Chapter 2 – Understanding Diffusion
These “computational experiments” test the dynamics of word-of-mouth diffusion on three different networks—a clustered spatial network (shown in fig. 2.9), a partially rewired network with a few weak ties (shown in fig. 2.10), and a random network composed entirely of weak ties (shown in fig. 2.11)
At the beginning of each of the three experiments, all of the nodes (except the two initial seeds) are unactivated, as shown in gray. They have not yet adopted the behavior. The two seed nodes are shown in black. They are the social innovators who initiate the diffusion process. Diffusion follows a basic social transmission rule. As with any word-of-mouth process, the only way that persons can become activated is by coming into contact with an activated neighbor. When activated, nodes turn black and pass the word along to their neighbors. Diffusion continues until the social contagion has spread through the entire network. In each of these simulations everyone has four neighbors, that is, two neighbors on the left and two on the right.
Figure 2.9: Diffusion in a Large World
Figure 2.9 shows that when the diffusion process is initiated, information spreads from the seed nodes to the neighbors on both sides. From there, it spreads to the neighbors’ neighbors, and so on around the network. By the end of the diffusion process in figure 2.9, it takes fourteen days for word of mouth to spill over from one neighborhood to the next, until it ultimately reaches the entire population.
Things get more interesting when we add some weak ties. Figure 2.10 repeats the diffusion experiment, except this time a few of the connections have been randomly rewired to create long-distance ties in the network. It is important to remember that the overall number of ties remains the same—everyone still has four neighbors. The only difference is that there is slightly less redundancy because a few of those neighbors are no longer connected to each other.
Figure 2.10: Diffusion with Weak Ties
At the start, the diffusion process initially unfolds as before. Word of mouth spreads out spatially until it hits one of the long-distance links. It then jumps across the network and begins to fan out across the new area until it hits another long-distance link and jumps again. Each long tie allows information about the job to spread to an untouched region of the network. The result is that word of the job spreads much faster than it did before. Instead of taking fourteen days to reach everyone in the network, now it only takes five days.
Figure 2.11: Diffusion in a Small World
What happens if we add more weak ties? Figure 2.11 repeats the same experiment in a completely random network, in which all of the ties have been rewired. In this network, redundancy is minimized, giving each person maximum exposure to the network. As in all the previous experiments, every individual has four contacts, but now there is no clustering in the neighborhoods. Consequently, as the diffusion process gets going, each new person that is reached creates exponentially more new exposures than before.