Final answer:
The largest eigenvalue of an adjacency matrix represents the maximum connectivity in a graph. Methods such as power iteration or the QR algorithm can be used to find the largest eigenvalue.
Step-by-step explanation:
The largest eigenvalue of an adjacency matrix represents the maximum connectivity in a graph. It is mathematically represented as the principal eigenvalue of the matrix. To find the largest eigenvalue, you can use methods such as power iteration or the QR algorithm. For example, let's say we have an adjacency matrix for a graph with vertices A, B, and C:
A = [[0, 1, 0], [1, 0, 1], [0, 1, 0]]
Using power iteration, we can repeatedly multiply a random vector by the matrix until it converges to the largest eigenvalue. The resulting vector will represent the corresponding eigenvector.