While a fundamental representation theory for compact Lie

algebras was settled by the work of Cartan (i.e. weights and

roots), no analogous conceptual structure exists for space-

time supersymmetry algebras. Progress in this direction

based on the graph theory concept of "adinkras" will be pre-

sented in this talk.

roots), no analogous conceptual structure exists for space-

time supersymmetry algebras. Progress in this direction

based on the graph theory concept of "adinkras" will be pre-

sented in this talk.