We have designed and synthesized five azulene derivatives containing gold-binding groups at different points of connectivity within the azulene core to probe the effects of quantum interference through single-molecule conductance measurements. We compare conducting paths through the 5-membered ring, 7-membered ring, and across the long axis of azulene. We find that changing the points of connectivity in the azulene impacts the optical properties (as determined from UV-vis absorption spectra) and the conductivity. Importantly, we show here that simple models cannot be used to predict quantum interference characteristics of nonalternant hydrocarbons. As an exemplary case, we show that azulene derivatives that are predicted to exhibit destructive interference based on widely accepted atom-counting models show a significant conductance at low biases. Although simple models to predict the low-bias conductance do not hold with all azulene derivatives, we demonstrate that the measured conductance trend for all molecules studied actually agrees with predictions based on the more complete GW calculations for model systems.