that isn't true. there are tradeoffs between using an adjacency matrix, and other representations. different operations will be more efficient on different representations.

and in the special case of extremely sparse graphs like trees, the adjacency matrix isn't going to win very often.

your copy of CLRS should discuss all of this. and for practical uses of non-adjacency matrix representations of trees, you can take a look at every functional programming language, ever.

But not very human-readable and therefore it is inadequate for editing.