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

The effect of distant connections on node anonymity in complex networks