Minority representation and fairness in network ranking: An application to school contact diary data

Considerations of bias, fairness and representation are a prerequisite of responsible modern statistics. In statistical network analysis, observed networks are often incomplete or systematically biased, which can lead to systematic underrepresentation of protected groups, and affect any downstream ranking or decision based on the observed network. In this paper, we study a high school contact network constructed from self-reported contact diaries and introduce a formal measure of minority representation, defined as the proportion of minority nodes among the top-ranked individuals. We model systematic bias through group-dependent missing edge mechanisms and develop statistical methods to estimate and test for such bias. When bias is detected, we propose a re-ranking procedure based on an asymptotic approximation that improves group representation. Applying the framework to the high school contact network reveals systematic underreporting of cross-group contacts consistent with recall bias. These findings highlight the importance of modeling and correcting systematic bias in social networks with heterogeneous groups.