  We propose a graph-theoretic description to determine and characterize 5d
superconformal field theories (SCFTs) that arise as circle reductions of 6d
$\mathcal{N} = (1,0)$ SCFTs. Each 5d SCFT is captured by a graph, called a
Combined Fiber Diagram (CFD). Transitions between CFDs encode mass deformations
that trigger flows between SCFTs. In this way, the complete set of descendants
of a given 6d theory are obtained from a single marginal CFD. The graphs encode
key physical information like the superconformal flavor symmetry and BPS
states. As an illustration, we ascertain the aforementioned data associated to
all the 5d SCFTs descending from 6d minimal $(E_6, E_6)$ and $(D_k, D_k)$
conformal matter for any $k$. This includes predictions for thus far unknown
flavor symmetry enhancements.
