## Resumo

An important computation on pedigree data is the calculation of condensed identity coefficients, which provide a complete description of the degree of relatedness of two individuals. The applications of condensed identity coefficients range from genetic counseling to disease tracking. Condensed identity coefficients can be computed using linear combinations of generalized kinship coefficients for two, three, four individuals, and two pairs of individuals and there are recursive formulas for computing those generalized kinship coefficients (Karigl, 1981). Path-counting formulas have been proposed for the (generalized) kinship coefficients for two (three) individuals but there have been no path-counting formulas for the other generalized kinship coefficients. It has also been shown that the computation of the (generalized) kinship coefficients for two (three) individuals using path-counting formulas is efficient for large pedigrees, together with path encoding schemes tailored for pedigree graphs. In this paper, we propose a framework for deriving path-counting formulas for generalized kinship coefficients. Then, we present the path-counting formulas for all generalized kinship coefficients for which there are recursive formulas and which are sufficient for computing condensed identity coefficients. We also perform experiments to compare the efficiency of our method with the recursive method for computing condensed identity coefficients on large pedigrees.

## Resumo Limpo

import comput pedigre data calcul condens ident coeffici provid complet descript degre related two individu applic condens ident coeffici rang genet counsel diseas track condens ident coeffici can comput use linear combin general kinship coeffici two three four individu two pair individu recurs formula comput general kinship coeffici karigl pathcount formula propos general kinship coeffici two three individu pathcount formula general kinship coeffici also shown comput general kinship coeffici two three individu use pathcount formula effici larg pedigre togeth path encod scheme tailor pedigre graph paper propos framework deriv pathcount formula general kinship coeffici present pathcount formula general kinship coeffici recurs formula suffici comput condens ident coeffici also perform experi compar effici method recurs method comput condens ident coeffici larg pedigre