  Given $n$ samples of a regular discrete distribution $\pi$, we prove in this
article first a serial of SLLNs results (of Dvoretzky and Erd\"{o}s' type)
which implies a typical power law when $\pi$ is heavy-tailed. Constructing a
(random) graph from the ordered $n$ samples, we can establish other laws for
the degree-distribution of the graph. The phenomena of small world is also
discussed.
