## AbstractThe product of compatible networks is determined by nonzero elements of the matrix of the product of matrices corresponding to the given networks. Considering only non-zero elements of matrices gives a fast algorithm for multiplication of sparse networks. We derived also some simple conditions that the product of two sparse networks is sparse itself. One application of product of networks is computation of different derived kinship relations (uncle, grandmother, niece, ...) in genealogies. This enables us to analyze the structure of genealogies with respect to these relations. Multiplying a vector with a sequence of kinship relations we can also efficiently count how many times a person is in selected kinship relation with other members of genealogy. The proposed approaches will be illustrated with analyses of some well known genealogies (Turkish nomads, Ragusa, ...)
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