  I present a simple graphical method to find the BPS spectra of $A_1$ theories
of class S. BPS graphs provide a bridge between spectral networks and BPS
quivers, the two main frameworks for the study of BPS states. Here I show how
to essentially read off from a BPS graph the quantum spectrum generator (or BPS
monodromy), expressed as a product of quantum dilogarithms. Thanks to the
framed wall-crossing phenomenon for line defects, the determination of the BPS
spectrum reduces to the computation of quantum parallel transport across the
edges of the BPS graph.
