Recently, the privacy guarantees of information dissemination protocols have attracted increasing research interests, among which the gossip protocols assume vital importance in various information exchange applications. In this work, we study the privacy guarantees of gossip protocols in general networks in terms of differential privacy and prediction uncertainty. First, lower bounds of the differential privacy guarantees are derived for gossip protocols in general networks in both synchronous and asynchronous settings. The prediction uncertainty of the source node given a uniform prior is also determined. For the private gossip algorithm, the differential privacy and prediction uncertainty guarantees are derived in closed form. Moreover, considering that these two metrics may be restrictive in some scenarios, the relaxed variants are proposed. It is found that source anonymity is closely related to some key network structure parameters in the general network setting. Then, we investigate information spreading in wireless networks with unreliable communications, and quantify the tradeoff between differential privacy guarantees and information spreading efficiency. Finally, considering that the attacker may not be present at the beginning of the information dissemination process, the scenario of delayed monitoring is studied and the corresponding differential privacy guarantees are evaluated.
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