2005
DOI: 10.1103/physrevlett.95.018701
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Diffusion Processes on Power-Law Small-World Networks

Abstract: We consider diffusion processes on power-law small-world networks in different dimensions. In one dimension, we find a rich phase diagram, with different transient and recurrent phases, including a critical line with continuously varying exponents. The results were obtained using self-consistent perturbation theory and can also be understood in terms of a scaling theory, which provides a general framework for understanding processes on small-world networks with different distributions of long-range links.PACS … Show more

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Cited by 45 publications
(56 citation statements)
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“…Networks of Kozma et al -These networks, defined in [39], are simple euclidian lattices in which long range links ("short-cuts") are added. A short-cut starts from each node with probability p, and leads to a node at a distance r where r is distributed according to a power law of index α.…”
Section: Numerical Simulationsmentioning
confidence: 99%
“…Networks of Kozma et al -These networks, defined in [39], are simple euclidian lattices in which long range links ("short-cuts") are added. A short-cut starts from each node with probability p, and leads to a node at a distance r where r is distributed according to a power law of index α.…”
Section: Numerical Simulationsmentioning
confidence: 99%
“…Although it may appear somewhat simplistic (and, indeed prototypical), such problems are motivated by the dynamics and fluctuations in task completion landscapes in causally-constrained queuing networks [32], with applications in manufacturing supply chains, e-commerce-based services facilitated by interconnected servers [33], and certain distributed-computing schemes on computer networks [9,10,11,12,13]. This simplified problem is the Edwards-Wilkinson (EW) process [34] on the respective network [35,36,37,38,39].…”
Section: Introductionmentioning
confidence: 99%
“…Such graphs have been used, for example, to improve scalability of parallel computer algorithms [6][7][8][9][10]. Furthermore, the critical behavior of models of materials, such as the Ising model, Heisenberg model, and random-walker models have been studied on SW graphs [11][12][13][14][15][16][17][18][19][20][21]. The result of these studies is that models on SW graphs exhibit mean-field scaling, namely they have an effective dimension at or above the upper critical dimension of the model (which for the Ising model without disorder is d=4).…”
Section: Introductionmentioning
confidence: 99%