A new graph representation of nonlinear large space structures is introduced. During the loading process the structural graph changes its levels as the nonlinear regions in the large space structure change configuration. This variable structured graph is used to order the nodes and members of the discretized nonlinear structural model. A new algorithm is used to change the established order of the nonlinear model and updates the condensed nonlinear stiffness matrix equation for the structure. In addition to accounting for structural nonlinearities this algorithm can take into consideration plastic hinge formation and fracture of members in large space structures.