A theoretic treatment of network diffusion
A seminal paper by Stephen Morris (linked below) in 1998 laid the groundwork for much of the work done in analyzing, among other things, decisions people take after looking at analogous decisions made by people in their friend circle – or local network. Studying how people make choices by , to put it simply, “looking around” is a vital field of research for people trying to maximize ad revenue, or people just trying to stem misinformation or rumor flow (an analysis of which, by Facebook Research, is linked to below).
As put forth by Morris (for a simpler version of this analysis), we suppose that “each player’s binary choice in each period is a best response to the population choices of the previous period”. In this kind of game, the decision each individual makes depends on the choices the people around them make.If there is near unanimous endorsement of one side by all the nearby people, then the choice becomes clearer. If however everyone in that individual’s local network is divided overall, the decision is based on factors other than just considering peer choices.
In highly connected networks, then, it is harder for new trends (or ideas, or any equivalent) to take hold, since a big fraction (and thus more individuals) per individual must be adopting the new trend for it to propagate. Taking the example of rumors: more people are likely to believe that a rumor is true if quite a few of their friends seem to believe it. However, if someone has a lot of friends, more of their friends must be convinced of the truth of the rumor for this to work.
Morris’s work is utilized extensively now that social networks exist online and there are ways to quantitatively estimate the efficacy of ideas and rumors.
References:
2. Facebook paper on Rumor cascades