About the definition of trees for directed graphs in “Introduction to Algorithms 3rd Edition” by CLRS(Cormen, Leiserson, Rivest, Stein)

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I am reading “Introduction to Algorithms 3rd Edition” by CLRS(Cormen, Leiserson, Rivest, Stein).

There is a section for trees in Appendix B.5 in this book.
There are definitions of several kinds of trees for undirected graphs in Appendix B.5.

But there is no definition of trees for directed graphs in Appendix B.5(and I think there is no definition in this book) and the authors use trees for directed graphs, for example in Chapter 24 "Single-Source Shortest Paths".

What is the definition of trees for directed graphs?