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.

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.

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.

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.

ANALISIS PERINGKAT TOP BRAND OJEK ONLINE MENGGUNAKAN JEJARING SOSIAL PERCAKAPAN TWITTER

2019 ◽  
Vol 24 (2) ◽  
pp. 88-104
Author(s):  
Ilham Aminudin ◽  
Dyah Anggraini
Keyword(s):  
Social Media ◽  
Social Network ◽  
Social Network Analysis ◽  
Network Analysis ◽  
Path Length ◽  
Average Path Length ◽  
Average Degree ◽  
Clustering Coefficient ◽  
R Programming

Banyak bisnis mulai muncul dengan melibatkan pengembangan teknologi internet. Salah satunya adalah bisnis di aplikasi berbasis penyedia layanan di bidang moda transportasi berbasis online yang ternyata dapat memberikan solusi dan menjawab berbagai kekhawatiran publik tentang layanan transportasi umum. Kemacetan lalu lintas di kota-kota besar dan ketegangan publik dengan keamanan transportasi umum diselesaikan dengan adanya aplikasi transportasi online seperti Grab dan Gojek yang memberikan kemudahan dan kenyamanan bagi penggunanya Penelitian ini dilakukan untuk menganalisa keaktifan percakapan brand jasa transportasi online di jejaring sosial Twitter berdasarkan properti jaringan. Penelitian dilakukan dengan dengan mengambil data dari percakapan pengguna di social media Twitter dengan cara crawling menggunakan Bahasa pemrograman R programming dan software R Studio dan pembuatan model jaringan dengan software Gephy. Setelah itu data dianalisis menggunakan metode social network analysis yang terdiri berdasarkan properti jaringan yaitu size, density, modularity, diameter, average degree, average path length, dan clustering coefficient dan nantinya hasil analisis akan dibandingkan dari setiap properti jaringan kedua brand jasa transportasi Online dan ditentukan strategi dalam meningkatkan dan mempertahankan keaktifan serta tingkat kehadiran brand jasa transportasi online, Grab dan Gojek.

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 Improvising Climate Smart Agricultural Practices Using Design Thinking by Undergraduate Student of Agriculture under Central Agricultural University, Imphal: A Case of Social Network Analysis

2020 ◽  
pp. 1-7
Author(s):  
Elly Kirwa ◽  
Rajkumar Josmee Singh
Keyword(s):  
Social Network ◽  
Social Network Analysis ◽  
Network Analysis ◽  
Path Length ◽  
Design Thinking ◽  
Agricultural Practices ◽  
Average Path Length ◽  
Average Degree ◽  
Clustering Coefficient ◽  
Collaborative Problem Solving

Aims: This study uses Social Network Analysis (SNA) to investigate the social interaction that shape student collaborative problem solving activity when undergoing Design Thinking (DT) to improvise Climate Smart Agricultural Practices (CSAPs). Place and Duration of Study: The study was conducted at the three Colleges of Agriculture (CoAs) under Central Agricultural University, Imphal at Manipur viz., the (1) CoA, Imphal at Manipur, (2) CoA, Pasighat at Arunachal Pradesh; and (3) CoA, Kyrdemkulai at Meghalaya. The study was conducted between November 2019 and February 2020. Methodology: A sample of 28 respondents who constituted fifty percent of population of final year B.Sc. (Agriculture) students was selected through simple random sampling without replacement from the three CoAs. SNA of respondent-students was analyzed using Gephi 0.9.2 software with the following attributes to understand the student community viz., average degree, modularity, average clustering coefficient and average path length. Results: The network for CoA, Imphal displayed the following characteristic as ‘Average Degree’ of 5.69, ‘Modularity’ of 0.149, ‘Average Clustering Coefficient’ of 0.468 and ‘Average Path Length’ of 1.57. In case of CoA, Pasighat, the attributes of social network were as ‘Average Degree’ of 3.63, ‘Modularity’ of 0.513, ‘Average Clustering Coefficient’ of 0.099 and ‘Average Path Length’ of 1.52j; while for the case of CoA, Kyrdemkulai, it had ‘Average Degree’ of 3.86, ‘Modularity’ of 0.024, ‘Average Clustering Coefficient’ of 0.650 and ‘Average Path Length’ of 1.360. Conclusion: For meaningful improvising of CSAPs using DT, the efficiency of social network was more functional on smaller collaborative working groups as information flow was found to be high in small groups leading to development of more ideas on DT.

AN IDEAL DISASSORTATIVE NETWORK AND SYNCHRONIZATION

2006 ◽  
Vol 16 (10) ◽  
pp. 3093-3102 ◽  
Author(s):  
DONG CHENGDONG ◽  
LIU ZENGRONG
Keyword(s):  
Dynamic System ◽  
Complex Network ◽  
Network Topology ◽  
Path Length ◽  
Average Path Length ◽  
Clustering Coefficient ◽  
Novel Complex ◽  
The Impact

This paper proposes a novel complex network with disassortative property based on multicenter networks. The average path length and clustering coefficient of the network are calculated, and the impact on the network topology is investigated. A simple dynamic system established on the proposed network is used to analyze how the disassortative property of the network affects synchronization.

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.

Complexity Analysis of Public Transportation Network in Zhangjiagang City Using Complex Network Theory

2012 ◽  
Vol 546-547 ◽  
pp. 1211-1216
Author(s):  
Yong Wang ◽  
Ta Zhou
Keyword(s):  
Complex Network ◽  
Public Transportation ◽  
Path Length ◽  
Complexity Analysis ◽  
Transportation Network ◽  
Average Path Length ◽  
Clustering Coefficient ◽  
Power Law Distribution ◽  
Complex Network Theory ◽  
Public Transportation Network

Public transportation network has been proven that it can be simulated as a complex network. In this paper, a bus transport system of Zhangjiagang city is considered. Network degree distribution, average path length, and clustering coefficient are utilized as criteria to analyze as the complexity of the network. Experimental results show that the network which is in line with power-law distribution has a smaller average path length and a large clustering coefficient. It also indicates that, the networks of Zhangjiagang public bus system are not a small-world network with scale-free property.

Sign in / Sign up

Export Citation Format

Share Document