:) My description of the problem is hopeless.

The boost::dijkstra_shortest_paths(m_ugraph, *vertex_iterator_begin, boost::predecessor_map(predecessorMap).distance_map(distanceMap));

currently works ok. Finds the shortest path based on the "edge_weight" (this is what I need).

The addition I need: I need the search for the shortest path to stop if outside a radius. (my graph is a street network).

lets say max "travel distance" = 4 
Source -> V1(length=1) -> V2(length=3) -> V3(length=2) -> V4(length=1) -> V5(length=1) ->VEnd

The search should end on V3 and V3 should be "unreachable" from the source (V4,V5 and Vend should be unreachable too)

The distance_map should have the distances for V1 and V2 based on the "edge_weight".

This explanation seems to be better.

Thanks
Tasos