Scientific journal
Scientific Review. Technical science
ISSN 2500-0799
ПИ №ФС77-57440

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ANALYSIS OF SOCIAL GRAPHS WITH A METHOD OF ESTIMATING DEGREE OF FUZZY GRAPH ISOMORPHISM USING FUZZY CLIQUES

Bershtein L.S. 1
1 Southern Federal University
This paper covers theoretical aspects of modeling social graphs using fuzzy graphs and hypergraphs. We consider notions of fuzzy homomorphism, monomorphism, epimorphism, and isomorphism from the point of view of fuzzy mappings and relations. We give an algorithm for building homomorphic images and determining the type of fuzzy homomorphism using basic graph-theoretical and algebraic operations. We introduce notions of a fuzzy clique, a maximal fuzzy clique and fuzzy sets of cliques in a fuzzy graph. We suggest a method of estimating degree of fuzzy graph isomorphism using fuzzy cliques. We provide an algorithm for finding maximal fuzzy cliques in a fuzzy graph. Obtained results can be used to solve a series of applied tasks that belong to a class of pattern recognition tasks and are closely related to an identification of social communities and social positions in a social network.