Differential Privacy for Network Connectedness Indices

TL;DR

This paper introduces a new method for releasing network connectedness indices under differential privacy, addressing high sensitivity and composition issues, and demonstrating its effectiveness on real social network data.

Contribution

The authors develop a straightforward, two-layer noise addition method with analytical debiasing for differentially private network connectedness indices, improving privacy and utility.

Findings

Method achieves consistency and asymptotic normality.

Works well on networks with as few as 200 nodes.

Effective in simulations and real-world social networks.

Abstract

Researchers increasingly use data on social and economic networks to study a range of social science questions, but releasing statistics derived from networks can raise significant privacy concerns. We show how to release network connectedness indices that quantify assortative mixing across node attributes under edge-adjacent differential privacy. Standard privacy techniques perform poorly in this setting both because connectedness indices have high global sensitivity and because a single node's attribute can potentially be an input to connectedness in thousands of cells, leading to poor composition. Our method, which is straightforward to apply, first adds noise to node attributes, then analytically debiases downstream statistics, and finally applies a second layer of noise to protect the presence or absence of individual edges. We prove consistency and asymptotic normality of our estimators for both discrete and continuous labels and show our method works well in simulations and on real networks with as few as 200 nodes collected by social scientists.