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Determining the thermodynamic stability of intermetallic phases in multicomponent alloys from Compound Energy Formalism (CEF), requires the formation enthalpy of up to millions of end-member configurations. Here, a graph neural network (GNN) model, trained from high-throughput DFT calculations, was used to construct such a database of intermetallic $\sigma$ phase for 19 metallic elements with a root mean squared error (RMSE) of 10 meV/atom. We show that a good prediction accuracy of GNN, even without prior knowledge of the relaxed structure, can be achieved by focusing on a single phase and using a regression model for structure prediction. The resulting $19^5% formation enthalpy data, corresponding to all end-member configurations up to quinaries, enables the characterization of the stability and chemical trends of $\sigma$-phase both at 0 K (configurations on the convex hull) and at high temperature (with disorder using CEF, also up to quinary systems). We quantified the important role of entropy in stabilizing the $\sigma$-phase in multicomponent systems and investigated the relationship between chemical composition, chemical ordering and enthalpy of formation in the phase. The chemical ordering further is discussed in detail in terms of site and pair preference of different elements. Through electronic structure based bonding analysis, we demonstrate the importance of valence electron concentration (VEC) in explaining and rationalizing the obtained theoretical results.