Non-representative sampled networks: Estimation of network structural properties by weighting

This paper analyzes statistical issues arising from non-representative samples of a network. Sampled network data could systematically bias the network properties and generate non-classical measurement error problems. Apart from the sampling rate and the elicitation procedure, the biases on network structural measures depend non-trivially on which subpopulations of nodes are missing with higher probability. We propose a methodology, adapting weighted estimators to networked contexts, which enables researchers to recover several network-level statistics and reduce the biases in the estimated network effects. The proposed weighted estimators are consistent and asymptotically normally distributed and have good performance in finite samples. Notably, our approach does not require users to assume any network formation model and is straightforward to implement.