Analyzing Network Connectivity via Eigenvalues

00:00 4 marks

Consider the network represented by the following adjacency matrix:

\( A = \begin{pmatrix} 0 & 1 & 1 \\ 1 & 0 & 1 \\ 1 & 1 & 0 \end{pmatrix} \).

(a) Compute the eigenvalues of the matrix \(A\).

(b) Identify the largest eigenvalue and explain briefly how it reflects the connectivity of the network.

Hint Hint

Hint

Remember that the eigenvalues are the roots of the characteristic polynomial \(\det(A – \lambda I) = 0\).

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Complete Answer

The eigenvalues are \(2, -1, -1\), so the largest eigenvalue is \(2\). This eigenvalue indicates strong connectivity as it represents the dominant interaction in the network.

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