Random Sequential Renormalization of Networks I: Application to Critical Trees

Details Random Sequential Renormalization of Networks I: Application to Critical Trees Random Sequential Renormalization of Networks I: Application to Critical Trees

2010-09-20

arxiv.org/abs/1009.3955v2

Phys. Rev. E 83, 036110 (2011)

Physics

Condensed Matter

Statistical Mechanics

Scientific paper

10.1103/PhysRevE.83.036110

We introduce the concept of Random Sequential Renormalization (RSR) for arbitrary networks. RSR is a graph renormalization procedure that locally aggregates nodes to produce a coarse grained network. It is analogous to the (quasi-)parallel renormalization schemes introduced by C. Song {\it et al.} (Nature {\bf 433}, 392 (2005)) and studied more recently by F. Radicchi {\it et al.} (Phys. Rev. Lett. {\bf 101}, 148701 (2008)), but much simpler and easier to implement. In this first paper we apply RSR to critical trees and derive analytical results consistent with numerical simulations. Critical trees exhibit three regimes in their evolution under RSR: (i) An initial regime $N_0^{\nu}\lesssim N

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