Centrality Estimation from Sampled Networks

Can a partially observed network reveal how central everyone is? Centrality shapes economic outcomes and guides policy. However, computing it requires full network data, which is costly and slow to collect. Simple random sampling biases centrality estimates. I propose a sequential sampling design: start with a random household, record its contacts, draw one of them at random, and repeat. The estimated eigenvector centrality is consistent at the rate of the average degree over the largest eigenvalue, for a fixed sampling fraction and nonvanishing spectral gaps. In least-squares regressions of an outcome on the estimated centrality, the robust $t$-statistics from the sampled and the full network are asymptotically equivalent under the null of a zero slope. In an application to the village networks of Banerjee et al. (2019), sequentially surveying half the households reproduces their full-network regression slopes within about one percent, whereas a simple random sample understates them by eleven to twelve percent.

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