This makes sense, because in a linguistically agnostic situation, all the links have the same weight, and hence the weight assigned to C i j will be the same regardless of which |C i j | − 1 links in C i j are chosen.
the same is no longer true in a linguistically aware setting: since the links may not necessarily have the same weight, the weight assigned to C i j depends on which |C i j | − 1 links are chosen.