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Systems with long-range interactions often exhibit power-law distributionsand can by described by the non-extensive statistical mechanics frameworkproposed by Tsallis. In this contribution we consider a simple modelreproducing continuous transition from the extensive to the non-extensivestatistics. The considered model is composed of agents interacting amongthemselves on a certain network topology. To generate the underlying network wepropose a new network formation algorithm, in which the mean degree scalessub-linearly with a number of nodes in the network (the scaling depends on asingle parameter). By changing this parameter we are able to continuouslytransition from short-range to long-range interactions in the agent-basedmodel.

Continuous transition from the extensive to the non-extensive statistics in an agent-based herding model