  The steady state heat currents of continuous absorption machines can be
decomposed into thermodynamically consistent contributions, each of them
associated with a circuit in the graph representing the master equation of the
thermal device. We employ this tool to study the functioning of absorption
refrigerators and heat transformers with an increasing number of active levels.
Interestingly, such an analysis is independent of the particular physical
implementation (classical or quantum) of the device. We provide new insights
into the understanding of scaling up thermal devices concerning both the
performance and the magnitude of the heat currents. Indeed, it is shown that
the performance of a multilevel machine is smaller or equal than the
corresponding to the largest circuit contribution. Besides, the magnitude of
the heat currents is well-described by a purely topological parameter which in
general increases with the connectivity of the graph. Therefore, we conclude
that for a fixed number of levels, the best of all different constructions of
absorption machines is the one whose associated graph is as connected as
possible, with the condition that the performance of all the contributing
circuits is equal.
