  Like simpler graphs, nested (hypernodal) graphs consist of two components: a
set of nodes and a set of edges, where each edge connects a pair of nodes. In
the hypernodal graph model, however, a node may contain other graphs, so that a
node may be contained in a graph that it contains. The inherently recursive
structure of the hypernodal graph model aptly characterizes both the structure
and dynamic of the 3-sat problem, a broadly applicable, though intractable,
computer science problem. In this paper I first discuss the structure of the
3-sat problem, analyzing the relation of 3-sat to 2-sat, a related, though
tractable problem. I then discuss sub-clauses and sub-clause thresholds and the
transformation of sub-clauses into implication graphs, demonstrating how
combinations of implication graphs are equivalent to hypernodal graphs. I
conclude with a brief discussion of the use of hypernodal graphs to model the
3-sat problem, illustrating how hypernodal graphs model both the conditions for
satisfiability and the process by which particular 3-sat assignments either
succeed or fail.
