# Quantum algorithm of graphs: How to create superposition of paths?

Let us allow path to have same vertexes in it. (defining)

So suppose we have a graph of $N$ vertexes and we want to separate it into some superposition of paths that have $N$ vertexes (so if the number of vertexes is $N$, there would be like $N^N$ paths.)

Is this possible? If it is, how can this be done?