  Decentralized Federated Learning (FL) has attracted significant attention due
to its enhanced robustness and scalability compared to its centralized
counterpart. It pivots on peer-to-peer communication rather than depending on a
central server for model aggregation. While prior research has delved into
various factors of decentralized FL such as aggregation methods and
privacy-preserving techniques, one crucial aspect affecting privacy is
relatively unexplored: the underlying graph topology. In this paper, we fill
the gap by deriving a stringent privacy bound for decentralized FL under the
condition that the accuracy is not compromised, highlighting the pivotal role
of graph topology. Specifically, we demonstrate that the minimum privacy loss
at each model aggregation step is dependent on the size of what we term as
'honest components', the maximally connected subgraphs once all untrustworthy
participants are excluded from the networks, which is closely tied to network
robustness. Our analysis suggests that attack-resilient networks will provide a
superior privacy guarantee. We further validate this by studying both Poisson
and power law networks, showing that the latter, being less robust against
attacks, indeed reveals more privacy. In addition to a theoretical analysis, we
consolidate our findings by examining two distinct privacy attacks: membership
inference and gradient inversion.
