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.

FRACTAL NETWORKS ON SIERPINSKI-TYPE POLYGON

Fractals ◽  
2020 ◽  
Vol 28 (05) ◽  
pp. 2050087
Author(s):  
CHENG ZENG ◽  
YUMEI XUE ◽  
MENG ZHOU
Keyword(s):  
Degree Distribution ◽  
Path Length ◽  
Small World ◽  
Average Path Length ◽  
Clustering Coefficient ◽  
Scale Free ◽  
Evolving Networks ◽  
Power Law Exponent ◽  
Self Similar ◽  
Encoding Method

In this paper, the evolving networks are created from a series of Sierpinski-type polygon by applying the encoding method in fractal and symbolic dynamical system. Based on the self-similar structures of our networks, we study the cumulative degree distribution, the clustering coefficient and the standardized average path length. The power-law exponent of the cumulative degree distribution is deduced to be [Formula: see text] and the average clustering coefficients have a uniform lower bound [Formula: see text]. Moreover, we find the asymptotic formula of the average path length of our proposed networks. These results show the scale-free and the small-world effects of these networks.

Fractal networks on 4m-sided Dürer-type polygon

2021 ◽  
pp. 2150428
Author(s):  
Yuke Huang ◽  
Cheng Zeng ◽  
Hanxiong Zhang ◽  
Yumei Xue
Keyword(s):  
Degree Distribution ◽  
Path Length ◽  
Small World ◽  
Average Path Length ◽  
Clustering Coefficient ◽  
Directed Networks ◽  
Scale Free ◽  
Theoretical Support

Dürer’s pentagon is known to the artist Albrecht Dürer, whose work has produced an effect on modern telecommunication. In this paper, we consider directed networks generated by Dürer-type polygons, which is based on an [Formula: see text]-sided polygon where [Formula: see text] and [Formula: see text]. This object is quite different from what we previously studied when [Formula: see text] is not a multiple of 4. We aim to study some properties of these networks, such as degree distribution, clustering coefficient and average path length. We show that such networks have the scale-free effect, but do not have the small-world effect. It is expected that our results will provide certain theoretical support to further applications in modern telecommunication.

scholarly journals An Approach for Understanding and Promoting Coal Mine Safety by Exploring Coal Mine Risk Network

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-17 ◽  
Author(s):  
Yongliang Deng ◽  
Liangliang Song ◽  
Zhipeng Zhou ◽  
Ping Liu
Keyword(s):  
Coal Mine ◽  
Path Length ◽  
Risk Control ◽  
Small World ◽  
Average Path Length ◽  
Clustering Coefficient ◽  
Mine Safety ◽  
Power Law Distribution ◽  
Complex Network Theory ◽  
Scale Free

Capturing the interrelations among risks is essential to thoroughly understand and promote coal mining safety. From this standpoint, 105 risks and 135 interrelations among risks had been identified from 126 typical accidents, which were also the foundation of constructing coal mine risk network (CMRN). Based on the complex network theory and Pajek, six parameters (i.e., network diameter, network density, average path length, degree, betweenness, and clustering coefficient) were employed to reveal the topological properties of CMRN. As indicated by the results, CMRN possesses scale-free network property because its cumulative degree distribution obeys power-law distribution. This means that CMRN is robust to random hazard and vulnerable to deliberate attack. CMRN is also a small-world network due to its relatively small average path length as well as high clustering coefficient, implying that accident propagation in CMRN is faster than regular network. Furthermore, the effect of risk control is explored. According to the result, it shows that roof collapse, fire, and gas concentration exceeding limit refer to three most valuable targets for risk control among all the risks. This study will help offer recommendations and proposals for making beforehand strategies that can restrain original risks and reduce accidents.

scholarly journals On the Influence of Topological Characteristics on Robustness of Complex Networks

2013 ◽  
Vol 3 (2) ◽  
pp. 89-100 ◽  
Author(s):  
Dharshana Kasthurirathna ◽  
Mahendra Piraveenan ◽  
Gnanakumar Thedchanamoorthy
Keyword(s):  
Path Length ◽  
Small World ◽  
Average Path Length ◽  
Clustering Coefficient ◽  
Small World Networks ◽  
Scale Free ◽  
Rich Club ◽  
Targeted Attacks ◽  
Topological Characteristics ◽  
Topological Robustness

Abstract In this paper, we explore the relationship between the topological characteristics of a complex network and its robustness to sustained targeted attacks. Using synthesised scale-free, small-world and random networks, we look at a number of network measures, including assortativity, modularity, average path length, clustering coefficient, rich club profiles and scale-free exponent (where applicable) of a network, and how each of these influence the robustness of a network under targeted attacks. We use an established robustness coefficient to measure topological robustness, and consider sustained targeted attacks by order of node degree. With respect to scale-free networks, we show that assortativity, modularity and average path length have a positive correlation with network robustness, whereas clustering coefficient has a negative correlation. We did not find any correlation between scale-free exponent and robustness, or rich-club profiles and robustness. The robustness of small-world networks on the other hand, show substantial positive correlations with assortativity, modularity, clustering coefficient and average path length. In comparison, the robustness of Erdos-Renyi random networks did not have any significant correlation with any of the network properties considered. A significant observation is that high clustering decreases topological robustness in scale-free networks, yet it increases topological robustness in small-world networks. Our results highlight the importance of topological characteristics in influencing network robustness, and illustrate design strategies network designers can use to increase the robustness of scale-free and small-world networks under sustained targeted attacks.

A deterministic pseudo-fractal networks with time-delay

2015 ◽  
Vol 29 (22) ◽  
pp. 1550155 ◽  
Author(s):  
Changming Xing ◽  
Lin Yang ◽  
Jun Ma
Keyword(s):  
Time Delay ◽  
Path Length ◽  
Small World ◽  
Average Path Length ◽  
Clustering Coefficient ◽  
The Novel ◽  
Delay Effect ◽  
Scale Free ◽  
Topological Parameters ◽  
Novel Model

In this paper, inspired by the pseudo-fractal networks (PFN) and the delayed pseudo-fractal networks (DPFN), we present a novel delayed pseudo-fractal networks model, denoted by NDPFN. Different from the generation algorithm of those two networks, every edge of the novel model has a time-delay to generate new nodes after producing one node. We derive exactly the main structural properties of the novel networks: degree distribution, clustering coefficient, diameter and average path length. Analytical results show that the novel networks have small-world effect and scale-free topology. Comparing topological parameters of these three networks, we find that the degree exponent of the novel networks is the largest while the clustering coefficient and the average path length are the smallest. It means that this kind of delay could weaken the heterogeneity and the small-world features of the network. Particularly, the delay effect in the NDPFN is contrary to that in the DPFN, which illustrates the variety of delay method could produce different effects on the network structure. These present findings may be helpful for a deeper understanding of the time-delay influence on the network topology.

scholarly journals Using Network Theory to Explore BIM Application Barriers for BIM Sustainable Development in China

2020 ◽  
Vol 12 (8) ◽  
pp. 3190
Author(s):  
Yongliang Deng ◽  
Jinyun Li ◽  
Qiuting Wu ◽  
Shuangshuang Pei ◽  
Na Xu ◽  
...  
Keyword(s):  
Sustainable Development ◽  
Network Theory ◽  
Path Length ◽  
Small World ◽  
Average Path Length ◽  
Clustering Coefficient ◽  
Information Modeling ◽  
Power Law Distribution ◽  
Complex Network Theory ◽  
Scale Free

Building Information Modeling (BIM) technology has promoted the development of the architecture, engineering, and construction (AEC) industry, but has encountered many barriers to its application in China. Therefore, identifying the barriers to BIM application and capturing their interactions are essential in order to control and eliminate the determined barriers. From this standpoint, 23 BIM application barriers were identified through a literature review and expert interviews. Furthermore, the interactions among them were determined based on the Delphi method, which was the foundation for establishing the BIM application barrier network (BABN). Then, the software Pajek was employed to construct the network model and reveal its topological characteristics based on complex network theory, including degree, betweenness, eigenvector, clustering coefficient, network diameter, and average path length. As indicated by the results, BABN possesses scale-free network property because its cumulative degree distribution obeys power–law distribution. BABN is also a small-world network, due to its relatively high clustering coefficient as well as small average path length, implying that barrier propagation in BABN is fast. In addition, the results are discussed and recommendations are proposed. This research will help BIM stakeholders to develop coping strategies to control and eliminate BIM application barriers for the sake of driving BIM sustainable development.

scholarly journals Co-Movement in Stock Markets Based on Directed Complex Network

2016 ◽  
Vol 8 (2) ◽  
pp. 179
Author(s):  
Zhen Du ◽  
Pujiang Chen ◽  
Na Luo ◽  
Yingjie Tang
Keyword(s):  
Complex Network ◽  
Power Law ◽  
Degree Distribution ◽  
Path Length ◽  
Stock Exchange ◽  
Small World ◽  
Clustering Coefficient ◽  
Power Law Distribution ◽  
Scale Free ◽  
Set Up

<p>In this paper, directed complex network is applied to the study of A shares in SSE (Shanghai Stock Exchange). In order to discuss the intrinsic attributes and regularities in stock market, we set up a directed complex network, selecting 450 stocks as nodes between 2012 and 2014 and stock yield correlation connected as edges. By discussing out-degree and in-degree distribution, we find essential nodes in stock network, which represent the leading stock,. Moreover, we analyze directed average path length and clustering coefficient in the condition of different threshold, which shows that the network doesn’t have a small- world effect. Furthermore, we see that when threshold is between 0.08 and 0.15, the network follows the power-law distribution and behaves scale-free.</p>

scholarly journals A Complex Network Approach for Quantitative Characterization and Robustness Analysis of Sandstone Pore Network Structure

Geofluids ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Yuhao Hu ◽  
Guannan Liu ◽  
Feng Gao ◽  
Fengtian Yue ◽  
Tao Gao
Keyword(s):  
Pore Structure ◽  
Complex Network ◽  
Degree Distribution ◽  
Path Length ◽  
Robustness Analysis ◽  
Pore Network ◽  
Average Path Length ◽  
Clustering Coefficient ◽  
Random Disturbance ◽  
Pagerank Algorithm

The rational characterization and quantitative analysis of the complex internal pore structure of rock is the foundation to solve many underground engineering problems. In this paper, CT imaging technology is used to directly characterize the three-dimensional pore network topology of sandstone with different porosity. Then, in view of the problem, which is difficult to quantify the detailed topological structure of the sandstone pore networks in the previous study, the new complex network theory is used to characterize the pore structure. PageRank algorithm is based on the number of connections between targets as a measure index to rank the targets, so the network degree distribution, average path length, clustering coefficient, and robustness based on PageRank algorithm and permeability-related topological parameters are studied. The research shows that the degree distribution of sandstone pore network satisfies power law distribution, and it can be characterized by scale-free network model. The permeability of rock is inversely proportional to the average path length of sandstone network. The sandstone pore network has strong robustness to random disturbance, while a small number of pores with special topological properties play a key role in the macroscopic permeability of sandstone. This study attempts to provide a new perspective of quantifying the microstructure of the pore network of sandstone and revealing the microscopic structure mechanism of macroscopic permeability of pore rocks.

Research on the Structure of Peer-to-Peer Overlay Based on the Complex Network Theory

2012 ◽  
Vol 263-266 ◽  
pp. 1096-1099
Author(s):  
Zhi Yong Jiang
Keyword(s):  
Complex Network ◽  
Network Theory ◽  
Degree Distribution ◽  
Path Length ◽  
Small World ◽  
Peer To Peer ◽  
Clustering Coefficient ◽  
Power Law Distribution ◽  
Complex Network Theory ◽  
The Mean

Relationship between nodes in peer-to-peer overlay, currently becomes a hot topic in the field of complex network. In this paper a model of peer-to-peer overlay was purposed. And then the paper focused on figuring out the mean-shortest path length (MSPL), clustering coefficient (CC) and the degree of every node which allowed us to discover the degree distribution. The results show that the degree distribution function follows approximately power law distribution and the network possesses notable clustering and small-world properties.

scholarly journals Statistical Analysis of Weighted Networks

2008 ◽  
Vol 2008 ◽  
pp. 1-16 ◽  
Author(s):  
I. E. Antoniou ◽  
E. T. Tsompa
Keyword(s):  
Degree Distribution ◽  
Path Length ◽  
Average Path Length ◽  
Clustering Coefficient ◽  
Weighted Graphs ◽  
Statistical Characterization ◽  
Weighted Networks ◽  
Weighted Clustering ◽  
Statistical Regularities

The purpose of this paper is to assess the statistical characterization of weighted networks in terms of the generalization of the relevant parameters, namely, average path length, degree distribution, and clustering coefficient. Although the degree distribution and the average path length admit straightforward generalizations, for the clustering coefficient several different definitions have been proposed in the literature. We examined the different definitions and identified the similarities and differences between them. In order to elucidate the significance of different definitions of the weighted clustering coefficient, we studied their dependence on the weights of the connections. For this purpose, we introduce the relative perturbation norm of the weights as an index to assess the weight distribution. This study revealed new interesting statistical regularities in terms of the relative perturbation norm useful for the statistical characterization of weighted graphs.

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