Question

question 19 points 2

consider the given network. represent the network in a matrix form.

Explanation:

Identify vertices and connections

Vertices: \(X, Y, Z\).
Edges:

• Between \(X\) and \(Y\) (bidirectional arrow): connection exists.
• Between \(X\) and \(Z\) (bidirectional arrow): connection exists.
• Between \(Y\) and \(Z\) (bidirectional arrow): connection exists.

Construct the adjacency matrix

Using alphabetical order \(X, Y, Z\) for rows and columns:

• Row 1 (\(X\)): no self-loop to \(X\) (0), connected to \(Y\) (1), connected to \(Z\) (1).
• Row 2 (\(Y\)): connected to \(X\) (1), no self-loop to \(Y\) (0), connected to \(Z\) (1).
• Row 3 (\(Z\)): connected to \(X\) (1), connected to \(Y\) (1), no self-loop to \(Z\) (0).

Formulate the final matrix

$$
LATEXBLOCK0
$$

Answer:

• **\(

$$\begin{bmatrix} 0 & 1 & 1 \\ 1 & 0 & 1 \\ 1 & 1 & 0 \end{bmatrix}$$

\) (Correct answer)**