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 ^{n}C2. 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-1}C_{2 }edges. Total edges are ^{n-1}C_{2..}