Semirings for social networks analysis

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Abstract
In the paper four semirings for solving social networks problems are constructed. The closure of relational matrix over geodetic semirings contains for every pair of vertices u and v the length and the number of u ‐ v geodesics; and for geosetic semiring the length and the set of vertices on u — v geodesics. The algorithms for computing the geodetic and the geosetic closure matrix are also given. The closures of the matrix of a given signed graph over balance and cluster semirings can be used to decide whether the graph is balanced or clusterable.