  In this paper, we demonstrate that it is possible to create an adiabatic
quantum computing algorithm that solves the shortest path between any two
vertices on an undirected graph with at most 3V qubits, where V is the number
of vertices of the graph. We do so without relying on any classical algorithms,
aside from creating a (V x V) adjacency matrix. The objective of this paper is
to demonstrate the fact that it is possible to model large graphs on an
adiabatic quantum computer using the maximum number of qubits available and
random graph generators such as the Barabasi-Albert and the Erdos-Renyi methods
which can scale based on a power law.
