scholarly journals Role of fractal dimension in random walks on scale-free networks

2011 ◽  
Vol 84 (2) ◽  
pp. 331-338 ◽  
Author(s):  
Zhongzhi Zhang ◽  
Yihang Yang ◽  
Shuyang Gao
Keyword(s):  
Fractal Dimension ◽  
Random Walks ◽  
Scale Free ◽  
Scale Free Networks

Role of Cutoff Scaling in Scale-Free Networks

2018 ◽  
Vol 68 (5) ◽  
pp. 563-569
Author(s):  
Meesoon HA*
Keyword(s):  
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 The role of detachment of in-links in scale-free networks

2014 ◽  
Vol 47 (34) ◽  
pp. 345002 ◽  
Author(s):  
P Lansky ◽  
F Polito ◽  
L Sacerdote
Keyword(s):  
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.

scholarly journals Synchronization in scale-free networks: The role of finite-size effects

2015 ◽  
Vol 110 (6) ◽  
pp. 66001 ◽  
Author(s):  
D. Torres ◽  
M. A. Di Muro ◽  
C. E. La Rocca ◽  
L. A. Braunstein
Keyword(s):  
Size Effects ◽  
Finite Size ◽  
Finite Size Effects ◽  
Scale Free ◽  
Scale Free Networks

scholarly journals MUTUAL SELECTION IN NETWORK EVOLUTION: THE ROLE OF THE INTRINSIC FITNESS

2010 ◽  
Vol 21 (01) ◽  
pp. 129-135 ◽  
Author(s):  
XIN-JIAN XU ◽  
LIU-MING ZHANG ◽  
LI-JIE ZHANG
Keyword(s):  
Distribution Function ◽  
Probability Distribution Function ◽  
Probability Function ◽  
Power Laws ◽  
Network Evolution ◽  
Scale Free ◽  
Scale Free Networks ◽  
Intrinsic Character ◽  
Fitness Distribution

We propose a new mechanism leading to scale-free networks which is based on the presence of an intrinsic character of a vertex called fitness. In our model, a vertex i is assigned a fitness xi, drawn from a given probability distribution function f(x). During network evolution, with rate p we add a vertex j of fitness xj and connect to an existing vertex i of fitness xi selected preferentially to a linking probability function g(xi, xj) which depends on the fitnesses of the two vertices involved and, with rate 1 - p we create an edge between two already existed vertices with fitnesses xi and xj, with a probability also preferential to the connection function g(xi, xj). For the proper choice of g, the resulting networks have generalized power-laws, irrespective of the fitness distribution of vertices.

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