Percolation transitions with nonlocal constraint

Abstract

We investigate percolation transitions in a nonlocal network model numerically. In this model, each node has an exclusive partner and a link is forbidden between two nodes whose $r$-neighbors share any exclusive pair. The $r$-neighbor of a node $x$ is defined as a set of at most $N^r$ neighbors of $x$, where $N$ is the total number of nodes. The parameter $r$ controls the strength of a nonlocal effect. The system is found to undergo a percolation transition belonging to the mean field universality class for $r<1/2$. On the other hand, for $r>1/2$, the system undergoes a peculiar phase transition from a non-percolating phase to a quasi-critical phase where the largest cluster size $G$ scales as $G\sim N^{\alpha }$ with $\alpha =0.74(1)$. In the marginal case with $r=1/2$, the model displays a percolation transition that does not belong to the mean field universality class.

4 pages, 5 figures

References in corpus (7)

• Cooperative Game Theory Approaches for Network Partitioning
• Percolation on correlated networks
• Evolution of scale-free random graphs: Potts model formulation
• Percolation transition in networks with degree-degree correlation
• Particle Condensation in Pair Exclusion Process
• Structural phase transition in evolving networks
• Condensation and Clustering in the Driven Pair Exclusion Process