  We consider few-body systems in which only a certain subset of the
particle-particle interactions is resonant. We characterize each subset by a
{\it unitary graph} in which the vertices represent distinguishable particles
and the edges resonant 2-body interactions. Few-body systems whose unitary
graph is connected will collapse unless a repulsive 3-body interaction is
included. We find two categories of graphs, distinguished by the kind of 3-body
repulsion necessary to stabilize the associated system. Each category is
characterized by whether the graph contains a loop or not: for tree-like graphs
(graphs containing a loop) the 3-body force renormalizing them is the same as
in the 3-body system with two (three) resonant interactions. We show
numerically that this conjecture is correct for the 4-body case as well as for
a few 5-body configurations. We explain this result in the 4-body sector
qualitatively by imposing Bethe-Peierls boundary conditions on the pertinent
Faddeev-Yakubovsky~decomposition of the wave function.
