Number of Loops in Elastic Scale-Free Networks

Model of scale-free networks with non-unit elasticity has been investigated. Applying the concept of non-unit elasticity, i.e. the concept of different relative growth rates for links and nodes, makes it possible to generate scale-free models for dense networks. An analytic expression for the number of loops as a function of network size has been found. As it was shown, the number of loops follows a power law with scaling factor linearly depends on elasticity factor. Numerical simulation was made and numerical results are in accordance with analytic ones.