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

An estimation formula for the average path length of scale-free networks

2008 ◽  
Vol 17 (7) ◽  
pp. 2327-2332 ◽  
Author(s):  
Li Ying ◽  
Cao Hong-Duo ◽  
Shan Xiu-Ming ◽  
Ren Yong
Keyword(s):  
Path Length ◽  
Average Path Length ◽  
Scale Free ◽  
Estimation Formula ◽  
Scale Free Networks

The average path length of scale free networks

2008 ◽  
Vol 13 (7) ◽  
pp. 1405-1410 ◽  
Author(s):  
Fei Chen ◽  
Zengqiang Chen ◽  
Xiufeng Wang ◽  
Zhuzhi Yuan
Keyword(s):  
Path Length ◽  
Average Path Length ◽  
Scale Free ◽  
Scale Free Networks

SCALE-FREE NETWORKS CAN BE LINEAR-WORLD

2011 ◽  
Vol 25 (32) ◽  
pp. 4593-4603
Author(s):  
LING-ZAN ZHU ◽  
BEI-BEI YIN ◽  
LEI ZHAO ◽  
KAI-YUAN CAI
Keyword(s):  
Numerical Simulations ◽  
Path Length ◽  
Small World ◽  
Average Path Length ◽  
Small Scale ◽  
Scale Free Network ◽  
Scale Free ◽  
Scale Free Networks ◽  
Free Network

It was generally believed that scale-free networks would be small-world. In this paper, two models, named Model A and Model B, are proposed to show that certain scale-free networks can be linear-world instead of small-world. By linear-world, it means that the average path length L of the network grows linearly with the total number of nodes N, i.e., L~N. Model A generates a deterministic scale-free network with high assortativity and numerical simulations demonstrate that the network is linear-world when it satisfies degree exponent λ>1. Model B constructs a partially deterministic scale-free network, which is connected by identical small scale-free networks following certain rules. Analytical arguments and numerical simulations both yield L~N which suggests that it is also linear-world. It is further discussed in this paper that the network generated by Model Bcould be either correlated or uncorrelated. This suggests that, inconsistent with the results in related works, uncorrelated scale-free networks can also be linear-world.

SCALE-FREE AND SMALL-WORLD PROPERTIES OF A SPECIAL HIERARCHICAL NETWORK

Fractals ◽  
2019 ◽  
Vol 27 (02) ◽  
pp. 1950010
Author(s):  
DAOHUA WANG ◽  
YUMEI XUE ◽  
QIAN ZHANG ◽  
MIN NIU
Keyword(s):  
Degree Distribution ◽  
Path Length ◽  
Small World ◽  
Average Path Length ◽  
Clustering Coefficient ◽  
Hierarchical Network ◽  
Scale Free

Many real systems behave similarly with scale-free and small-world structures. In this paper, we generate a special hierarchical network and based on the particular construction of the graph, we aim to present a study on some properties, such as the clustering coefficient, average path length and degree distribution of it, which shows the scale-free and small-world effects of this network.

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.

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