Graph Algorithms · Superchallenge problem

A network of $13$ computers has connections $12, 23, 34, 45, 56, 67, 78, 89, 2\text{-}10, 10\text{-}11, 11\text{-}6, 10\text{-}12, 12\text{-}13$. Computers $1$, $5$, and $9$ all begin broadcasting the SAME message at the same instant; it spreads one hop per second along a connection, in either direction. How many seconds pass before every one of the $13$ computers has received it?