  The directed network of telephone subscribers is considered in the article.
It can be described as a dynamic network with vertices that correspond to the
subscribers of the telephone network and emerging directional edges that
correspond to the connections between the respective subscribers. The position
of the edge and its direction is determined by the incoming and outgoing calls
from the corresponding vertices. The subject of the article is the statistical
properties of the connections of a certain subset of telephone network
subscribers. Such connections are dynamic in nature due to their appearance and
disappearance. The number of outgoing (or incoming) connections occurred during
a day at a selected vertex is used as the main characteristic. The distribution
density of the number of outgoing (or incoming) connections (or calls) of such
a network has been analyzed using the experimental data. It has been shown that
such a distribution density over the number of calls obeys the lognormal
distribution density, which depends on the two parameters. The values of two
parameters, namely the mean value and the variance, determining the lognormal
distribution density are established. The reasons for the appearance of a
lognormal distribution density over the number of incoming (or outgoing)
connections have been discussed. The statistical properties of other groups of
subscribers have been considered as well. In particular, the group that makes a
large number of outgoing calls to various subscribers of the telephone network
has been selected for a separate study. The members of this group, who create
and distribute spam can be called spammers. It has been shown that these
groups, spammers for example, also obeys the lognormal distribution density
over the number of calls but they are characterized by the different mean value
and variance.
