Reidentification and k-anonymity: a model for disclosure risk in graphs

TL;DR

This paper introduces a formal framework for reidentification risks in graphs, proposing new definitions for k-anonymity and (k,l)-anonymity, along with algorithms for graph anonymization.

Contribution

It formalizes reidentification modeling, introduces a correct definition of k-anonymous graphs, and presents algorithms for achieving k-anonymity in graphs.

Findings

n-confusion generalizes k-anonymity

New definition of k-anonymous graph provided

Algorithms for k-anonymization of graphs developed

Abstract

In this article we provide a formal framework for reidentification in general. We define n-confusion as a concept for modelling the anonymity of a database table and we prove that n-confusion is a generalization of k- anonymity. After a short survey on the different available definitions of k- anonymity for graphs we provide a new definition for k-anonymous graph, which we consider to be the correct definition. We provide a description of the k-anonymous graphs, both for the regular and the non-regular case. We also introduce the more flexible concept of (k,l)-anonymous graph. Our definition of (k,l)-anonymous graph is meant to replace a previous definition of (k, l)-anonymous graph, which we here prove to have severe weaknesses. Finally we provide a set of algorithms for k-anonymization of graphs.