The problem of labeling the vertices of an undirected, connected graph with binaryn-tuple addresses is considered. These addresses are to have the property that if two vertices are a distancekapart in the graph then the Hamming distance between the corresponding addresses must bekdwheredis a positive integer which is constant for the graph. Not all graphs may be so addressed. A weak characterization of addressable graphs in terms of the eigenvalues of a certain matrix associated with the graph is given. It is shown that any addressable bipartite graph may always be addressed withd = 1. For nonbipartite addressable graphs,dmust be even, and it is shown that there exist graphs requiring an arbitrarily largedfor addressing. An addressing algorithm is given which is guaranteed to address any addressable graph.