Volatilities analysis of first-passage time and first-return time on a small-world scale-free network

We study the critical properties of the Bak–Sneppen coevolution model on scale-free networks by Monte Carlo method. We report the distribution of the avalanche size and fractal activity through the branching process. We observe that the critical fitness fc(N) depends on the number of the node such as fc(N) ~ 1/ log (N) for both the scale-free network and the directed scale-free network. Near the critical fitness many physical quantities show power-law behaviors. The probability distribution P(s) of the avalanche size at the critical fitness shows a power-law like P(s) ~ s-τ with τ = 1.53(5) regardless of the scale-free network and the directed scale free network. The probability distribution Pf(t) of the first return time also shows a power-law such as Pf(t) ~ t-τf. The critical exponents τf are equivalent for both the scale-free network and the directed scale-free network. We obtain the critical exponents as τf = 1.776(5) at the scalinge regime. The directionality of the network does not change the universality on the network.

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EXACT CALCULATIONS OF FIRST-PASSAGE QUANTITIES ON A CLASS OF WEIGHTED TREE-LIKE FRACTAL NETWORKS

Fractals ◽

10.1142/s0218348x20500425 ◽

2020 ◽

Vol 28 (03) ◽

pp. 2050042

Author(s):

BO WU ◽

ZHIZHUO ZHANG ◽

WEIYI SU

Keyword(s):

First Passage Time ◽

Probability Generating Function ◽

Return Time ◽

Passage Time ◽

Weighted Tree ◽

First Passage ◽

Second Moments ◽

Analytic Expressions ◽

Exact Calculations ◽

First Return Time

This paper concerns the weight-dependent random walk on a class of weighted tree-like fractal networks controlled by a positive integer parameter [Formula: see text] [Formula: see text] and the weight factor [Formula: see text] [Formula: see text]. We study the first return time (FRT) of a given hub and the global first-passage time (GFPT) to a given hub on the networks. By the probability generating function method, we derive the analytic expressions of the first and second moments of FRT and GFPT. In order to evaluate the fluctuation of FRT and GFPT, we further calculate the variance and the reduced moments of FRT and GFPT.

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Mean First-Passage Time on Scale-Free Networks Based on Rectangle Operation

Frontiers in Physics ◽

10.3389/fphy.2021.675833 ◽

2021 ◽

Vol 9 ◽

Author(s):

Xiaomin Wang ◽

Jing Su ◽

Fei Ma ◽

Bing Yao

Keyword(s):

Statistical Physics ◽

First Passage Time ◽

Passage Time ◽

Theory And Practice ◽

Clustering Coefficient ◽

Mean First Passage Time ◽

First Passage ◽

Kirchhoff Index ◽

Scale Free ◽

Free Network

The mean first-passage time of random walks on a network has been extensively applied in the theory and practice of statistical physics, and its application effects depend on the behavior of first-passage time. Here, we firstly define a graphic operation, namely, rectangle operation, for generating a scale-free network. In this paper, we study the topological structures of our network obtained from the rectangle operation, including degree distribution, clustering coefficient, and diameter. And then, we also consider the characteristic quantities related to the network, including Kirchhoff index and mean first-passage time, where these characteristic quantities can not only be used to evaluate the properties of our network, but also have remarkable applications in science and engineering.

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Moments of global first passage time and first return time on tree-like fractals

Journal of Statistical Mechanics Theory and Experiment ◽

10.1088/1742-5468/aadb04 ◽

2018 ◽

Vol 2018 (9) ◽

pp. 093205 ◽

Cited By ~ 2

Author(s):

Junhao Peng ◽

Renxiang Shao ◽

Lin Chen ◽

H Eugene Stanley

Keyword(s):

First Passage Time ◽

Return Time ◽

Passage Time ◽

First Passage ◽

First Return Time

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Analysis on Invulnerability of Wireless Sensor Network towards Cascading Failures Based on Coupled Map Lattice

Complexity ◽

10.1155/2018/6386324 ◽

2018 ◽

Vol 2018 ◽

pp. 1-14 ◽

Cited By ~ 4

Author(s):

Xiuwen Fu ◽

Yongsheng Yang ◽

Haiqing Yao

Keyword(s):

Random Network ◽

Small World ◽

Coupled Map Lattice ◽

Wireless Sensor ◽

Cascading Failures ◽

Scale Free Network ◽

Scale Free ◽

Network Topologies ◽

Free Network ◽

Entire Network

Previous research of wireless sensor networks (WSNs) invulnerability mainly focuses on the static topology, while ignoring the cascading process of the network caused by the dynamic changes of load. Therefore, given the realistic features of WSNs, in this paper we research the invulnerability of WSNs with respect to cascading failures based on the coupled map lattice (CML). The invulnerability and the cascading process of four types of network topologies (i.e., random network, small-world network, homogenous scale-free network, and heterogeneous scale-free network) under various attack schemes (i.e., random attack, max-degree attack, and max-status attack) are investigated, respectively. The simulation results demonstrate that the rise of interference R and coupling coefficient ε will increase the risks of cascading failures. Cascading threshold values Rc and εc exist, where cascading failures will spread to the entire network when R>Rc or ε>εc. When facing a random attack or max-status attack, the network with higher heterogeneity tends to have a stronger invulnerability towards cascading failures. Conversely, when facing a max-degree attack, the network with higher uniformity tends to have a better performance. Besides that, we have also proved that the spreading speed of cascading failures is inversely proportional to the average path length of the network and the increase of average degree k can improve the network invulnerability.

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EXPRESS PASSENGER TRANSPORT SYSTEM AS A SCALE-FREE NETWORK

Modern Physics Letters B ◽

10.1142/s0217984906011803 ◽

2006 ◽

Vol 20 (27) ◽

pp. 1755-1761 ◽

Cited By ~ 8

Author(s):

BAIBAI FU ◽

ZIYOU GAO ◽

FASHENG LIU ◽

XIANJUAN KONG

Keyword(s):

Transport System ◽

Network Topology ◽

Small World ◽

Power Exponent ◽

Scale Free Network ◽

Passenger Transport ◽

Scale Free ◽

Scale Free Networks ◽

Highway Network ◽

Free Network

An express highway itself is not a scale-free network, while the Express Passenger Transport System (EPTS) on the express highway network has the properties of a small-world and scale-free network. Data analysis based on the observation of the EPTS in Shandong province, China, shows that the EPTS has the properties of scale-free networks and the power exponent λ of the distribution is equal to about 2.1. Based on the scale-free network topology structure of the EPTS network, the construction of the EPTS network will be more efficient and robust.

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

Modern Physics Letters B ◽

10.1142/s0217984919501793 ◽

2019 ◽

Vol 33 (16) ◽

pp. 1950179 ◽

Cited By ~ 3

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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The Evolution of Price Competition Game on Complex Networks

Complexity ◽

10.1155/2018/9649863 ◽

2018 ◽

Vol 2018 ◽

pp. 1-13

Author(s):

Feng Jie Xie ◽

Jing Shi

Keyword(s):

Complex Networks ◽

Real World ◽

Price Competition ◽

Small World ◽

Square Lattice ◽

Small World Network ◽

Scale Free Network ◽

The Real ◽

Scale Free ◽

Free Network

The well-known “Bertrand paradox” describes a price competition game in which two competing firms reach an outcome where both charge a price equal to the marginal cost. The fact that the Bertrand paradox often goes against empirical evidences has intrigued many researchers. In this work, we study the game from a new theoretical perspective—an evolutionary game on complex networks. Three classic network models, square lattice, WS small-world network, and BA scale-free network, are used to describe the competitive relations among the firms which are bounded rational. The analysis result shows that full price keeping is one of the evolutionary equilibriums in a well-mixed interaction situation. Detailed experiment results indicate that the price-keeping phenomenon emerges in a square lattice, small-world network and scale-free network much more frequently than in a complete network which represents the well-mixed interaction situation. While the square lattice has little advantage in achieving full price keeping, the small-world network and the scale-free network exhibit a stronger capability in full price keeping than the complete network. This means that a complex competitive relation is a crucial factor for maintaining the price in the real world. Moreover, competition scale, original price, degree of cutting price, and demand sensitivity to price show a significant influence on price evolution on a complex network. The payoff scheme, which describes how each firm’s payoff is calculated in each round game, only influences the price evolution on the scale-free network. These results provide new and important insights for understanding price competition in the real world.

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Getting scale-free network from a small world network without growth

2012 IEEE Fifth International Conference on Advanced Computational Intelligence (ICACI) ◽

10.1109/icaci.2012.6463112 ◽

2012 ◽

Author(s):

Guangping Chen ◽

Jiabo Hao ◽

Zhiyuan Zhang ◽

Yu Tang

Keyword(s):

Small World ◽

Small World Network ◽

Scale Free Network ◽

Scale Free ◽

Free Network

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Evolution of Scale-Free Wireless Sensor Networks with Feature of Small-World Networks

Complexity ◽

10.1155/2017/2516742 ◽

2017 ◽

Vol 2017 ◽

pp. 1-15 ◽

Cited By ~ 7

Author(s):

Ying Duan ◽

Xiuwen Fu ◽

Wenfeng Li ◽

Yu Zhang ◽

Giancarlo Fortino

Keyword(s):

Wireless Sensor Networks ◽

Sensor Networks ◽

Small World ◽

Wireless Sensor ◽

Small World Network ◽

Scale Free Network ◽

Theoretical Derivation ◽

Scale Free ◽

Cluster Heads ◽

Free Network

Scale-free network and small-world network are the most impacting discoveries in the complex networks theories and have already been successfully proved to be highly effective in improving topology structures of wireless sensor networks. However, currently both theories are not jointly applied to have further improvements in the generation of WSN topologies. Therefore, this paper proposes a cluster-structured evolution model of WSNs considering the characteristics of both networks. With introduction of energy sensitivity and maximum limitation of degrees that a cluster head could have, the performance of our model can be ensured. In order to give an overall assessment of lifting effects of shortcuts, four placement schemes of shortcuts are analyzed. The characteristics of small-world network and scale-free network of our model are proved via theoretical derivation and simulations. Besides, we find that, by introducing shortcuts into scale-free wireless sensor network, the performance of the network can be improved concerning energy-saving and invulnerability, and we discover that the schemes constructing shortcuts between cluster heads and the sink node have better promoted effects than the scheme building shortcuts between pairs of cluster heads, and the schemes based on the preferential principle are superior to the schemes based on the random principle.

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