What is the maximum number of edges in a directed graph with n nodes? Is there any upper bound?
There can be as many as n(n-1)/2 edges in the graph if not multi-edge is allowed.
n(n-1)/2
And this is achievable if we label the vertices 1,2,...,n and there's an edge from i to j iff i>j.
1,2,...,n
i
j
i>j
See here.