# Graphs Problem 4

### Solution

Any edge in a graph links two distinct vertices. The graph is undirected, therefore the way to pick such two vertices out of a total of n vertices is $$n(n-1)/2$$. Furthermore, for any possible edge, there are two possibilities: either it is in the graph or it is not. So the number of possible graphs is $$2^{n(n-1)/2}$$.