Figure 2 shows the conceptually same red–black tree without these NIL leaves. To arrive at the same notion of a path, one must notice that e.g., 3 paths run through the node 1, namely a path through 1left plus 2 added paths through 1right, namely the paths through 6left and 6right. This way, these ends of the paths are also docking points for new nodes to be inserted, fully equivalent to the NIL leaves of figure 1.
Figure 2 shows the conceptually same red–black tree without these NIL le,aves. To arrive at the same notion of a path one must notice that e.g., 3 paths run through the node 1, namely a path through 1left plus 2 added paths through 1right, namely the paths through 6left and 6right. This way, these ends of the paths are also docking points for new nodes to be inserted, fully equivalent to the NIL leaves of figure 1.