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.

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.

ASYMPTOTIC FORMULA OF AVERAGE DISTANCES ON FRACTAL NETWORKS MODELED BY SIERPINSKI TETRAHEDRON

Fractals ◽  
2019 ◽  
Vol 27 (07) ◽  
pp. 1950120
Author(s):  
JUAN DENG ◽  
QIN WANG
Keyword(s):  
Asymptotic Formula ◽  
Geodesic Distance ◽  
Average Distance ◽  
The Self ◽  
Renewal Theorem ◽  
Self Similarity ◽  
Evolving Networks

This paper concerns the average distances of evolving networks modeled by Sierpinski tetrahedron. We express the limit of average distances on reorganized networks as an integral of geodesic distance on Sierpinski tetrahedron. Based on the self-similarity and renewal theorem, we obtain the asymptotic formula on the average distance of our evolving networks.

ECCENTRIC DISTANCE SUM OF SIERPIŃSKI GASKET AND SIERPIŃSKI NETWORK

Fractals ◽  
2019 ◽  
Vol 27 (02) ◽  
pp. 1950016 ◽  
Author(s):  
JIN CHEN ◽  
LONG HE ◽  
QIN WANG
Keyword(s):  
Asymptotic Formula ◽  
Complex Networks ◽  
Sierpinski Gasket ◽  
The Self ◽  
Self Similarity ◽  
Sierpiński Gasket ◽  
Similar Measure ◽  
Self Similar ◽  
Eccentric Distance

The eccentric distance sum is concerned with complex networks. To obtain the asymptotic formula of eccentric distance sum on growing Sierpiński networks, we study some nonlinear integral in terms of self-similar measure on the Sierpiński gasket and use the self-similarity of distance and measure to obtain the exact value of this integral.

Existence of phase transition of percolation on Sierpiński carpet lattices

2002 ◽  
Vol 39 (01) ◽  
pp. 1-10 ◽  
Author(s):  
Masato Shinoda
Keyword(s):  
Phase Transition ◽  
Bond Percolation ◽  
Sufficient Condition ◽  
Self Similarity ◽  
Sierpinski Carpet ◽  
Sierpiński Carpet ◽  
Sierpinski Carpets

We study Bernoulli bond percolation on Sierpiński carpet lattices, which is a class of graphs corresponding to generalized Sierpiński carpets. In this paper we give a sufficient condition for the existence of a phase transition on the lattices. The proof is suitable for graphs which have self-similarity. We also discuss the relation between the existence of a phase transition and the isoperimetric dimension.

Existence of phase transition of percolation on Sierpiński carpet lattices

2002 ◽  
Vol 39 (1) ◽  
pp. 1-10 ◽  
Author(s):  
Masato Shinoda
Keyword(s):  
Phase Transition ◽  
Bond Percolation ◽  
Sufficient Condition ◽  
Self Similarity ◽  
Sierpinski Carpet ◽  
Sierpiński Carpet ◽  
Sierpinski Carpets

We study Bernoulli bond percolation on Sierpiński carpet lattices, which is a class of graphs corresponding to generalized Sierpiński carpets. In this paper we give a sufficient condition for the existence of a phase transition on the lattices. The proof is suitable for graphs which have self-similarity. We also discuss the relation between the existence of a phase transition and the isoperimetric dimension.

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 VAF FRACTAL NETWORKS

Fractals ◽  
2016 ◽  
Vol 24 (03) ◽  
pp. 1650033 ◽  
Author(s):  
HAO LI ◽  
JIAN HUANG ◽  
ANBO LE ◽  
QIN WANG ◽  
LIFENG XI
Keyword(s):  
Small World ◽  
The Self ◽  
Sierpinski Carpet ◽  
Scale Free ◽  
Evolving Networks ◽  
Self Similar ◽  
Sierpiński Carpet

In this paper, we investigate the vertical-affiliation-free (VAF) evolving networks whose node set is the basic squares in the process of generating the Sierpinski carpet and edge exists between any two nodes if and only if the corresponding basic squares intersect just on their boundary. Although the VAF networks gets rid of the hierarchial organizations produced naturally by the self-similar structures of fractals, we still prove that they are scale-free and have the small-world effect.

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