what is the maximum number of non-loop edges that can exist in an undirected graph

Question

please tell me a equation to find maximum number of non loop edges that can exist in an undirected graph.

for example if vertices are 10 then how many non loop edges can exist?

Answer 1

If you have a simple graph, then the extremal case is a complete graph. In which case, there is an edge between each vertex, so there are $\binom{n}{2}$ such edges at most.

Answer 2

An undirected graph is one in which edges have no orientation. The edge (a, b) is identical to the edge (b, a), i.e., they are not ordered pairs, but sets {u, v} (or 2-multisets) of vertices. The maximum number of edges in an undirected graph without a self-loop is n(n - 1)/2. So , 10 * 9 / 2 = 45

Source : http://en.wikipedia.org/wiki/Graph_(mathematics)