Growing network with j-redirectionR. Lambiotte and M. Ausloos
GRAPES, Université de Liège - B5 Sart-Tilman, B-4000 Liège, Belgium
received 4 December 2006; accepted in final form 8 January 2007; published March 2007
published online 21 February 2007
A model for growing information networks is introduced where nodes receive new links through j-redirection, i.e. the probability for a node to receive a link depends on the number of paths of length j arriving at this node. In detail, when a new node enters the network, it either connects to a randomly selected node, or to the j-ancestor of this selected node. The j-ancestor is found by following j links from the randomly selected node. The system is shown to undergo a transition to a phase where condensates develop. We also find analytical predictions for the height statistics and show numerically the non-trivial behaviour of the degree distribution.
89.75.Fb - Structures and organization in complex systems.
87.23.Ge - Dynamics of social systems.
89.75.Hc - Networks and genealogical trees.
© Europhysics Letters Association 2007