Discussion
If A is an adjacency matrix of a graph G, if A = AT, where AT is the transpose matrix of A, then G is :
Answer: A
The key's answer is A simple undirected graph.
The adjacency matrix records \(a_{ij} = 1\) when there is an edge from vertex i to vertex j. If \(A = A^{T}\), then \(a_{ij} = a_{ji}\) for every pair: every edge from i to j is matched by one from j to i. That is the adjacency matrix of an undirected graph, which is what the key's option describes.
Symmetry says nothing about the graph having only self loops (those are the diagonal entries) or only parallel edges, which a 0-1 adjacency matrix cannot even show. A 'general graph' would include directed graphs, whose matrices are usually not symmetric.
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