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The problem of modeling scale-free networks is considered. Mediation-driven attachment rule with nonconstant number of added links is proposed. Applying the copy-factor as the control parameter instead of traditionally used number of incoming links makes it possible to generate networks model, which combines the key benefits of mediation- driven attachment, such as indirect using the nodes degree, and elasticity, such as different relative growth rates for links and nodes. The properties of proposed networks model were studied analytically and confirmed by simulation results.