  The rapid diffusion of information and the adoption of social behaviors are
of critical importance in situations as diverse as collective actions, pandemic
prevention, or advertising and marketing. Although the dynamics of large
cascades have been extensively studied in various contexts, few have
systematically examined the impact of network topology on the efficiency of
information diffusion. Here, by employing the linear threshold model on
networks with communities, we demonstrate that a prominent network
feature---the modular structure---strongly affects the speed of information
diffusion in complex contagion. Our simulations show that there always exists
an optimal network modularity for the most efficient spreading process. Beyond
this critical value, either a stronger or a weaker modular structure actually
hinders the diffusion speed. These results are confirmed by an analytical
approximation. We further demonstrate that the optimal modularity varies with
both the seed size and the target cascade size, and is ultimately dependent on
the network under investigation. We underscore the importance of our findings
in applications from marketing to epidemiology, from neuroscience to
engineering, where the understanding of the structural design of complex
systems focuses on the efficiency of information propagation.
