Given a graph G = (V,E), consider Poisson(|V|) walkers performing independent lazy simple random walks on G simultaneously, where the initial position of each walker is chosen independently with probability proportional to the degrees. When two walkers visit the same vertex at the same time they are declared to be acquainted. The social connectivity time SC(G) is defined as the first time in which there is a path of acquaintances between every pair of walkers. It is shown that when the average degree of G is d, with high probability clog|V| ≤ SC(G)≤Cd1+5⋅1G is not regular log3|V|. When G is regular the lower bound is improved to SC(G) ≥ log|V| - 6 log log|V|, with high probability. We determine SC(G) up to a constant factor in the cases that G is an expander and when it is the n-cycle.