Dendrimers belong to a class of complex hyperbranched structures through which electron transfer has been observed; in this work, we study the effect of the bridge topology on long-range transfer. Electron-transfer rates for bridge-mediated electron transfer are calculated by solving the steady-state Liouville equation with phenomenological corrections far solvent interaction. While the behavior of linear bridge groups is well-known, branched structures display interesting electron transport properties. Addition of a small side group with nodes equivalent to the bridge nodes increases the steady-state rate, and this effect is amplified by increasing the site-site couplings in the side group. The effect for a single side group is small, but increases with each additional side group producing a noticeable increase in electron transfer rates for structures with several side groups such as dendrimers. Addition of an electron withdrawing side group at the acceptor end of the bridge creates a structure that can manifest asymmetric tunneling in the weak solvent limit. We demonstrate that this potential for rectification as well as the electron transfer rates can readily be manipulated by varying the on-site energies of the side group.