Random walks on non-homogenous weighted Koch networks

Dai, Meifeng; Li, Xingyi; Xi, Lifeng

doi:10.1063/1.4810927

Cited by 38 publications

(13 citation statements)

References 40 publications

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“…The average weighted receiving time (AWRT) is the sum of mean weighted first-passage times (MFPTs) for all nodes absorpt at the trap located at a given target node 16 17 18 . In 2013, Dai et al introduced the non-homogenous weighted Koch networks depending on the three weight factors 19 . They defined the average weighted receiving time (AWRT) for the first time and studied the AWRT on random walk.…”

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confidence: 99%

RETRACTED ARTICLE: Modified box dimension and average weighted receiving time on the weighted fractal networks

Dai

Sun

Shao

et al. 2015

Sci Rep

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In this paper a family of weighted fractal networks, in which the weights of edges have been assigned to different values with certain scale, are studied. For the case of the weighted fractal networks the definition of modified box dimension is introduced, and a rigorous proof for its existence is given. Then, the modified box dimension depending on the weighted factor and the number of copies is deduced. Assuming that the walker, at each step, starting from its current node, moves uniformly to any of its nearest neighbors. The weighted time for two adjacency nodes is the weight connecting the two nodes. Then the average weighted receiving time (AWRT) is a corresponding definition. The obtained remarkable result displays that in the large network, when the weight factor is larger than the number of copies, the AWRT grows as a power law function of the network order with the exponent, being the reciprocal of modified box dimension. This result shows that the efficiency of the trapping process depends on the modified box dimension: the larger the value of modified box dimension, the more efficient the trapping process is.

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confidence: 99%

RETRACTED ARTICLE: Modified box dimension and average weighted receiving time on the weighted fractal networks

Dai

Sun

Shao

et al. 2015

Sci Rep

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“…Based on that work, they developed the non-homogeneous weighted Koch networks [19] and the weighted tetrahedron Koch networks [20]. The average weighted receiving time (AWRT) was defined for the first time in [19]. They introduced a family of deterministic non-homogeneous weighted Koch networks on random walk with three scaling factors (i.e., r 1 , r 2 , r 3 ∈ (0, 1)), and showed that in a large network, the AWRT grows as power-law function of the network order with the exponent, represented by log 4 (1 + r 1 + r 2 + r 3 ).…”

Section: Introductionmentioning

confidence: 99%

“…In 2012, Dai et al presented weighted Koch networks on weight-dependent walk with one weight factor [18], and developed a multilayered division method to determine the average receiving time (ART). Based on that work, they developed the non-homogeneous weighted Koch networks [19] and the weighted tetrahedron Koch networks [20]. The average weighted receiving time (AWRT) was defined for the first time in [19].…”

Section: Introductionmentioning

confidence: 99%

Average weighted receiving time in recursive weighted Koch networks

Dai

et al. 2016

Pramana - J Phys

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Motivated by the empirical observation in airport networks and metabolic networks, we introduce the model of the recursive weighted Koch networks created by the recursive division method. As a fundamental dynamical process, random walks have received considerable interest in the scientific community. Then, we study the recursive weighted Koch networks on random walk i.e., the walker, at each step, starting from its current node, moves uniformly to any of its neighbours. In order to study the model more conveniently, we use recursive division method again to calculate the sum of the mean weighted first-passing times for all nodes to absorption at the trap located in the merging node. It is showed that in a large network, the average weighted receiving time grows sublinearly with the network order.

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“…During the past decade, complex network theory is exclusively focused on the single network. [4][5][6][7][8][9][10][11][12][13][14][15][16] In reality, networks rarely appear in isolation, but always are coupled together. Recently, the proposed concepts of interdependent networks and interacting networks mark a turning point in the research field of complex network.…”

Section: Introductionmentioning

confidence: 99%

Percolation on interacting networks with feedback-dependency links

Dong

et al. 2015

Chaos

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When real networks are considered, coupled networks with connectivity and feedback-dependency links are not rare but more general. Here, we develop a mathematical framework and study numerically and analytically the percolation of interacting networks with feedback-dependency links. For the case that all degree distributions of intra- and inter- connectivity links are Poissonian, we find that for a low density of inter-connectivity links, the system undergoes from second order to first order through hybrid phase transition as coupling strength increases. It implies that the average degree k of inter-connectivity links has a little influence on robustness of the system with a weak coupling strength, which corresponds to the second order transition, but for a strong coupling strength corresponds to the first order transition. That is to say, the system becomes robust as k increases. However, as the average degree k of each network increases, the system becomes robust for any coupling strength. In addition, we find that one can take less cost to design robust system as coupling strength decreases by analyzing minimum average degree kmin of maintaining system stability. Moreover, for high density of inter-connectivity links, we find that the hybrid phase transition region disappears, the first order region becomes larger and second order region becomes smaller. For the case of two coupled scale-free networks, the system also undergoes from second order to first order through hybrid transition as the coupling strength increases. We find that for a weak coupling strength, which corresponds to the second order transitions, feedback dependency links have no effect on robustness of system relative to no-feedback condition, but for strong coupling strength which corresponds to first order or hybrid phase transition, the system is more vulnerable under feedback condition comparing with no-feedback condition. Thus, for designing resilient system, designers should try to avoid the feedback dependency links, because the existence of feedback-dependency links makes the system extremely vulnerable and difficult to defend.

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Random walks on non-homogenous weighted Koch networks

Cited by 38 publications

References 40 publications

RETRACTED ARTICLE: Modified box dimension and average weighted receiving time on the weighted fractal networks

RETRACTED ARTICLE: Modified box dimension and average weighted receiving time on the weighted fractal networks

Average weighted receiving time in recursive weighted Koch networks

Percolation on interacting networks with feedback-dependency links

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