1111.2005 (Shu Tanaka et al.)

Network-Growth Rule Dependency of Percolation Criticality -- Generalized
Explosive Percolation    [PDF]

Shu Tanaka, Ryo Tamura

To consider relation between percolation criticality and network-growth rule in an evolving network model, we propose a general network-growth rule which includes the conventional network-growth rule and the rule proposed by Achlioptas {\it et al.} very recently [Science {\bf 323} (2009) 1453]. We introduce the generalized parameter $q$ which characterizes how to evolve a network. We obtain size dependency of percolation step and fractal dimension of percolated cluster at the percolation step for several $q$'s. Strong size dependency of percolation step and sudden change of fractal dimension are observed for intermediate $q$. From these facts, we find that the percolation criticality changes between at the conventional network-growth rule and at the rule proposed by Achlioptas {\it et al.}

View original: http://arxiv.org/abs/1111.2005