  Adinkras are signed graphs used to study supersymmetry in physics. We provide
an introduction to these objects, and study the properties of their signed
adjacency and signed Laplacian matrices. These matrices each have exactly two
distinct eigenvalues (of equal multiplicity), making Adinkras closely related
to the notions of strongly regular graphs. We also study the critical groups of
Adinkras, and in particular determine their odd components. A novel technique
of independent interest is used which considers critical groups over polynomial
rings.
