paths of length 1 or 2 between each pair of vertices in the graph shown.
2. Consider the following network (G, w). V1 2 1 V2 V3 V4 2 1 4 4 2 2 V5 1 (i) an increase of w(v3v4) from 1 to 2; (ii) a decrease of w(v6v7) from 2 to 1; (iii) a decrease of w(v3v5) from 4 to 1. V6 2 2 V7 (a) Use Dijkstra's algorithm to find a shortest v₁-07-path. Give V(T) and E(T) after each iteration of the algorithm. (b) Explain the effect each of the following changes of the length of a single edge would have on the length of a shortest v₁-V7-path:
1. Find the adjacency matrix of the given directed multigraph with respect to the vertices listed in alphabetic order.
What is the minimum number of links I of an undirected network of N nodes which is connected? Select one: O a. 0 O b. N + 1 О с. N O d. None of the above.

SEE MORE QUESTIONS

Recommended textbooks for you

Linear Algebra: A Modern Introduction

Algebra

ISBN:

9781285463247

Author:

David Poole

Publisher:

Cengage Learning

Linear Algebra: A Modern Introduction

Algebra

ISBN:

9781285463247

Author:

David Poole

Publisher:

Cengage Learning

SEE MORE TEXTBOOKS