Currently, most of the online social networks (OSN) keep their data secret and in centralized manner. Researchers are allowed to crawl the underlying social graphs (and data) but with limited rates, leading to only partial views of the true social graphs. To overcome this constraint, we may start from user perspective, the contributors of the OSNs. More precisely, if users cautiously collaborate with one another, they can use the very infrastructure of the OSNs to exchange noisy friend lists with their neighbors in several rounds. In the end, they can build local subgraphs, also called local views of the true social graph. In this paper, we propose such protocols for the problem of \textit{private link exchange} over social graphs. The problem is unique in the sense that the disseminated data over the links are the links themselves. However, there exist fundamental questions about the feasibility of this model. The first question is how to define simple and effective privacy concepts for the link exchange processes. The second question comes from the high volume of link lists in exchange which may increase exponentially round after round. While storage and computation complexity may be affordable for desktop PCs, communication costs are non-trivial. We address both questions by a simple $(α,β)$-exchange using Bloom filters.