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.

中文翻译：

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电话通信网的统计特性

文章中考虑了电话订户的定向网络。它可以被描述为一个动态网络，其顶点对应于电话网络的用户，出现的方向边对应于各个用户之间的连接。边的位置及其方向由来自相应顶点的呼入和呼出决定。这篇文章的主题是电话网络用户的某个子集的连接的统计特性。由于它们的出现和消失，这种连接在本质上是动态的。一天内在选定顶点发生的传出（或传入）连接数用作主要特征。已经使用实验数据分析了这种网络的传出（或传入）连接（或呼叫）数量的分布密度。已经表明，这种在调用次数上的分布密度服从对数正态分布密度，这取决于两个参数。确定对数正态分布密度的两个参数的值，即平均值和方差。已经讨论了在传入（或传出）连接数上出现对数正态分布密度的原因。还考虑了其​​他订户组的统计特性。特别是，已选择向电话网络的各个用户进行大量呼出呼叫的组进行单独研究。这个小组的成员，创建和分发垃圾邮件的人可以称为垃圾邮件发送者。已经表明，这些群体，例如垃圾邮件发送者，也遵循呼叫次数的对数正态分布密度，但它们的特征在于不同的平均值和方差。