  The evolution of random undirected graphs by the clustering attachment (CA)
both without node and edge deletion and with uniform node or edge deletion is
investigated. Theoretical results are obtained for the CA without node and edge
deletion when a newly appended node is connected to two existing nodes of the
graph at each evolution step. Theoretical results concern to (1) the sequence
of increments of the consecutive mean clustering coefficients tends to zero;
(2) the sequences of node degrees and triangle counts of any fixed node which
are proved to be submartingales. These results were obtained for any initial
graph. The simulation study is provided for the CA with uniform node or edge
deletion and without any deletion. It is shown that (1) the CA leads to
light-tailed distributed node degrees and triangle counts; (2) the average
clustering coefficient tends to a constant over time; (3) the mean node degree
and the mean triangle count increase over time with the rate depending on the
parameters of the CA. The exposition is accompanied by a real data study.
