Timing in diffusion networks
As learnt in chapter 19, certain behaviors can be diffused in a social network with threshold q. q meaning if the fraction of friends who are adapting the diffusing behavior is larger than q, the friend in question would adapt the behavior. After understanding the concept, I realized how the timing of diffusion is important in swaying the outcome of the network. An example is the past presidential election. Let’s say every node in the network starts with belief n (none), there will be a node starting with b (Biden) and a node starting with t (Trump). I will place them at the opposite ends of the network, as it is reasonable to believe two people with opposite political beliefs wouldn’t be as close as the ones that do. Let q be 1/3.
When analyzing figure 1, each node has 3 friends. Node A start with behavior b and node B starts with behavior t. All nodes C, D, and E have 1/3 of their friends behaving either b or c. Thus, the nodes fulfill the requirement to adapt both behaviors. But one can’t adapt both as one only has one vote. Therefore, this brings me back to my argument – timing. If behavior b reaches a node first, the node will follow behavior b and vice versa. As it is harder to persuade a node to change from b to t or from t to b than to change from none to t or from none to b. The implication of this model is that to diffuse information in a network, one not only has to minimize q, but also the time of diffusion from one node to another.
Figure 1: Example of a social network during the election.