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.