The mathematical framework of matrix decomposition implies the possibility to perform statistical analyses of directed graphs focused on the distributions of the independent cyclic and starlike hierarchical components. In this approach the weighted directed graphs with n nodes are built up as a linear combination of starlike graphs with n outgoing edges and a suitable set of three-edge cyclic subgraphs. The applicability of this approach is illustrated by quantifying several general features: e.g., ratio of the cyclic and hierarchical components and asymmetry in the hierarchical components. The applicability of these methods is illustrated by considering the averages over random directed graphs and comparing these values with those characterizing simple directed graphs of tournaments.

The true teaching occupations have the basic conditions-listening to each other and the co-operation. The students in elementary schools are often require the presence of adult guidance persons. In the high school, it is more likely to develop the uncontrolled willingness to cooperate, even without the guidance or coordinating teacher.Co-operation without external control mechanisms are in other areas with different shapes. We tested what can happen in the classroom in a series of experiments. When the model was implemented, the students did not know the purpose of the experiment or the interaction chosen. The game was made on a voluntary basis, and its experiences were reported at the next meeting. The analyses were done in mathematics lessons with GeoGebra and Excel programs in the computer. It was a good basis for introducing game theory, but the versatility of its use also serves the relationship among sciences.