Optimal Network Modularity for Information Diffusion

We investigate the impact of community structure on information diffusion with the linear threshold model. Our results demonstrate that modular structure may have counterintuitive effects on information diffusion when social reinforcement is present. We show that strong communities can facilitate global diffusion by enhancing local, intracommunity spreading. Using both analytic approaches and numerical simulations, we demonstrate the existence of an optimal network modularity, where global diffusion requires the minimal number of early adopters.

Figure 1

Example of networks with different degrees of clustering $\mu$ (0.03, 0.12, and 0.3 from left to right, respectively). Parameters values are set to $N=100$, $M=750$, and $n=2$.

Figure 2

The tradeoff between intracommunity and intercommunity spreading. Stronger communities (small $\mu$) facilitate spreading within the originating community (local), while weak communities (large $\mu$) provide bridges that allow spreading between communities (global). There is a range of $\mu$ values that allow both (optimal). The blue squares represent ${\rho }_{\infty }^A$, the final density of active nodes in the community $A$, and the red circles represent ${\rho }_{\infty }^B$. The parameters for the simulation are ${\rho }_0=0.17$, $\theta =0.4$, $N=131056$, and $z=20$.

Figure 3

(a) Phase diagram of the threshold model in the presence of community structures with $N=131056$, $z=20$, and $\theta =0.4$. There are three phases: no diffusion (white), local diffusion that saturates the community $A$ (blue, light-gray), and global diffusion (red, dark-gray). The dotted and dashed lines indicate the values of ${\rho }_0$ shown in (b) and (c). (b) Cross sections of the phase diagram [dotted lines in (a)]. TL approximations (solid lines) show excellent agreement with the simulation while MF approximations (dotted lines) overestimate the possibility of global diffusion. (c) Cross sections represented by dashed lines in (a).