Abstract Two algorithms have been proposed for the enumeration of pathsets of complex reliability graphs. In algorithm-1, the indices of the connection matrix and higher order row vectors are repeatedly made and subsequently used in each step of matrix operation for the enumeration of pathsets of reliability graphs. In algorithm-2, the indices of the connection matrices are made and used subsequently, each time after every node removal step. In both algorithms, multiplications that are 100% useless are eliminated, thereby saving a substantial amount of CPU time. Both the algorithms have been elucidated by suitable example illustrations. To justify the effectiveness of these algorithms, they have been implemented in computer programs which enumerate pathsets much faster in comparison to existing algorithms.