  Systems with long-range interactions often exhibit power-law distributions
and can by described by the non-extensive statistical mechanics framework
proposed by Tsallis. In this contribution we consider a simple model
reproducing continuous transition from the extensive to the non-extensive
statistics. The considered model is composed of agents interacting among
themselves on a certain network topology. To generate the underlying network we
propose a new network formation algorithm, in which the mean degree scales
sub-linearly with a number of nodes in the network (the scaling depends on a
single parameter). By changing this parameter we are able to continuously
transition from short-range to long-range interactions in the agent-based
model.
