Why the adjacency matrix can be used to determine whether or not the graph is connected.
I saw it from the wikipedia.
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The adjacency matrix is just another way of representing the information of a graph. It contains all the relevant information of a graph¹ – each edge corresponds to a 1 somewhere in the adjacency matrix (assuming a binary graph). If you know the adjacency matrix, you know the graph; and vice versa. Therefore all properties of a graph can be deduced from its adjacency matrix, including connectedness.
¹ with the exception of what exactly the nodes are (if you consider this relevant), but that information is obviously irrelevant for connectedness