Gossip: Identifying Central Individuals in a Social Network

Because dynamics of networks depend on the small interactions between many components, networks are an important topic in complexity theory. Social networks describe individuals and their connections to one another. Professor of Economics at Stanford, Matthew O. Jackson is interested in how social network shape affects the flow of information on a network.

Stanford Complexity Group hosted a seminar entitled “Gossip: Identifying Central Individuals in a Social Network” by Matt Jackson on 3/13/2017. His talk focused on his research on microfinance efforts in a collection of rural south Indian villages. Advertising via means that might be more obvious in a Western context- for example via the internet or printed posters- are less effective in these villages, in part due to low literacy rates. Instead, more effective efforts of advertising the availability of these microfinance loans rely on person to person communication. Spreading information person to person over a social network relies on identifying who are the “most central” individuals in a social network. But what does it mean for an individual to be “central”? How do different measures of centrality lead to differences in the spread of information flow on the network?

Professor Jackson and his co-authors on the study simulated the flow of information over the social network structure from actual villages where the information spread from most “central” individuals and centrality was measured in different ways. “Degree centrality,” the number of edges a node has, was not particularly effective in identifying individuals who could spread information over the network. Identifying individuals by their eigenvector centrality was a more effective centrality measure for identifying good candidates to spread information over the network. Eigenvector centrality takes into account the first-degree connections of an individual, like degree centrality, but also considers the connectedness of the individual’s neighbors.

Eigenvector centrality, however, assumes that the probability of someone sharing information doesn’t decay with time. Thus, they developed a new model of centrality- diffusion centrality, which is parameterized by time.

Ultimately, the different measures of centrality rely on delineating the entire social network. In reality this would not be an effective strategy for a company to figure out how to best advertise their service (consider: a representative going door to door survey each family’s connectedness might as well advertise the service to each individual family. This quandary motivated another tool for measuring centrality- gossip. By asking few members of the community to identify who they had heard news about recently. They termed this measure of centrality “communication centrality”. Individuals with high “communication centrality” were often also those who were most central when centrality was defined by “diffusion centrality.”

Testing these theoretical results in a few dozen South Indian villages, Matt Jackson and collaborators considered the participation in microfinance when the loans were advertised to a few “central” individuals, using the different measures of centrality. While degree centrality did not have a high correlation with the percent of individuals participating in microfinance from a village, both “diffusion centrality” and “communication centrality” did.

While the results of these projects may be specific to microfinance in small villages, the question of how to spread helpful important information over a network extends to other types of social networks as well. Matt Jackson is also interested in studying the flow of information over larger web-based social networks, for example, how simple parenting tips like talking to babies from an early age, could effectively spread through social networks.

Matt Jackson’s work is a fascinating example of applying complexity theory to real world problems and we thank him for a wonderful seminar.

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