The effect of distant connections on node anonymity in complex networks

TL;DR

This paper introduces new measures for assessing node anonymity in complex networks that account for distant connections, revealing significant privacy risks in real-world social network data.

Contribution

It proposes d-k-anonymity and anonymity-cascade as novel methods to evaluate and understand the impact of distant network connections on node privacy.

Findings

Distant connections greatly reduce node anonymity.

Extending knowledge beyond ego networks decreases anonymity by over 50%.

Methods are scalable to large networks with millions of nodes.

Abstract

Ensuring privacy of individuals is of paramount importance to social network analysis research. Previous work assessed anonymity in a network based on the non-uniqueness of a node's ego network. In this work, we show that this approach does not adequately account for the strong de-anonymizing effect of distant connections. We first propose the use of d-k-anonymity, a novel measure that takes knowledge up to distance d of a considered node into account. Second, we introduce anonymity-cascade, which exploits the so-called infectiousness of uniqueness: mere information about being connected to another unique node can make a given node uniquely identifiable. These two approaches, together with relevant "twin node" processing steps in the underlying graph structure, offer practitioners flexible solutions, tunable in precision and computation time. This enables the assessment of anonymity in large-scale networks with up to millions of nodes and edges. Experiments on graph models and a wide range of real-world networks show drastic decreases in anonymity when connections at distance 2 are considered. Moreover, extending the knowledge beyond the ego network with just one extra link often already decreases overall anonymity by over 50%. These findings have important implications for privacy-aware sharing of sensitive network data.