  We develop a network in which the natural numbers are the vertices. We use
the decomposition of natural numbers by prime numbers to establish the
connections. We perform data collapse and show that the degree distribution of
these networks scale linearly with the number of vertices. We compare the
average distance of the network and the clustering coefficient with the
distance and clustering coefficient of the corresponding random graph. In case
we set connections among vertices each time the numbers share a common prime
number the network is not a small-world type. If the criterium for establishing
links becomes more selective, only prime numbers greater than $p_l$ are used to
establish links, the network shows small-world effect, it means, it has high
clustering coefficient and low distance.
