  We show a direct matching between individual Feynman diagrams and integration
measures in the scattering equation formalism of Cachazo, He and Yuan. The
connection is most easily explained in terms of triangular graphs associated
with planar Feynman diagrams in $\phi^3$-theory. We also discuss the
generalization to general scalar field theories with $\phi^p$ interactions,
corresponding to polygonal graphs involving vertices of order $p$. Finally, we
describe how the same graph-theoretic language can be used to provide the
precise link between individual Feynman diagrams and string theory integrands.
