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Toumpis-Goldsmith introduced a strong theoretical formulation of capacity regions by computing achievable rate combinations between all pairs of communication within arbitrary topology and number of nodes. Our paper proposes a new formulation of their capacity regions with the same strong mathematical definition and results, but with less complexity computation. We use interference model of conflict graph with different levels of SINRth to reduce the complexity of computation and reach the same previous result. Our results show that for the same conditions of simulation present in previous works, we keep the same capacity regions with 75% of complexity reduction. The range of 0 to 0.61 dB represents the SINRth levels that keep more in touch with optimal results in terms of complexity and time computation. More higher values move away from optimal results.