Graph Algorithms · Superchallenge problem

A network of $10$ computers has two hub computers, $9$ and $10$, each connected to several others and to each other: $9\text{-}1, 9\text{-}3, 9\text{-}5, 9\text{-}7, 10\text{-}2, 10\text{-}4, 10\text{-}6, 10\text{-}8, 9\text{-}10$, plus direct connections $12, 34, 56, 78$, and one more direct connection $23$. If both hubs fail (removed along with their connections), into how many connected pieces does the remaining $8$-computer network split?