I'm a bit confused by Wikipedia's tables of algorithms for the shortest path problem.
For an unweighted graph with $E$ edges and $V$ vertices, it gives the best algorithm as breadth-first search, with a time complexity of $O(V+E)$. But above that, for an undirected graph with natural-number weights, it gives the best algorithm as an $O(E)$ algorithm due to Thorup (1999). This seems faster than the $O(V+E)$ for breadth-first search despite applying to a more general problem.
Am I correct in understanding that the $O(V+E)$ breadth-first search algorithm applies to a directed unweighted graph, and for an undirected and unweighted graph, Thorup's 1999 $O(E)$ algorithm is faster even though it's capable of handling arbitrary natural number edge weights? This seems surprising to me.