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Exercise #1: Number of Edges

The edges in a graph represent pairs of connected vertices. A graph with V has V2 such pairs.

Consider V = {1,2,3,4,5}   with all possible pairs:

E = { (1,1), (1,2), (1,3), (1,4), (1,5), (2,1), (2,2), …, (4,5), (5,5) }

Why do we say that the maximum #edges is V(V-1)/2?