Our research aims, first of all, at reviewing the mathematical methods and computer science tools used by specialists in political science. The mathematical models and computerized systems are useful both to the political science researcher and the politician. Various problems of political science can be solved by making use of different mathematical, linguistic or computerized models. Secondly, our research aims at designing new and original methodological tools to facilitate a thorough and impartial analysis of any electoral campaign for local elections. We introduce the concepts of accord between political discourses, from three perspectives: themes, solutions, and political values. Also, we use graph theory for analyzing political discourses. Some problems (like minimal spanning tree or Hamiltonian cycle) will help us to analyze the political discourse. Also, graph theory can be a useful mathematical tool in analyzing the electoral platforms or political discourses, highlighting nuclei of interest and links between topics.