Over the years, population-level tobacco control policies have considerably reduced smoking prevalence worldwide. However, the rate of decline of smoking prevalence is slowing down. Therefore, there is a need for models that capture the full complexity of the smoking epidemic. These models can then be used as test-beds to develop new policies to limit the spread of smoking. Current models of smoking dynamics mainly use ordinary differential equation (ODE) models, where studying the effect of an individual's contact network is challenging. They also do not consider all the interactions between individuals that can lead to changes in smoking behaviour, implying that they do not consider valuable information on the spread of smoking behaviour. In this context, we develop an agent-based model (ABM), calibrate and then validate it on historical trends observed in the US and UK. Our ABM considers spontaneous terms, interactions between agents, and the agent's contact network. To explore the effect of the underlying network on smoking dynamics, we test the ABM on six different networks, both synthetic and real-world. In addition, we also compare the ABM with an ODE model. Our results suggest that the dynamics from the ODE model are similar to the ABM only when the network structure is fully connected (FC). The FC network performs poorly in replicating the empirical trends in the data, while the real-world network best replicates it amongst the six networks. Further, when information on the real-world network is unavailable, our ABM on Lancichinetti-Fortunato-Radicchi benchmark networks (or networks with a similar average degree as the real-world network) can be used to model smoking behaviour. These results suggest that networks are essential for modelling smoking behaviour and that our ABM can be used to develop network-based intervention strategies and policies for tobacco control.