Graph Algorithms · Hard problem

A network of $8$ computers numbered $1$ through $8$ has connections $12, 13, 24, 34, 35, 46, 56, 57, 67, 78$. A message hops along one connection at a time, in either direction, and always takes a shortest route. What is the greatest number of hops needed for a message starting at computer $1$ to reach some other computer?