Finding gene clusters in genomes is an essential process in establishing relationship among organisms. Gene clusters may express functional dependencies among genes and may give insight into expression of specific traits. The problem of finding gene clusters among several genomes is referred to as Gene Cluster Discovery and several models have already been formulated for its definition. One formulation of this problem in is the Approximate Gene Cluster Discovery Problem (AGCDP) which is modeled as a combinatorial optimization problem in some works. In this paper we propose an approach which produces a transformation of AGCDP into a minimum-weight star finding problem in graph. Detailed examples are also presented to further clarify the notion of the transformation. Proof of equivalence is also presented in the paper to show the equivalence of input parameters of AGCDP and the construction of the graph representing the input parameters to the problem.