This paper describes the modeling of social networks subject to a recommendation. The Cold Start User-Item Model (CSUIM) of a bipartite graph is considered, which simulates bipartite graph growth based on several parameters. An algorithm is proposed to compute parameters of this model with desired properties. The primary desired property is that the generated graph has similar graph metrics. The next is a change in our graph growth process due to recommendations. The meaning of CSUI model parameters in the recommendation process is described. We make several simulations generating networks from the CSUI model to verify theoretical properties. Also, proposed methods are tested on real-life networks. We prove that the CSUIM model of bipartite graphs is very flexible and can be applied to many different problems. We also show that the parameters of this model can be easily obtained from an unknown bipartite graph.
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