Consider a network with S = {1,2,..., 10} and the adjacency matrix A given byA00100010000110000001100101000-ooooo-0 00 010011 0110 00010101010100oooooo0100110000coooOOOO-0000ooooo0 0000 000 00 00 1001 00 0Evaluate s(i, j) for all i, j € S.(a) Describe the mathematical method used in these numerical computations.(b) Derive the result and state it in a table.

Answered: Consider a network with S = 10} and the…

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

Consider a network with S = {1,2,..., 10} and the adjacency matrix A given by
A
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
00
0
0
1
1
0
0
1
0
1
000-ooooo-
0 0
0 0
1
0
0
1
1 0
1
1
0 0
0
0
1
0
10101
0100oooooo
0100
11000
0
coooOOOO-
0000
ooooo
0 0
0
0
0 0
0
0 0
0 0
0 1
001 0
0 0
Evaluate s(i, j) for all i, j € S.
(a) Describe the mathematical method used in these numerical computations.
(b) Derive the result and state it in a table.

Expert Solution

Step 1: Definition:

The adjacency matrix also called the connection matrix is a matrix containing rows and columns which is used to represent a simple labelled graph, with 0 or 1 in the position of (V_i ,V_j)according to the condition whether V_i and V_j are adjacent or not.

It is a compact way to represent the finite graph containing n vertices of a m x m matrix M.

Sometimes adjacency matrix is also called a vertex matrix and it is defined in the general form as,

$open curly brackets table row cell 1 comma space i f space S subscript i rightwards arrow S subscript j end cell row cell 0 comma space space o t h e r w i s e. end cell end table close$