Isnt it running DFS on every node?
1) Pick any node in the graph say n
2) With n as root, run DFS. While running DFS, if you visit node x, mark
M[n,x]=1 and M[x,n]=1 .
The running time is O(k+E) [not k, you are forgetting the case when E !=
O(n)] .Also have a hash finished[n]=true.
3) Repeat steps 1-2 for each node until finished[node] = true for all of
them.

So overall time is not O(n^2). A proof of O(n^2) is also reqd. with the
solution

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