Longitudinal Network Centrality Using Incomplete Data

How do individuals’ influence in a large social network change? Social scientists have difficulty answering this question because measuring influence requires frequent observations of a population of individuals’ connections to each other, while sampling that social network removes information in a way that can bias inferences. This paper introduces a method to measure influence over time accurately from sampled network data. Ranking individuals by the sum of their connections’ connections—neighbor cumulative indegree centrality—preserves the rank influence ordering that would be achieved in the presence of complete network data, lowering the barrier to measuring influence accurately. The paper then shows how to measure that variable changes each day, making it possible to analyze when and why an individual’s influence in a network changes. This method is demonstrated and validated on 21 Twitter accounts in Bahrain and Egypt from early 2011. The paper then discusses how to use the method in domains such as voter mobilization and marketing.