I found an interesting empirical paper about networks.
Daniel W. Franks, Jason Noble, Peter Kaufmann and Sigrid Stagl
Extremism Propagation in Social Networks with Hubs
2008; 16; 264
Even when negative extremists are twice as prevalent in the population, opinion convergence to the positive extreme can regularly occur if positive extremists are placed on network hubs.
A positively skewed degree distribution increase extremism transmission in a social network.
We suspect that the creation of some well-connected nodes (hubs), along with the creation of many poorly connected individuals, is responsible. Extremists located at these key nodes are connected to more agents, and more parts on the network. Thus, their influence is more frequent and wider reaching, making it less likely that certain parts of the network remain socially isolated from the extremist’s opinion.
A positively skewed degree distribution increases opinion convergence towards extremes, and encourages opinion convergence on a single extreme under a wider range of conditions than topologies that were not skewed in their degree distribution.
However, extremists take advantage of non-extremists at hubs, as a means of transmitting their opinion.
Non-extremists are initially less confident about their opinion than extremists.
Thus, extremists have more influence over non-extremists than non-extremists have over extremists (and more influence than non-extremists have over each other). Once an extremist has spent time influencing a non-extremist at a hub, the former non-extremist will transmit the opinion throughout the network. Because agents at hubs are well-connected, it is likely that they are connected to an extremist. In the real world, extremists might purposely attempt to influence people in high status positions.
Valente (1995) investigated some effects of propagating innovations first to more “strategic” nodes of the network, showing that an individual’s network position can affect innovation diffusion in a social network.
Valente, T. (1995). Network models of the diffusion of innovations. Cresskill, NJ: Hampton Press.
By placing positive extremists at the well-connected nodes (i.e., nodes to the tail-end of the degree distribution) we found that when the network converges on a single extreme, it is always to the positive extreme.
This is because when positive extremists are placed on key nodes they are able to directly influence more agents (as they would have more direct connections) and have a higher chance of having a random connection that allows them to influence a different social network neighborhood.
The importance of social position for social influence was highlighted by the result that, when positive extremists are placed on hubs, all population convergence is to the positive extreme even when there are twice as many negative extremists. Thus, the position of an opinion in the social network is more important than the initial proportion of individuals with the opinion.
The network does not have to have a power-law distribution for this result to stand. However, the network must have multiple hubs, and social networks are known to produce such hubs.