In this article, we present a privacy-preserving technique for user-centric multi-release graphs. Our technique consists of sequentially releasing anonymized versions of these graphs under Blowfish Privacy. To do so, we introduce a graph model that is augmented with a time dimension and sampled at discrete time steps. We show that the direct application of state-of-the-art privacy-preserving Differential Private techniques is weak against background knowledge attacker models. We present different scenarios where randomizing separate releases independently is vulnerable to correlation attacks. Our method is inspired by Differential Privacy (DP) and its extension Blowfish Privacy (BP). To validate it, we show its effectiveness as well as its utility by experimental simulations.