  We define a normal graph algebra modeled on algebras used in genetics.
Although the algebra does not always determine its graph, it often highlights
special features. After developing basic properties of the algebra, we examine
those of certain minimal graphs. We then apply the results to the Petersen
graph, finding connections between some of its many aspects. For example, the
outer automorphisms of Sym(6) emerge naturally. The normal algebra of the
Petersen graph is unique among normal graph algebras.
