The aim is to study the characteristics of information and communication technologies in teaching discrete mathematics. Objectives of the study is to develop the technique for implementing a computer problem solving discrete mathematics and define the features of the environment in Maple for solving a wide range of tasks. The object of research is teaching discrete mathematics. The subject of research is the method of using ICT in the classroom discrete mathematics. In this work using package ‘networks’ are solving problems of discrete mathematics (section “Graph theory”). By examples is clearly demonstrated that package ‘networks’ can transforms hard-to-understand graphs in a simple working tool to the majority of users. Results of the study – improved methodology for the study of graph theory based Maple, visualized build graphs and remove some of their peaks.