Average path length and degree distribution of networks generated by random sequence

2021 ◽  
pp. 2150347
Author(s):  
Daohua Wang ◽  
Yumei Xue
Keyword(s):  
Degree Distribution ◽  
Path Length ◽  
Random Sequence ◽  
Average Path Length ◽  
Hierarchical Network ◽  
Self Similarity ◽  
Sequence Structure ◽  
Total Path Length ◽  
Iterative Calculation ◽  
Encoding Method

Considering that many real networks do not have strict self-similarity property, compared with deterministic evolutionary fractal networks, networks with random sequence structure may be more in accordance with the properties of real networks. In this paper, we generate a hierarchical network by a random sequence based on BRV model. Using the encoding method, we present a way to judge whether two nodes are neighbors and calculate the total path length of the network. We get the degree distribution and limit formula of the average path length of a class of networks, which are obtained by analytical method and iterative calculation.

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.

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.

ASYMPTOTIC FORMULA ON AVERAGE PATH LENGTH OF A SPECIAL NETWORK BASED ON SIERPINSKI CARPET

Fractals ◽  
2018 ◽  
Vol 26 (03) ◽  
pp. 1850039 ◽  
Author(s):  
YUMEI XUE ◽  
DONGXUE ZHOU
Keyword(s):  
Asymptotic Formula ◽  
Path Length ◽  
Average Path Length ◽  
The Self ◽  
Renewal Theorem ◽  
Self Similarity ◽  
Sierpinski Carpet ◽  
Sierpiński Carpet

In this paper, we construct a special network based on the construction of the Sierpinski carpet. Using the self-similarity and renewal theorem, we obtain the asymptotic formula for the average path length of our evolving network.

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.

ENHANCING NETWORK PERFORMANCE BY EDGE ADDITION

2011 ◽  
Vol 22 (11) ◽  
pp. 1211-1226 ◽  
Author(s):  
ZHONGYUAN JIANG ◽  
MANGUI LIANG ◽  
DONGCHAO GUO
Keyword(s):  
Network Topology ◽  
Degree Distribution ◽  
Path Length ◽  
Network Performance ◽  
Service Providers ◽  
Network Planning ◽  
Transmission Efficiency ◽  
Average Path Length ◽  
Edge Addition

Transmission efficiency and robustness are two important properties of various networks and a number of optimization strategies have been proposed recently. We propose a scheme to enhance the network performance by adding a small fraction of links (or edges) to the currently existing network topology, and we present four edge addition strategies for adding edges efficiently. We aim at minimizing the maximum node betweenness of any node in the network to improve its transmission efficiency, and a number of experiments on both Barabási–Albert (BA) and Erdös–Rényi (ER) networks have confirmed the effectiveness of our four edge addition strategies. Also, we evaluate the effect of some other measure metrics such as average path length, average betweenness, robustness, and degree distribution. Our work is very valuable and helpful for service providers to optimize their network performance by adding a small fraction of edges or to make good network planning on the existing network topology incrementally.

The Influence of the Randomness on Average Path Length

2011 ◽  
Vol 219-220 ◽  
pp. 791-794
Author(s):  
Xin Chun Wang ◽  
Yu Bo Jiang
Keyword(s):  
Degree Distribution ◽  
Path Length ◽  
Network Formation ◽  
Preferential Attachment ◽  
Mean Field ◽  
Average Path Length ◽  
Current Structure ◽  
Field Approach ◽  
Evolving Model

The evolving rule includes random attachment and preferential attachment and so on. It forms different network formation by different attachment. In order to analyze this character, this paper put forward an evolving model. It contains two kinds of attachment: some are connected at random, and others are connected based on current structure of the network, and in the model the deleted links are considered. The degree distribution and degree exponent are obtained by mean-field approach. Then it discusses the influence of randomness on the average path length.

A Kind of Deterministic Small-World Network Derived from Polygonal Nesting

2014 ◽  
Vol 614 ◽  
pp. 543-549
Author(s):  
Hui Li ◽  
Liang Yuan
Keyword(s):  
Long Range ◽  
Outer Layer ◽  
Degree Distribution ◽  
Path Length ◽  
Small Diameter ◽  
Small World ◽  
Average Path Length ◽  
Node Degree ◽  
Small World Network ◽  
Central Node

A kind of deterministic small-world network is constructed based on polygonal nesting with discrete degree distribution. By adding contrapuntal edges and alternate-position edges between adjacent nests, the intra-nest edges and the long-range edges from the central node to certain outer layer nodes, the proposed polygonal nesting small-world (PNSW) networks have the property of large clustering coefficients. Also these kinds of PNSW networks have small diameter, average node degree and average path length, whose moments ofkorder are given.

THE SCALE-FREE AND SMALL-WORLD PROPERTIES OF COMPLEX NETWORKS ON SIERPINSKI-TYPE HEXAGON

Fractals ◽  
2020 ◽  
Vol 28 (03) ◽  
pp. 2050054
Author(s):  
KUN CHENG ◽  
DIRONG CHEN ◽  
YUMEI XUE ◽  
QIAN ZHANG
Keyword(s):  
Power Law ◽  
Path Length ◽  
Small World ◽  
The Self ◽  
Renewal Theorem ◽  
Self Similarity ◽  
Scale Free ◽  
Power Law Exponent ◽  
Self Similar ◽  
Encoding Method

In this paper, a network is generated from a Sierpinski-type hexagon by applying the encoding method in fractal. The criterion of neighbor is established to quantify the relationships among the nodes in the network. Based on the self-similar structures, we verify the scale-free and small-world effects. The power-law exponent on degree distribution is derived to be [Formula: see text] and the average clustering coefficients are shown to be larger than [Formula: see text]. Moreover, we give the bounds of the average path length of our proposed network from the renewal theorem and self-similarity.

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.

Sign in / Sign up

Export Citation Format

Share Document