A Certain Complexity Threshold during Growth of Functioning Networks

Abstract

Certain threshold on network size axis was observed in statistical mechanisms of adaptive evolution. Now it is investigated. This threshold is connected with maturation of chaos and lies far above the critical point of percolation. It can be treated as complexity threshold defining the term 'complex network' for Kauffman chaotic networks. Distributions of damage size are obtained using simulation for a representative set of network parameters and network types (including scale-free, RBN and networks with more than two signal variants) for network sizes up to 4000 nodes. Based on them a criterion of the threshold is sought. We do not find any critical point in the investigated area, however a certain practical criterion is proposed. It is zero occurrence in-between two peaks of damage size frequency - left of real fadeout of damage which is ordered behaviour and right of equilibrium level after damage avalanche which is chaotic behaviour.