  Uniform Lie algebras are combinatorially defined two-step nilpotent Lie
algebras which can be used to define Einstein solvmanifolds. These Einstein
spaces often have nontrivial isotropy groups. We derive basic properties of
uniform Lie algebras and we classify uniform Lie algebras with five or fewer
generators. We define a type of directed colored graph called a uniformly
colored graph and establish a correspondence between uniform Lie algebras and
uniformly colored graphs. We present several methods of constructing infinite
families of uniformly colored graphs and corresponding uniform Lie algebras.
