Adaptive codes associate variable-length codewords to symbols being encoded depending on the previous symbols in the input data string. This class of codes has been introduced in [Dragos Trinca, cs.DS/0505007] as a new class of non-standard variable-length codes. New algorithms for data compression, based on adaptive codes of order one, have been presented in [Dragos Trinca, ITCC-2004], where we have behaviorally shown that for a large class of input data strings, these algorithms substantially outperform the Lempel-Ziv universal data compression algorithm. EAH has been introduced in [Dragos Trinca, cs.DS/0505061], as an improved generalization of these algorithms. In this paper, we present a translation of the EAH algorithm into the graph theory.