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This paper presents the graphical analysis of stabilization loss and gains for three-port networks. The analysis considers the three-port stabilization loss, the three-port maximum available gain and the three-port maximum stable gain, which are functions of three-port S-parameters and third port termination Γ3. Extending its advantages, the three-port quasi-invariant stability parameter is exploited in introducing the new concept of stabilization loss, which corresponds to the loss of maximum available gain for more stabilization. To provide quick and apt representation in the Γ3 plane, a graphical approach is developed using the plots of constant stabilization loss curves and constant maximum stable gain circles. Their constructions are facilitated via explicit quartic polynomial and circle equations. Moreover, constant maximum available gain curves can also be constructed readily with reference to the appropriate curves and circles. All these plots facilitate the selection of proper Γ3 terminations for trade-off between stabilization loss and gains. Applications of graphical analysis for three-port network are illustrated along with measurements using an amplifier paralleled with feedback element.