  In the study of reaction networks and the polynomial dynamical systems that
they generate, special classes of networks with important properties have been
identified. These include reversible, weakly reversible}, and, more recently,
endotactic networks. While some inclusions between these network types are
clear, such as the fact that all reversible networks are weakly reversible,
other relationships are more complicated. Adding to this complexity is the
possibility that inclusions be at the level of the dynamical systems generated
by the networks rather than at the level of the networks themselves. We
completely characterize the inclusions between reversible, weakly reversible,
endotactic, and strongly endotactic network, as well as other less well studied
network types. In particular, we show that every strongly endotactic network in
two dimensions can be generated by an extremally weakly reversible network. We
also introduce a new class of source-only networks, which is a computationally
convenient property for networks to have, and show how this class relates to
the above mentioned network types.
