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..