Minimal Measure of Balancedness of the Complete Signed Graphs

Student: Kizilov Roman

Educational Programme: Applied Mathematics and Information Science (Bachelor)

Year of Graduation: 2016

Research has two main purposes. First purpose - checking hypotheses about minimal measure of the complete signed graphs. By means of probabilistic method was constructed probabilistic function. Research of this function confirmed that if graph has odd number of vertices, than minimal measure will be achieved at graph with all negative edges. Applied purpose was to compare distribution of measure of balancedness of the complete signed graphs with «empirical distribution» - measure of balancedness for Russian State Duma at different times. It turned out, that these distributions are distinct. Algorithm for finding minimal measure was constructed and complexity of this algorithm found.

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