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

Evolutionary Prisoners' Dilemma Game on Scale-Free Networks with Degree-Degree Correlation

2010 ◽  
Vol 27 (10) ◽  
pp. 100201 ◽  
Author(s):  
Cheng Hong-Yan ◽  
Dai Qiong-Lin ◽  
Li Hai-Hong ◽  
Yang Jun-Zhong
Keyword(s):  
Scale Free ◽  
Degree Correlation ◽  
Prisoners Dilemma ◽  
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 Diagonal Degree Correlations vs. Epidemic Threshold in Scale-Free Networks

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
M. L. Bertotti ◽  
G. Modanese
Keyword(s):  
Correlation Matrix ◽  
Large Scale ◽  
Network Size ◽  
Epidemic Threshold ◽  
Correlation Matrices ◽  
Scale Free ◽  
Degree Correlation ◽  
Scale Free Networks ◽  
Degree Correlations

We prove that the presence of a diagonal assortative degree correlation, even if small, has the effect of dramatically lowering the epidemic threshold of large scale-free networks. The correlation matrix considered is P h | k = 1 − r P h k U + r δ h k , where P U is uncorrelated and r (the Newman assortativity coefficient) can be very small. The effect is uniform in the scale exponent γ if the network size is measured by the largest degree n . We also prove that it is possible to construct, via the Porto–Weber method, correlation matrices which have the same k n n as the P h | k above, but very different elements and spectra, and thus lead to different epidemic diffusion and threshold. Moreover, we study a subset of the admissible transformations of the form P h | k ⟶ P h | k + Φ h , k with Φ h , k depending on a parameter which leaves k n n invariant. Such transformations affect in general the epidemic threshold. We find, however, that this does not happen when they act between networks with constant k n n , i.e., networks in which the average neighbor degree is independent from the degree itself (a wider class than that of strictly uncorrelated networks).

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.

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