A network is said to be traversable if we can trace every edge without ever tracing the same edge twice. A path is said to be an Euler circuit if the network istraversable and we can start and end at the same edge. If we can visit each vert exexactly once and end back where we started, the path is said to be a Hamiltonian cycle. (See section 9.1 in your book if this is unclear)