(b) Let G' be the graph defined by the adjacency matrix A'. For the graph G'(i) determine whether the graph G' is weakly connected? Is it stronglyconnected? Find all strongly connected components of the graph G';(ii) determine the in-degree and the out-degree sequences;(iii) determine the in-degree and the out-degree distributions;(iv) evaluate the normalised Katz centrality of all nodes of the graph G'.Hint: You may wish to use the definition of the Katz centrality in terms ofnodes connectivities instead of a formula in terms of the inverse matrix. Question 1Let A and A' be two matrices defined below(0 1 1 1 0 0 0 0 0 0V1 0 0 0 1 1 0 0 0 01 0 0 0 0 0 1 10 01 0 0 0 00 0 0 10 10 0 0 0 0 0 0 00 1 0 0 0 0 0 0 0 00 0 10 0 0 0 0 0 00 0 10 00 0 0 0 00 0 0 10 00 0 0 00 0 0 10 00000,0 0 0 0 0 0 0 0 0 0Y1 0 0 0 0 00 0 001 0 0 0 0 0 0 0 0 01 0 0 0 0 0 0 0 0 00 1 0 0 0 0 0 0 0 00 1 0 0 0 0 0 0 0 00 0 10 0 0 0 0 0 00 0 1 0 00 0 0 0 00 0 0 1 0 0 0 0 0 00 0 0 1 0 0 0 0 0 0A =A'(a) Let G be the graph defined by the adjacency matrix A. For the graph G(i) determine whether the graph G is directed or undirected;(ii) find the number of nodes and edges of the graph G;(iii) draw the graph G;(iv) evaluate normalized degree centralities for all nodes;(v) evaluate average clustering coefficient and the transitivity of the graph G;(vi) compute the diameter Dg of the graph G, and indicate at least one pair ofnodes which are at distance DG;(vii) find the minimal number of edges that need to be added to the graph G toreduce its diameter. Give at least one example of such edges;(b) Let G' be the graph defined by the adjacency matrix A'. For the graph G'

Since the questions contains many subparts as per the guidelines I am answering the first three…

Question 1 Let A and A' be two matrices defined below (0 1 1 1 00 0 0 0 0V 100 0 1 10 0 0 0 100 0 00 1 10 0 100 0 00 0 0 1 1 010000 0 0 0 0 0 10 0 00 0 0 0 0 0 0 10 0 0 0 0 0 0 0 0 10 0 0 0o0 0 0 0 0 0 1 00 0 0 0 0 0 0 0 10 000 00, 1 00 0 0000 00 100 0 000 0 0 0 1000 000 0 00 0 10 0 00 00 0 0 A = A' = %3D 010 0 0000 0 0 0 0 10 0 0 0 0 0 0 0 0 10 0 0 0 0 00 0 0 0 100 0 0 0 0 0 0 0 1 0 00 0 0 0 (a) Let G be the graph defined by the adjacency matrix A. For the graph G (i) determine whether the graph G is directed or undirected; (ii) find the number of nodes and edges of the graph G; (iii) draw the graph G;

Question 1 Let A and A' be two matrices defined below (0 1 1 1 00 0 0 0 0V 100 0 1 10 0 0 0 100 0 00 1 10 0 100 0 00 0 0 1 1 010000 0 0 0 0 0 10 0 00 0 0 0 0 0 0 10 0 0 0 0 0 0 0 0 10 0 0 0o0 0 0 0 0 0 1 00 0 0 0 0 0 0 0 10 000 00, 1 00 0 0000 00 100 0 000 0 0 0 1000 000 0 00 0 10 0 00 00 0 0 A = A' = %3D 010 0 0000 0 0 0 0 10 0 0 0 0 0 0 0 0 10 0 0 0 0 00 0 0 0 100 0 0 0 0 0 0 0 1 0 00 0 0 0 (a) Let G be the graph defined by the adjacency matrix A. For the graph G (i) determine whether the graph G is directed or undirected; (ii) find the number of nodes and edges of the graph G; (iii) draw the graph G;

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

(b) Let G' be the graph defined by the adjacency matrix A'. For the graph G'
(i) determine whether the graph G' is weakly connected? Is it strongly
connected? Find all strongly connected components of the graph G';
(ii) determine the in-degree and the out-degree sequences;
(iii) determine the in-degree and the out-degree distributions;
(iv) evaluate the normalised Katz centrality of all nodes of the graph G'.
Hint: You may wish to use the definition of the Katz centrality in terms of
nodes connectivities instead of a formula in terms of the inverse matrix.

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