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Effectively Spreading Behavior: Clusters


This article from Science Magazine explores a study conducted by Damon Centola, a Sloan School of Management student who studied how fast behaviors spread in different types of networks. The study tested two different types of networks – one with a greater number of weak ties and overall connections and another network with more clusters. Ultimately, the study found that a network with more clusters of overlapping ties is more effective at influencing the behavior of a network. Studying networks can allow us to explore why clusters are tightly-knit structures that can have a larger impact on the individuals within them.


A cluster of nodes is formed when the density of connections within a group of the network is greater than the density of connections that group forms with other groups in the network. This means that it is quite easy to popularize an opinion or a trend within a cluster as it is densely connected and an individual node receives the same message numerous times (and is more likely to favor that opinion if his/her cluster popularizes it). To more concretely substantiate this, we can assign payoffs to choices individuals face and see how a cluster influences nodes.


For example, suppose individuals need to decide between two products, one made by Apple (product A) and one made by Microsoft (product M). For each connected pair that prefers the same product, the payoff for choosing A is 15 and their payoff for choosing M is 40. Suppose a, b, c, and d initially choose A. The 4 nodes are a part of a cluster in this network. Let us examine what happens when one node converts to another product. For example, supposeconverts from A to M.

The payoffs b faces are 40 for M (from c) and 30 for A (from a and d). Thus, it makes sense for b to switch over to M. Once switches to M, a will follow as it faces a payoff of 80 for M and 15 for A (from d). Once is converted, all nodes in the cluster can convert. This can explain why the clusters an individual is a part of heavily bias his/her choices. Although this is a very specific examples of how an opinion very easily spreads within a cluster, this can shed light on why Centola found that a network with more clusters influences a network more. Once a member of a cluster is affected, it can be quite easy for others in the cluster to adopt his idea/mannerism/choices.

Since only weak ties alone may not share overlaps and tightly-knit connections like nodes in clusters do, an epidemic may not spread as easily in a network without clusters.


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November 2018