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In the present paper we construct an equivalence between the set of graph-knots and the set of homotopy classes of looped graphs. Moreover, the graph-knot and the homotopy class constructed from a given knot are related by this equivalence. This equivalence is given by a simple formula.

AN EQUIVALENCE BETWEEN THE SET OF GRAPH-KNOTS AND THE SET OF HOMOTOPY CLASSES OF LOOPED GRAPHS