Undirected Simple Graph Adjacency Matrix: Always Symmetric

Yes, the adjacency matrix of an undirected simple graph is always symmetric. This is because if there is an edge between vertex 'i' and vertex 'j', then there is also an edge between vertex 'j' and vertex 'i'. Therefore, the entry in row 'i' and column 'j' of the adjacency matrix is the same as the entry in row 'j' and column 'i', making the matrix symmetric.