  We demonstrate the validity of Murray's law, which represents a scaling
relation for branch conductivities in a transportation network, for discrete
and continuum models of biological networks. We first consider discrete
networks with general metabolic coefficient and multiple branching nodes and
derive a generalization of the classical 3/4-law. Next we prove an analogue of
the discrete Murray's law for the continuum system obtained in the continuum
limit of the discrete model on a rectangular mesh. Finally, we consider a
continuum model derived from phenomenological considerations and show the
validity of the Murray's law for its linearly stable steady states.
