You can go through the pathways with no clearance required until you get to a node where the clearance can be obtained (in the test case it says that nodes 1-6 have NONE meaning they don't have the option to get a new clearance, 7 has green, 8 has red and 9 has blue). Then you can choose to pick up that clearance colour, once you do that you are able to traverse the paths between nodes that require that colour. TLDR you pick up clearance colours at certain nodes on the graph and then you can go through any pathway with either NONE as the clearance colour or whichever of the colours you picked up last.