We present a simple and efficient algorithm that generates all labeled graphs with a given graphical degree sequence. The algorithm does not discard any isomorphic duplicates during the generation process. It works by constructing a conceptual search tree each of whose leaf nodes represents a labeled realization of the input sequence. Furthermore, a natural lexicographical ordering is imposed on the labels of the vertices of the constructed graphs so that a corresponding lexicographical ordering is induced on all labeled realizations of the input sequence and the algorithm generates all outputs in this ordering. The algorithm can also be easily parallelized.