In a dissociated culture, neuronal networks spontaneously generate highly stereotypical activity characterized by synchronous bursting. With recent advancements in microfabrication technology, the topologies of cultured neuronal networks can now be engineered to have, e.g., the modular connectivity that is often found in vivo. In this paper, we construct networks of leaky integrate-and-fire neurons to theoretically investigate the effect of modular connectivity on the synchronous bursting activity of cultured neuronal networks. Modular network models are created by defining the number of modules and changing the connection formation probability within a given module, while maintaining a constant connection density. We find that the synchronized bursting frequencies in networks with the same numbers of neurons and connections are solely dependent on their modularity. We also investigate the mechanism behind the network-to-network variation of the activity in random networks, finding that local measures, such as the neuron in-degree and the self-connection, are the important factors. Out results indicate an economic advantage for networks bearing a modular structure and provides a graph-theoretical description of this mechanism.