Kinetic-growth self-avoiding walks on small-world networks

Herrero, Carlos P.

doi:10.1140/epjb/e2007-00086-6

Cited by 10 publications

(13 citation statements)

References 46 publications

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“…This reflects the fact that the SAW paths which are actually pursued are typically shorter than SAW paths chosen at random from the list of all SAW paths. The former SAW paths are often referred to as kinetic growth self-avoiding walks [23], or true selfavoiding walks [24], in contrast to the SAW paths which are uniformly sampled among all possible self avoiding paths of a given lengths.…”

Section: Summary and Discussionmentioning

confidence: 99%

“…A special type of random walk which has been studied extensively on regular lattices is the self avoiding walk (SAW), also referred to as the kinetic growth self-avoiding walk [23], or true or myopic self-avoiding walk [24]. This is a random walk which does not visit the same node more than once [25].…”

Section: Introductionmentioning

confidence: 99%

“…These studies provided much insight on the structure and thermodynamics of polymers [6,7]. However, SAWs on networks have not attracted much attention [32,33,34,23,35].…”

Section: Introductionmentioning

confidence: 99%

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The distribution of path lengths of self avoiding walks on Erdős–Rényi networks

Tishby¹,

Biham²,

Katzav³

2016

J. Phys. A: Math. Theor.

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Abstract. We present an analytical and numerical study of the paths of self avoiding walks (SAWs) on random networks. Since these walks do not retrace their paths, they effectively delete the nodes they visit, together with their links, thus pruning the network. The walkers hop between neighboring nodes, until they reach a deadend node from which they cannot proceed. Focusing on Erdős-Rényi networks we show that the pruned networks maintain a Poisson degree distribution, p t (k), with an average degree, k t , that decreases linearly in time. We enumerate the SAW paths of any given length and find that the number of paths, n T (ℓ), increases dramatically as a function of ℓ. We also obtain analytical results for the path-length distribution, P (ℓ), of the SAW paths which are actually pursued, starting from a random initial node. It turns out that P (ℓ) follows the Gompertz distribution, which means that the termination probability of an SAW path increases with its length.

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Section: Summary and Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

The distribution of path lengths of self avoiding walks on Erdős–Rényi networks

Tishby¹,

Biham²,

Katzav³

2016

J. Phys. A: Math. Theor.

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show abstract

“…For SF networks, in particular, this has allowed to distinguish different regimes depending on the exponent γ of the distribution P sf (k) [53]. One can also consider kinetic-growth self-avoiding walks on complex networks, to study the influence of attrition on the maximum length of the paths [58,59], but this kind of walks will not be addressed here.…”

Section: Introductionmentioning

confidence: 99%

Self-avoiding walks and connective constants in clustered scale-free networks

Herrero

2019

Phys. Rev. E

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Various types of walks on complex networks have been used in recent years to model search and navigation in several kinds of systems, with particular emphasis on random walks. This gives valuable information on network properties, but self-avoiding walks (SAWs) may be more suitable than unrestricted random walks to study long-distance characteristics of complex systems. Here we study SAWs in clustered scale-free networks, characterized by a degree distribution of the form P (k) ∼ k −γ for large k. Clustering is introduced in these networks by inserting three-node loops (triangles). The long-distance behavior of SAWs gives us information on asymptotic characteristics of such networks. The number of self-avoiding walks, an, has been obtained by direct enumeration, allowing us to determine the connective constant µ of these networks as the large-n limit of the ratio an/an−1. An analytical approach is presented to account for the results derived from walk enumeration, and both methods give results agreeing with each other. In general, the average number of SAWs an is larger for clustered networks than for unclustered ones with the same degree distribution. The asymptotic limit of the connective constant for large system size N depends on the exponent γ of the degree distribution: For γ > 3, µ converges to a finite value as N → ∞; for γ = 3, the size-dependent µN diverges as ln N , and for γ < 3 we have µN ∼ N (3−γ)/2 .

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“…The typical length scale of SAWs for trapping is characterized by the attrition length. The average attrition length, L , of SAWs on complex networks with N nodes is known to scale as L ∼ N δ with δ < 1 [18,19].…”

Section: Introductionmentioning

confidence: 99%

Network exploration using true self-avoiding walks

2016

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We study the mean first passage time (MFPT) of true self-avoiding walks (TSAWs) on various networks as a measure of searching efficiency. From the numerical analysis, we find that the MFPT of TSAWs, τ^{TSAW}, approaches the theoretical minimum τ^{th}/N=1/2 on synthetic networks whose degree-degree correlations are positive. On the other hand, for biased random walks (BRWs) we find that the MFPT, τ^{BRW}, depends on the parameter α, which controls the degree-dependent bias. More importantly, we find that the minimum MFPT of BRWs, τ_{min}^{BRW}, always satisfies the inequality τ_{min}^{BRW}>τ^{TSAW} on any synthetic network. The inequality is also satisfied on various real networks. From these results, we show that the TSAW is one of the most efficient models, whose efficiency approaches the theoretical limit in network explorations.

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Kinetic-growth self-avoiding walks on small-world networks

Cited by 10 publications

References 46 publications

The distribution of path lengths of self avoiding walks on Erdős–Rényi networks

The distribution of path lengths of self avoiding walks on Erdős–Rényi networks

Self-avoiding walks and connective constants in clustered scale-free networks

Network exploration using true self-avoiding walks

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