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Abstract

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.
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电话网络的统计特性
本文研究了电话用户定向网络。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和新兴的方向边对应于各自用户之间的连接。边缘的位置和方向由相应顶点的呼入和呼出决定。本文的主题是某一电话网用户子集的连接的统计特性。由于这种联系的出现和消失,它在本质上是动态的。一天内在选定顶点发生的传出(或传入)连接的数量被用作主要特征。用实验数据分析了这种网络的出站(或入站)连接(或呼叫)的分布密度。已经证明,这样的分布密度对调用次数服从对数正态分布密度,这取决于这两个参数。建立了决定对数正态分布密度的两个参数的值,即均值和方差。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。其他用户组的统计特性也被考虑在内。特别是,向电话网络的各种用户拨打大量电话的群体被选为单独的研究对象。创建和分发垃圾邮件的这个组的成员可以被称为垃圾邮件发送者。研究表明,这些群体,例如垃圾邮件发送者,也服从呼叫数量的对数正态分布密度,但它们的特征是不同的平均值和方差。
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