Random walks in modular scale-free networks with multiple traps - PubMed

Affiliations

• PMID: 22400511
• DOI: 10.1103/PhysRevE.85.011106

Random walks in modular scale-free networks with multiple traps

Zhongzhi Zhang et al. Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Jan.

Abstract

Extensive empirical investigation has shown that a plethora of real networks synchronously exhibit scale-free and modular structure and it is thus of great importance to uncover the effects of these two striking properties on various dynamical processes occurring on such networks. In this paper, we examine two cases of random walks performed on a class of modular scale-free networks with multiple traps located at several given nodes. We first derive a formula of the mean first-passage time (MFPT) for a general network, which is the mean of the expected time to absorption originating from a specific node, averaged over all nontrap starting nodes. Although the computation is complex, the expression of the formula is exact; moreover, the computational approach and procedure are independent of the number and position of the traps. We then determine analytically the MFPT for the two random walks being considered. The obtained analytical results are in complete agreement with the numerical ones. Our results show that the number and location of traps play an important role in the behavior of the MFPT, since for both cases the MFPT grows as a power-law function of the number of nodes, but their exponents are quite different. We demonstrate that the root of the difference in the behavior of MFPT is attributed to the modular and scale-free topologies of the networks. This work can deepen the understanding of diffusion on networks with modular and scale-free architecture and motivate relevant studies for random walks running on complex random networks with multiple traps.

Similar articles

• Trapping in scale-free networks with hierarchical organization of modularity.

  Zhang Z, Lin Y, Gao S, Zhou S, Guan J, Li M. Zhang Z, et al. Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Nov;80(5 Pt 1):051120. doi: 10.1103/PhysRevE.80.051120. Epub 2009 Nov 20. Phys Rev E Stat Nonlin Soft Matter Phys. 2009. PMID: 20364960

• Standard random walks and trapping on the Koch network with scale-free behavior and small-world effect.

  Zhang Z, Zhou S, Xie W, Chen L, Lin Y, Guan J. Zhang Z, et al. Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Jun;79(6 Pt 1):061113. doi: 10.1103/PhysRevE.79.061113. Epub 2009 Jun 16. Phys Rev E Stat Nonlin Soft Matter Phys. 2009. PMID: 19658479

• Distinct scalings for mean first-passage time of random walks on scale-free networks with the same degree sequence.

  Zhang Z, Xie W, Zhou S, Li M, Guan J. Zhang Z, et al. Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Dec;80(6 Pt 1):061111. doi: 10.1103/PhysRevE.80.061111. Epub 2009 Dec 8. Phys Rev E Stat Nonlin Soft Matter Phys. 2009. PMID: 20365122

• Random walks in weighted networks with a perfect trap: an application of Laplacian spectra.

  Lin Y, Zhang Z. Lin Y, et al. Phys Rev E Stat Nonlin Soft Matter Phys. 2013 Jun;87(6):062140. doi: 10.1103/PhysRevE.87.062140. Epub 2013 Jun 28. Phys Rev E Stat Nonlin Soft Matter Phys. 2013. PMID: 23848660

• Random walks on weighted networks.

  Zhang Z, Shan T, Chen G. Zhang Z, et al. Phys Rev E Stat Nonlin Soft Matter Phys. 2013 Jan;87(1):012112. doi: 10.1103/PhysRevE.87.012112. Epub 2013 Jan 14. Phys Rev E Stat Nonlin Soft Matter Phys. 2013. PMID: 23410288

Cited by

• Lévy random walks on multiplex networks.

  Guo Q, Cozzo E, Zheng Z, Moreno Y. Guo Q, et al. Sci Rep. 2016 Nov 28;6:37641. doi: 10.1038/srep37641. Sci Rep. 2016. PMID: 27892508 Free PMC article.

Publication types

MeSH terms

Substances