I think the explanation is for edges for which graph is always connected.
Let a SIMPLE graph with n nodes . max no of edges possible are nC2. if we want to disconnect graph then do one thing just partition original graph in two portion with 1 and n-1 nodes respectively. now find number of edges in each component. with 1 node : no edge with n-1 nodes : n-1C2 edges. Total edges are n-1C2..
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