We consider interactive proofs for social graphs, where the verifier has only oracle access to the graph and can query for the ith neighbor of a vertex v, given i and v. In this model, we construct a doubly-efficient public-coin two-message interactive protocol for estimating the size of the graph to within a multiplicative factor ε >0. The verifier performs O(1/ε2 · τmix· Δ) queries to the graph, where τmix is the mixing time of the graph and Δ is the average degree of the graph. The prover runs in quasi-linear time in the number of nodes in the graph. Furthermore, we develop a framework for computing the quantiles of essentially any (reasonable) function f of vertices/edges of the graph. Using this framework, we can estimate many health measures of social graphs such as the clustering coefficients and the average degree, where the verifier performs only a small number of queries to the graph. Using the Fiat-Shamir paradigm, we are able to transform the above protocols to a non-interactive argument in the random oracle model. The result is that social media companies (e.g., Facebook, Twitter, etc.) can publish, once and for all, a short proof for the size or health of their social network. This proof can be publicly verified by any single user using a small number of queries to the graph.