Social graphs are widely used in research (e.g., epidemiology) and business (e.g., recommender systems). However, sharing these graphs poses privacy risks because they contain sensitive information about individuals. Graph anonymization techniques aim to protect individual users in a graph, while graph de-anonymization aims to re-identify users. The effectiveness of anonymization and de-anonymization algorithms is usually evaluated with privacy metrics. However, it is unclear how strong existing privacy metrics are when they are used in graph privacy. In this paper, we study 26 privacy metrics for graph anonymization and de-anonymization and evaluate their strength in terms of three criteria: monotonicity indicates whether the metric indicates lower privacy for stronger adversaries; for within-scenario comparisons, evenness indicates whether metric values are spread evenly; and for between-scenario comparisons, shared value range indicates whether metrics use a consistent value range across scenarios. Our extensive experiments indicate that no single metric fulfills all three criteria perfectly. We therefore use methods from multi-criteria decision analysis to aggregate multiple metrics in a metrics suite, and we show that these metrics suites improve monotonicity compared to the best individual metric. This important result enables more monotonic, and thus more accurate, evaluations of new graph anonymization and de-anonymization algorithms.
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