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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 newclustering attachment model which can be considered as the limit of the formerclustering attachment model as model parameter $\alpha$ tends to zero. We focuson the study of a total triangle count that is considered in the literature asan important characteristic of the network clustering. It is proved that totaltriangle count tends to infinity a.s. for the proposed model. Our simulationstudy is used for the modeling of sequences of triangle counts. It is based onthe interpretation of the clustering attachment as a generalizedP\'{o}lya-Eggenberger urn model that is introduced here at first time.

Investigation of triangle counts in graphs evolved by uniform clustering attachment