  Suppose N is a phylogenetic network indicating a complicated relationship
among individuals and taxa. Often of interest is a much simpler network, for
example, a species tree T, that summarizes the most fundamental relationships.
The meaning of a species tree is made more complicated by the recent discovery
of the importance of hybridizations and lateral gene transfers. Hence it is
desirable to describe uniform well-defined procedures that yield a tree given a
network N. A useful tool toward this end is a connected surjective digraph
(CSD) map f from N to N' where N' is generally a much simpler network than N. A
set W of vertices in N is "restricted" if there is at most one vertex from
which there is an arc into W, thus yielding a bottleneck in N. A CSD map f from
N to N' is "restricted" if the inverse image of each vertex in N' is restricted
in N. This paper describes a uniform procedure that, given a network N, yields
a well-defined tree called the "restricted tree" of N. There is a restricted
CSD map from N to the restricted tree. Many relationships in the tree can be
proved to appear also in N.
