In this paper we analyze solutions of the problems of the graph theory with computer mathematics systems MAPLE and MATHEMATICA with purpose to reveal the opportunity of the syntax of the main commands, theirs similarities and differences. It facilitates the choice of the computer mathematics systems for solving the practical problems of the graph theory and to study this theory. To learn to create sophisticated programs of the problems of the graph theory with computer mathematics systems is easy, if the initial knowledge of programming is at least one language of the programming The analysis of the opportunities of computer mathematics systems by solving problems of the graph theory facilitate creation of the applied programs.