What is the maximum number of edges in a directed graph with n nodes?

Question

What is the maximum number of edges in a directed graph with n nodes? Is there any upper bound?

Answer 1

Putting it another way:

A complete graph is an undirected graph where each distinct pair of vertices has an unique edge connecting them. This is intuitive in the sense that, you are basically choosing 2 vertices from a collection of n vertices.

nC2 = n!/(n-2)!*2! = n(n-1)/2

This is the maximum number of edges an undirected graph can have. Now, for directed graph, each edge converts into two directed edges. So just multiply the previous result with two. That gives you the result: n(n-1)