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Skarpalezos L, Kittas A, Argyrakis P, et al. Efficiency of message transmission using biased random walks in complex networks in the presence of traps. Phys Rev E Stat Nonlin Soft Matter Phys. 2015;91(1):012817doi: 10.1103/PhysRevE.91.012817.
Skarpalezos, L., Kittas, A., Argyrakis, P., Cohen, R., & Havlin, S. (2015). Efficiency of message transmission using biased random walks in complex networks in the presence of traps. Physical review. E, Statistical, nonlinear, and soft matter physics, 91(1), 012817. https://doi.org/10.1103/PhysRevE.91.012817
Skarpalezos, Loukas, et al. "Efficiency of message transmission using biased random walks in complex networks in the presence of traps." Physical review. E, Statistical, nonlinear, and soft matter physics vol. 91,1 (2015): 012817. doi: https://doi.org/10.1103/PhysRevE.91.012817
Skarpalezos L, Kittas A, Argyrakis P, Cohen R, Havlin S. Efficiency of message transmission using biased random walks in complex networks in the presence of traps. Phys Rev E Stat Nonlin Soft Matter Phys. 2015 Jan;91(1):012817. doi: 10.1103/PhysRevE.91.012817. Epub 2015 Jan 26. PMID: 25679667.
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Phys Rev E Stat Nonlin Soft Matter Phys. 2015 Jan;91(1):012817. doi: 10.1103/PhysRevE.91.012817. Epub 2015 Jan 26.

Efficiency of message transmission using biased random walks in complex networks in the presence of traps.

Physical review. E, Statistical, nonlinear, and soft matter physics

Loukas Skarpalezos, Aristotelis Kittas, Panos Argyrakis, Reuven Cohen, Shlomo Havlin

Affiliations

  1. Department of Physics, University of Thessaloniki, 54124 Thessaloniki, Greece.
  2. Department of Mathematics, Bar-Ilan University, Ramat-Gan 5290002, Israel.
  3. Department of Physics, Bar-Ilan University, Ramat-Gan 5290002, Israel.

PMID: 25679667 DOI: 10.1103/PhysRevE.91.012817

Abstract

We study the problem of a particle or message that travels as a biased random walk towards a target node in a network in the presence of traps. The bias is represented as the probability p of the particle to travel along the shortest path to the target node. The efficiency of the transmission process is expressed through the fraction f(g) of particles that succeed to reach the target without being trapped. By relating f(g) with the number S of nodes visited before reaching the target, we first show that, for the unbiased random walk, f(g) is inversely proportional to both the concentration c of traps and the size N of the network. For the case of biased walks, a simple approximation of S provides an analytical solution that describes well the behavior of f(g), especially for p>0.5. Also, it is shown that for a given value of the bias p, when the concentration of traps is less than a threshold value equal to the inverse of the mean first passage time (MFPT) between two randomly chosen nodes of the network, the efficiency of transmission is unaffected by the presence of traps and almost all the particles arrive at the target. As a consequence, for a given concentration of traps, we can estimate the minimum bias that is needed to have unaffected transmission, especially in the case of random regular (RR), Erdős-Rényi (ER) and scale-free (SF) networks, where an exact expression (RR and ER) or an upper bound (SF) of the MFPT is known analytically. We also study analytically and numerically, the fraction f(g) of particles that reach the target on SF networks, where a single trap is placed on the highest degree node. For the unbiased random walk, we find that f(g)∼N(-1/(γ-1)), where γ is the power law exponent of the SF network.

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