Exercise 1.1.3
These are the solutions to the exercises of the book Graph Theory with Applications by J. A. Bondy and U. S. R. Murty.
If G is simple, then at most, G could have an edge between every two distinct vertices. The total number of possible combinations are \binom{\nu}{2} (there are \binom{\nu}{2} ways of choosing 2 distinct vertices from a set of \nu vertices). Hence \epsilon\leq \binom{\nu}{2}. \square
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