Graph Algorithms · Challenge problem

A delivery company has $7$ locations numbered $1$–$7$ with roads $12, 13, 14, 25, 35, 46, 56, 67$. It may put its dispatch office at any ONE of the $7$ locations; from there, deliveries travel one road-hop at a time to any other location by a shortest route. Over all possible choices of dispatch location, what is the smallest possible value of the greatest number of hops needed to reach any other location?