  We give a constructive method for realizing an arbitrary directed graph (with
no one-cycles) as a heteroclinic or an excitable dynamic network in the phase
space of a system of coupled cells of two types. In each case, the system is
expressed as a system of first order differential equations. One of the cell
types (the $p$-cells) interacts by mutual inhibition and classifies which
vertex (state) we are currently close to, while the other cell type (the
$y$-cells) excites the $p$-cells selectively and becomes active only when there
is a transition between vertices. We exhibit open sets of parameter values such
that these dynamical networks exist and demonstrate via numerical simulation
that they can be attractors for suitably chosen parameters.
