Polycations are a promising class of nonviral DNA delivery agents that bind to negatively charged DNA and transfect the DNA into target cells. The architecture and chemistry of the polycation strongly affect polycation-DNA complexation and in turn the ability of polycations to transfect DNA into cells. Here we develop coarse-grained models and conduct Langevin dynamics simulations to understand how the architecture of lysine-based polycations affects their complexation with DNA-like polyanions. We first characterize the structure of linear polylysine and oligolysines grafted to a polyolefin backbone and then the structure of complexes (termed polyplexes) formed by these polycations with polyanions of varying flexibility. We find that increasing oligolysine graft length and decreasing graft spacing both increase the size and rigidity of the grafted oligolysines, although they remain less rigid than semiflexible linear polylysine. Increasing ionic strength or counterion valency reduces polycation size and most architecture-dependent effects. The effects of polycation architecture on polyplex size and flexibility are dependent on the charge ratio in the system. Polyp lex surface charge increases with increasing graft length or decreasing graft spacing.