Numeration models of extensional $\lambda$-calculus have been studied (see [5,7]). In this paper, we study numeration models of $\lambda \beta$-calculus. Engeler's graph algebra construction  is applied to the category of numerations and is used as a tool to obtain numeration models of $\lambda \beta$-calculus. Several classes of numeration models are studied and several examples of them are presented.
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