  Different mathematical methods have been applied to obtain the analytic
result for the massless triangle Feynman diagram yielding a sum of four
linearly independent hypergeometric functions of two variables $F_4$. These are
defined for especific regions of convergence for the ratios of the squares of
momentum variables. In this paper I work out the diagram and show that that
result, though mathematically sound, is not physically acceptable when it is
embedded in higher loops - meaning further momentum integrations - because it
misses a fundamental physical constraint imposed by the conservation of
momentum, which should reduce by one the total number of linearly independent
(l.i.) functions $F_4$ in the overall solution. Taking into account that the
momenta flowing along the three legs of the diagram are constrained by momentum
conservation, the number of overall l.i. functions that enter the most general
solution must reduce accordingly.
  To determine the exact structure and content of the analytic solution for the
three-point function that can be embedded in higher loops, I use the analogy
that exists between Feynman diagrams and electric circuit networks, in which
the electric current flowing in the network plays the role of the momentum
flowing in the lines of a Feynman diagram. This analogy is employed to define
exactly which three out of the four hypergeometric functions are relevant to
the analytic solution for the Feynman diagram. The analogy is built based on
the equivalence between electric resistance circuit networks of type "Y" and
"Delta" in which flows a conserved current. The equivalence is established via
the theorem of minimum energy dissipation within circuits having these
structures.
