A unique method for the establishment of the reaction scheme of a multi-component phase diagram is proposed in terms of graph theory. A geometrical representation of the connections between invariant reactions is considered for the basis to introduce matrix formula of a graph which models a reaction scheme, then the number of all possible reaction schemes is enumerated through the graphical representation of the multi-component phase diagrams. Finally, a method to select more rational hypothetical reaction schemes is shown by utilizing matrix operation. With available experimental data they can further be utilized to decide the multi-component phase diagram of interest. A ternary phase diagram will be chosen as an example. with both related binary phase diagrams and experimental data based on DTA and microstructure observations.