  In our study of electrical networks we develop two themes: finding explicit
formulas for special classes of functions defined on the vertices of a
transient network, namely monopoles, dipoles, and harmonic functions. Secondly,
our interest is focused on the properties of electrical networks supported on
Bratteli diagrams. We show that the structure of Bratteli diagrams allows one
to describe algorithmically harmonic functions as well as monopoles and
dipoles. We also discuss some special classes of Bratteli diagrams (stationary,
Pascal, trees), and we give conditions under which the harmonic functions
defined on these diagrams have finite energy.
