Active–passive networks are composed of nodes that meet specific criteria depending on applications (active nodes) and nodes that do not (passive nodes). This paper investigates the network size estimation problem, which involves determining the number of active nodes in anonymous active–passive networks in a distributed way. To this end, a distributed counting architecture is proposed to locally manipulate the criteria for being an active node via a variable and to count the number of active nodes, where this is accomplished without prior knowledge of the network or a procedure for initialization. Several properties of an anonymous network such as network size, number of nodes for a given degree, the maximum and minimum degrees, and so on, can be deduced using the proposed architecture by varying the criteria variable. Stability and convergence analysis of the proposed architecture are presented, and its effectiveness is also demonstrated through a numerical example.

主动-被动网络由满足特定条件的节点（取决于应用程序）（主动节点）和不满足特定标准的节点（被动节点）组成。本文研究了网络规模估计问题，该问题涉及以分布式方式确定匿名主动-被动网络中主动节点的数量。为此，提出了一种分布式计数体系结构，以通过变量在本地操纵作为活动节点的标准并计算活动节点的数量，其中这是在没有网络或初始化过程的先验知识的情况下完成的。匿名网络的几个属性，例如网络大小、给定度数的节点数、最大和最小度数等，可以使用所提出的架构通过改变标准变量来推断。