scholarly journals Optimal and suboptimal networks for efficient navigation measured by mean-first passage time of random walks

2012 ◽  
Vol 22 (4) ◽  
pp. 043129 ◽  
Author(s):  
Zhongzhi Zhang ◽  
Yibin Sheng ◽  
Zhengyi Hu ◽  
Guanrong Chen
Keyword(s):  
Random Walks ◽  
First Passage Time ◽  
Passage Time ◽  
Mean First Passage Time ◽  
First Passage

Calculations of first passage time of delayed tree-like networks

2015 ◽  
Vol 29 (28) ◽  
pp. 1550200
Author(s):  
Shuai Wang ◽  
Weigang Sun ◽  
Song Zheng
Keyword(s):  
Random Walks ◽  
First Passage Time ◽  
Passage Time ◽  
The Novel ◽  
Mean First Passage Time ◽  
First Passage ◽  
Initial Node ◽  
Network Parameters ◽  
Self Similar ◽  
The Mean

In this paper, we study random walks in a family of delayed tree-like networks controlled by two network parameters, where an immobile trap is located at the initial node. The novel feature of this family of networks is that the existing nodes have a time delay to give birth to new nodes. By the self-similar network structure, we obtain exact solutions of three types of first passage time (FPT) measuring the efficiency of random walks, which includes the mean receiving time (MRT), mean sending time (MST) and mean first passage time (MFPT). The obtained results show that the MRT, MST and MFPT increase with the network parameters. We further show that the values of MRT, MST and MFPT are much shorter than the nondelayed counterpart, implying that the efficiency of random walks in delayed trees is much higher.

scholarly journals Mean first-passage time for random walks on the T-graph

2009 ◽  
Vol 11 (10) ◽  
pp. 103043 ◽  
Author(s):  
Zhongzhi Zhang ◽  
Yuan Lin ◽  
Shuigeng Zhou ◽  
Bin Wu ◽  
Jihong Guan
Keyword(s):  
Random Walks ◽  
First Passage Time ◽  
Passage Time ◽  
Mean First Passage Time ◽  
First Passage

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 Mean first-passage time for random walks on undirected networks

2011 ◽  
Vol 84 (4) ◽  
pp. 691-697 ◽  
Author(s):  
Zhongzhi Zhang ◽  
Alafate Julaiti ◽  
Baoyu Hou ◽  
Hongjuan Zhang ◽  
Guanrong Chen
Keyword(s):  
Random Walks ◽  
First Passage Time ◽  
Passage Time ◽  
Mean First Passage Time ◽  
First Passage

MEAN FIRST PASSAGE TIME OF RANDOM WALKS ON THE GENERALIZED PSEUDOFRACTAL WEB

2013 ◽  
Vol 27 (10) ◽  
pp. 1350070 ◽  
Author(s):  
LONG LI ◽  
WEIGANG SUN ◽  
JING CHEN ◽  
GUIXIANG WANG
Keyword(s):  
Random Walks ◽  
First Passage Time ◽  
Passage Time ◽  
Scaling Exponent ◽  
Mean First Passage Time ◽  
Initial State ◽  
First Passage ◽  
Subsequent Step ◽  
Power Law Function ◽  
Exact Scaling

In this paper, we study the scaling for mean first passage time (MFPT) of random walks on the generalized pseudofractal web (GPFW) with a trap, where an initial state is transformed from a triangle to a r-polygon and every existing edge gives birth to finite nodes in the subsequent step. We then obtain an analytical expression and an exact scaling for the MFPT, which shows that the MFPT grows as a power-law function in the large limit of network order. In addition, we determine the exponent of scaling efficiency characterizing the random walks, with the exponent less than 1. The scaling exponent of the MFPT is same for the initial state of the web being a polygon with finite nodes. This method could be applied to other fractal networks.

scholarly journals Mean First Passage Time of Preferential Random Walks on Complex Networks with Applications

2017 ◽  
Vol 2017 ◽  
pp. 1-14
Author(s):  
Zhongtuan Zheng ◽  
Gaoxi Xiao ◽  
Guoqiang Wang ◽  
Guanglin Zhang ◽  
Kaizhong Jiang
Keyword(s):  
Complex Networks ◽  
Random Walks ◽  
First Passage Time ◽  
Network Models ◽  
Passage Time ◽  
Main Role ◽  
Mean First Passage Time ◽  
Eigenvalues And Eigenvectors ◽  
First Passage ◽  
The Mean

This paper investigates, both theoretically and numerically, preferential random walks (PRW) on weighted complex networks. By using two different analytical methods, two exact expressions are derived for the mean first passage time (MFPT) between two nodes. On one hand, the MFPT is got explicitly in terms of the eigenvalues and eigenvectors of a matrix associated with the transition matrix of PRW. On the other hand, the center-product-degree (CPD) is introduced as one measure of node strength and it plays a main role in determining the scaling of the MFPT for the PRW. Comparative studies are also performed on PRW and simple random walks (SRW). Numerical simulations of random walks on paradigmatic network models confirm analytical predictions and deepen discussions in different aspects. The work may provide a comprehensive approach for exploring random walks on complex networks, especially biased random walks, which may also help to better understand and tackle some practical problems such as search and routing on networks.

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