scholarly journals Random walks in unweighted and weighted modular scale-free networks with a perfect trap

2013 ◽  
Vol 139 (23) ◽  
pp. 234106 ◽  
Author(s):  
Yihang Yang ◽  
Zhongzhi Zhang
Keyword(s):  
Random Walks ◽  
Scale Free ◽  
Scale Free Networks

scholarly journals Random walks in modular scale-free networks with multiple traps

2012 ◽  
Vol 85 (1) ◽  
Author(s):  
Zhongzhi Zhang ◽  
Yihang Yang ◽  
Yuan Lin
Keyword(s):  
Random Walks ◽  
Scale Free ◽  
Scale Free Networks

scholarly journals Random walks and diameter of finite scale-free networks

2008 ◽  
Vol 387 (12) ◽  
pp. 3033-3038 ◽  
Author(s):  
Sungmin Lee ◽  
Soon-Hyung Yook ◽  
Yup Kim
Keyword(s):  
Random Walks ◽  
Scale Free ◽  
Scale Free Networks

scholarly journals Biased random walks in the scale-free networks with the disassortative degree correlation

2015 ◽  
Vol 64 (2) ◽  
pp. 028901
Author(s):  
Hu Yao-Guang ◽  
Wang Sheng-Jun ◽  
Jin Tao ◽  
Qu Shi-Xian
Keyword(s):  
Random Walks ◽  
Scale Free ◽  
Degree Correlation ◽  
Scale Free Networks ◽  
Biased Random Walks

Mean first passage time on a family of weighted directed hierarchical scale-free networks

2019 ◽  
Vol 33 (16) ◽  
pp. 1950179 ◽  
Author(s):  
Yu Gao ◽  
Zikai Wu
Keyword(s):  
Random Walks ◽  
Numerical Solutions ◽  
First Passage Time ◽  
Passage Time ◽  
Mean First Passage Time ◽  
First Passage ◽  
Scale Free ◽  
Weight Parameter ◽  
Scale Free Networks ◽  
Hierarchical Scale

Random walks on binary scale-free networks have been widely studied. However, many networks in real life are weighted and directed, the dynamic processes of which are less understood. In this paper, we firstly present a family of directed weighted hierarchical scale-free networks, which is obtained by introducing a weight parameter [Formula: see text] into the binary (1, 3)-flowers. Besides, each pair of nodes is linked by two edges with opposite direction. Secondly, we deduce the mean first passage time (MFPT) with a given target as a measure of trapping efficiency. The exact expression of the MFPT shows that both its prefactor and its leading behavior are dependent on the weight parameter [Formula: see text]. In more detail, the MFPT can grow sublinearly, linearly and superlinearly with varied [Formula: see text]. Last but not least, we introduce a delay parameter p to modify the transition probability governing random walk. Under this new scenario, we also derive the exact solution of the MFPT with the given target, the result of which illustrates that the delay parameter p can only change the coefficient of the MFPT and leave the leading behavior of MFPT unchanged. Both the analytical solutions of MFPT in two distinct scenarios mentioned above agree well with the corresponding numerical solutions. The analytical results imply that we can get desired transport efficiency by tuning weight parameter [Formula: see text] and delay parameter p. This work may help to advance the understanding of random walks in general directed weighted scale-free networks.

EXACT SOLUTIONS FOR AVERAGE TRAPPING TIME OF RANDOM WALKS ON WEIGHTED SCALE-FREE NETWORKS

Fractals ◽  
2017 ◽  
Vol 25 (02) ◽  
pp. 1750013 ◽  
Author(s):  
CHANGMING XING ◽  
YIGONG ZHANG ◽  
JUN MA ◽  
LIN YANG ◽  
LEI GUO
Keyword(s):  
Random Walks ◽  
Exact Solutions ◽  
Weight Distribution ◽  
Close Relation ◽  
The Other ◽  
Trapping Time ◽  
Scale Free ◽  
Weight Parameter ◽  
Scale Free Networks ◽  
Fractal Network

In this paper, we present two deterministic weighted scale-free networks controlled by a weight parameter [Formula: see text]. One is fractal network, the other one is non-fractal network, while they have the same weight distribution when the parameter [Formula: see text] is identical. Based on their special network structure, we study random walks on network with a trap located at a fixed node. For each network, we calculate exact solutions for average trapping time (ATT). Analyzing and comparing the obtained solutions, we find that their ATT all grow asymptotically as a power-law function of network order (number of nodes) with the exponent [Formula: see text] dependent on the weight parameter, but their exponent [Formula: see text] are obviously different, one is an increasing function of [Formula: see text], while the other is opposite. Collectively, all the obtained results show that the efficiency of trapping on weighted Scale-free networks has close relation to the weight distribution, but there is no stable positive or negative correlation between the weight distribution and the trapping time on different networks. We hope these results given in this paper could help us get deeper understanding about the weight distribution on the property and dynamics of scale-free networks.

scholarly journals Influences of degree inhomogeneity on average path length and random walks in disassortative scale-free networks

2009 ◽  
Vol 50 (3) ◽  
pp. 033514 ◽  
Author(s):  
Zhongzhi Zhang ◽  
Yichao Zhang ◽  
Shuigeng Zhou ◽  
Ming Yin ◽  
Jihong Guan
Keyword(s):  
Random Walks ◽  
Path Length ◽  
Average Path Length ◽  
Scale Free ◽  
Scale Free Networks
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