  We study a class of graphs with finitely many edges in order to understand
the nature of the formal logarithm of the generating series for Severi degrees
in elementary combinatorial terms. These graphs are related to floor diagrams
associated to plane tropical curves originally developed by Brugalle and
Mikhalkin, and used by Block, Fomin, and Mikhalkin to calculate Severi degrees
of the projective plane and node polynomials of plane curves.
