"Path" in graph theory: Can a vertex occur more than once? I don't understand the definition of "path". The path is no vertex occur more than once. But this example use $a$ and $b$ twice.






Thank you in advance.

Different sources use slightly different definitions, just like $\mathbb{N}$ sometimes is defined to include $0$ and sometimes not. Nowadays paths generally don't allow repeated vertices, though we often still talk about Eulerian paths instead of Eulerian trails.
In your first book they use "simple paths" and "paths" instead of the currently more common "paths" and "walks".
