  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 $\mathrm{SC}(G)$ 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 \[ c\log |V| \le \mathrm{SC}(G) \le C d^{1+5 \cdot 1_{G
\text{ is not regular}} } \log^3 |V|.\] When $G$ is regular the lower bound is
improved to $\mathrm{SC}(G) \ge \log |V| -6 \log \log |V| $, with high
probability.
  We determine $\mathrm{SC}(G)$ up to a constant factor in the cases that $G$
is an expander and when it is the $n$-cycle.
