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.