Calculation of general recoupling coefficients using graphical methods. A new program to generate a summation formula in terms of 6-j coefficients for a general angular momentum recoupling coefficient is described. This algorithm makes use of the graphical techniques as developed by A. P. Yutsis, I. B. Levinson and V. V. Vanagas [Mathematical apparatus of the theory of angular momentum (1962; Zbl 0111.42704)]. Attention is paid to providing an appropriate data structure for the graph representing a general recoupling coefficient, and to reducing the coefficient to a summation formula with a minimum number of summation variables. Our results are compared to those of A. Bar-Shalom and M. Klapisch [Comput. Phys. Commun. 50, 375 (1988)], who developed the program NJGRAF for the same purpose, also using graphical methods.