The clustering attachment model introduced in the paper Bagrow and Brockmann (2013) may be used as an evolution tool of random networks. We propose a new clustering attachment model which can be considered as the limit of the former clustering attachment model as model parameter $\alpha$ tends to zero. We focus on the study of a total triangle count that is considered in the literature as an important characteristic of the network clustering. It is proved that total triangle count tends to infinity a.s. for the proposed model. Our simulation study is used for the modeling of sequences of triangle counts. It is based on the interpretation of the clustering attachment as a generalized P\'{o}lya-Eggenberger urn model that is introduced here at first time.

翻译：Bagrow和Brockmann (2013) 提出的聚类附着模型可作为随机网络的演化工具。我们提出了一种新的聚类附着模型，该模型可视为原模型在模型参数 $\alpha$ 趋近于零时的极限形式。重点关注总三角形数量的研究——该指标在文献中被视为网络聚类的重要特征。本文证明了所提出的模型中总三角形数量几乎必然趋向无穷大。基于聚类附着模型首次被解释为广义Pólya-Eggenberger urn模型这一发现，我们利用仿真研究对三角形数量序列进行建模。