I have a graph consisting of a start point $S$, a finish point $F$ and a number of intermediate points $P_i$. The points are connected by a set of edges, as shown in the graph below. I need to determine the number of unique paths connecting the start to the finish. The rules:

- The number of points per path is not fixed
- Each path can pass by a point one time only (to avoid loops)

I'm a graph theory noob and I'm sure this is a quite common problem. Do you have suggestions to where should I look to get an introduction to the problem, and suggestions on how to solve it? Ideally, I'm looking for an equation or numerical procedure.