The Property of Hierarchical Structure in Manufacturing

2013 ◽  
Vol 748 ◽  
pp. 1188-1193
Author(s):  
Ying Xin Zhang ◽  
Chao Chen ◽  
Jian Mai Shi
Keyword(s):  
Complex Systems ◽  
Network Model ◽  
Hierarchical Structure ◽  
Real Life ◽  
Small World ◽  
Hierarchical Network ◽  
Hierarchical Networks ◽  
Scale Free ◽  
The Hierarchical Structure ◽  
Simulation Results

Hierarchical structure is one of the most ubiquitous structures in various networked complex systems. In order to investigate the properties of the hierarchical structure, a deterministic hierarchical network model is first proposed. The statistical properties of the constructed networks are also discussed. The simulation results prove that the artificial networks simultaneously possess the small-world and scale-free properties well. This may be useful in furthering study of the topology properties of the hierarchical networks in real life.

scholarly journals Afrikaans as a complex network: The word co-occurrence network in André P. Brink’s Donkermaan in Afrikaans, Dutch and English

2016 ◽  
Vol 35 (1) ◽  
Author(s):  
Burgert A. Senekal ◽  
Cornelia Geldenhuys
Keyword(s):  
Complex Systems ◽  
Network Model ◽  
Network Structure ◽  
Random Network ◽  
Small World ◽  
Distribution Patterns ◽  
Small World Networks ◽  
Scale Free ◽  
Free Network ◽  
Link Distribution

Language has already been approached as a system since De Saussure, and recently the theory of complex systems has been applied within Linguistics as well. Complex systems, however, can also be modelled as complex networks, and a variety of studies investigating the network structure of language have already been undertaken worldwide. The current study follows in the footsteps of overseas studies and investigates the network structure of Afrikaans by analysing a word co-occurrence network compiled from André P. Brink’s novel Donkermaan. Link distribution patterns and the small-world phenomenon are investigated and then compared to the English and Dutch translations of this novel. The current study represents the first network study of Afrikaans. Firstly, the random network model of Erdös and Rényi and the scale-free network model by Barabási and Albert are used to indicate that the link distribution patterns in a word co-occurrence network of Afrikaans are better described according to the network model of Barabási and Albert than by that of Erdös and Rényi. Furthermore, the method proposed by Humphreys and Gurney to define smallworldedness (S) was used to quantify this phenomenon for the Afrikaans, as well as English and Dutch versions of the text. With 522 ≤ S ≤ 797, it is indicated that Afrikaans, English and Dutch are all clearly small-world networks. Suggestions are also made for further research.

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.

The Research of Complex Network on Archives Blog

2011 ◽  
Vol 181-182 ◽  
pp. 14-18
Author(s):  
Yi He
Keyword(s):  
Information Sharing ◽  
Complex Network ◽  
Network Model ◽  
Degree Distribution ◽  
Small World ◽  
Scale Free ◽  
Set Up

At the background of archives blog on Internet, this paper constructs a directed complex network model, and analyzes the network characters such as degree distribution. To verify its efficiency, we collect blogs’ information and set up a complex network..From the analysis result of the simulation and demonstration network, we know that they have the same characters, which show that, the virtual society network has small-world effect and scale-free character compared with real society network. The results indicate that the establishment of archives blog is favor to spread rapidly archives information, improve information sharing efficiency and promote the development of archives technology.

scholarly journals Studies on the Decrease Mechanisms of Typical Complex Networks

2021 ◽  
Author(s):  
Yuhu Qiu ◽  
Tianyang Lyu ◽  
Xizhe Zhang ◽  
Ruozhou Wang
Keyword(s):  
Average Length ◽  
Shortest Paths ◽  
Real Life ◽  
Network Models ◽  
Small World ◽  
Clustering Coefficient ◽  
Network Growth ◽  
Scale Free ◽  
Complex Network Models ◽  
High Degree

Network decrease caused by the removal of nodes is an important evolution process that is paralleled with network growth. However, many complex network models usually lacked a sound decrease mechanism. Thus, they failed to capture how to cope with decreases in real life. The paper proposed decrease mechanisms for three typical types of networks, including the ER networks, the WS small-world networks and the BA scale-free networks. The proposed mechanisms maintained their key features in continuous and independent decrease processes, such as the random connections of ER networks, the long-range connections based on nearest-coupled network of WS networks and the tendency connections and the scale-free feature of BA networks. Experimental results showed that these mechanisms also maintained other topology characteristics including the degree distribution, clustering coefficient, average length of shortest-paths and diameter during decreases. Our studies also showed that it was quite difficult to find an efficient decrease mechanism for BA networks to withstand the continuous attacks at the high-degree nodes, because of the unequal status of nodes.

Complex Systems in a Nutshell

2020 ◽  
pp. 19-32
Author(s):  
Megan S. Patterson ◽  
Michael K. Lemke ◽  
Jordan Nelon
Keyword(s):  
Complex Systems ◽  
Path Length ◽  
Path Dependence ◽  
Small World ◽  
Cardiometabolic Disease ◽  
Small World Networks ◽  
Stable States ◽  
Scale Free ◽  
Critical Transitions ◽  
Random Scale

This chapter provides an overview of the key foundational concepts and principles of the study of complex systems. First, a definition for system is provided, and the distinctions between complicated and complex systems are demarcated, as are detail, disorganized, organized, and dynamic types of complexity. Common properties across complex systems are defined and described, including stable states and steady states, path dependence, resilience, critical transitions and tipping points, early warning signals, feedback loops, and nonlinearity. This chapter also delves into how complex issues often consist of networks, with random, scale-free, and small world networks defined and network concepts such as degrees, path length, and heterogeneity defined. The concept of emergence is also emphasized, as well as related principles such as adaptation and self-organization. Cardiometabolic disease (and associated comorbidities) is used in this chapter as a thematic population health example.

scholarly journals A Note on a New General Family of Deterministic Hierarchical Networks

2019 ◽  
Vol 19 (02) ◽  
pp. 1950005
Author(s):  
C. DALFÓ ◽  
M. A. FIOL
Keyword(s):  
Real Life ◽  
Small Diameter ◽  
Stochastic Methods ◽  
Local Algorithm ◽  
Hierarchical Networks ◽  
Binomial Tree ◽  
Scale Free ◽  
Local Clustering ◽  
Specific Rule

It is known that many networks modeling real-life complex systems are small-word (large local clustering and small diameter) and scale-free (power law of the degree distribution), and very often they are also hierarchical. Although most of the models are based on stochastic methods, some deterministic constructions have been recently proposed, because this allows a better computation of their properties. Here a new deterministic family of hierarchical networks is presented, which generalizes most of the previous proposals, such as the so-called binomial tree. The obtained graphs can be seen as graphs on alphabets (where vertices are labeled with words of a given alphabet, and the edges are defined by a specific rule relating different words). This allows us the characterization of their main distance-related parameters, such as the radius and diameter. Moreover, as a by-product, an efficient shortest-path local algorithm is proposed.

Survivability of public transit network based on network structure entropy

2015 ◽  
Vol 26 (09) ◽  
pp. 1550104 ◽  
Author(s):  
Bai-Bai Fu ◽  
Lin Zhang ◽  
Shu-Bin Li ◽  
Yun-Xuan Li
Keyword(s):  
Network Model ◽  
Network Structure ◽  
Public Transit ◽  
Small World ◽  
Clustering Coefficient ◽  
Statistical Characteristics ◽  
Network Efficiency ◽  
Transit Network ◽  
Scale Free ◽  
The Public

In this work, we have collected 195 bus routes and 1433 bus stations of Jinan city as sample date to build up the public transit geospatial network model by applying space L method, until May 2014. Then, by analyzing the topological properties of public transit geospatial network model, which include degree and degree distribution, average shortest path length, clustering coefficient and betweenness, we get the conclusion that public transit network is a typical complex network with scale-free and small-world characteristics. Furthermore, in order to analyze the survivability of public transit network, we define new network structure entropy based on betweenness importance, and prove its correctness by giving that the new network structure entropy has the same statistical characteristics with network efficiency. Finally, the "inflexion zone" is discovered, which can be taken as the momentous indicator to determine the public transit network failure.

Real-World Networks Are Not Always Fast Mixing

2020 ◽  
Author(s):  
Yi Qi ◽  
Wanyue Xu ◽  
Liwang Zhu ◽  
Zhongzhi Zhang
Keyword(s):  
Real World ◽  
Transition Matrix ◽  
Mixing Time ◽  
Real Life ◽  
Small World ◽  
Design Of Algorithms ◽  
Scale Free ◽  
Analytical Research ◽  
Second Largest Eigenvalue ◽  
Recursive Relations

Abstract The mixing time of random walks on a graph has found broad applications across both theoretical and practical aspects of computer science, with the application effects depending on the behavior of mixing time. It is extensively believed that real-world networks, especially social networks, are fast mixing with their mixing time at most $O(\log N)$ where $N$ is the number of vertices. However, the behavior of mixing time in the real-life networks has not been examined carefully, and exactly analytical research for mixing time in models mimicking real networks is still lacking. In this paper, we first experimentally evaluate the mixing time of various real-world networks with scale-free small-world properties and show that their mixing time is much higher than anticipated. To better understand the behavior of the mixing time for real-world networks, we then analytically study the mixing time of the Apollonian network, which is simultaneously scale-free and small-world. To this end, we derive the recursive relations for all eigenvalues, especially the second largest eigenvalue modulus of the transition matrix, based on which we deduce a lower bound for the mixing time of the Apollonian network, which approximately scales sublinearly with $N$. Our results indicate that real-world networks are not always fast mixing, which has potential implications in the design of algorithms related to mixing time.

Analysis and Visualization of Japanese Law Networks Based on Granular Computing -Visual Law: Visualization System of Japanese Law-

2010 ◽  
Vol 14 (2) ◽  
pp. 150-154
Author(s):  
Tetsuya Toyota ◽  
◽  
Hajime Nobuhara
Keyword(s):  
Network Structure ◽  
Granular Computing ◽  
Network Science ◽  
Closeness Centrality ◽  
Network Visualization ◽  
Hierarchical Network ◽  
Hierarchical Networks ◽  
Visualization System ◽  
The Hierarchical Structure ◽  
Japanese Law

In order to grasp a perspective of the over 7,000 laws in Japan, and to find the relationships between law and laws, a method of creating a hierarchical network of laws using granular computing, is proposed. The proposed method analyze hierarchical networks by using an index of network science such as degree distribution and closeness centrality. Furthermore, it visualizes the hierarchical structure within the setting of granular computing. Using the JAVA-based language ‘Prefuse,’ a law network visualization system ‘Visual Law’ is implemented, and it is confirmed that users can easily analyze/understand the law network structure using our proposal.

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