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.

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 Study on Wireless Sensor Network Topological Structure for Improving Network Energy Utilization

2013 ◽  
Vol 443 ◽  
pp. 509-512
Author(s):  
Yan Zhu ◽  
Yun Yu
Keyword(s):  
Energy Consumption ◽  
Wireless Sensor Network ◽  
Sensor Network ◽  
Complex Network ◽  
Path Length ◽  
Small World ◽  
Average Path Length ◽  
Clustering Coefficient ◽  
Wireless Sensor ◽  
Small World Network

Based on the complex network property of wireless sensor networks, this study focus on the topology of wireless sensor network and carry out series simulation according to complex network research methods. The characteristic of topology for the wireless sensor network is probed in the experiment. The degree distribution, clustering coefficient and average path length are analyzed during the experimental process. Our results verify that the topology of wireless sensor network is neither regular nor random. It is between random network and small-world network which has comparatively smaller average path length and bigger cluster coefficient. In order to form a network that is similar to the property of small-world network, which can reduce network energy consumption by decrease the average hops, our experiment constructs a network model which has significant small-world network characteristic. The results indicate that the added small sum of long range edges in the network will not increase the network load while it can reduce the energy consumption of the network effectively.

scholarly journals Synchronizability of Small-World Networks Generated from a Two-Dimensional Kleinberg Model

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Yi Zhao ◽  
Jianwen Feng ◽  
Jingyi Wang
Keyword(s):  
Path Length ◽  
Small World ◽  
Average Path Length ◽  
Small World Network ◽  
Two Dimensional ◽  
Small World Networks

This paper investigates the synchronizability of small-world networks generated from a two-dimensional Kleinberg model, which is more general than NW small-world network. The three parameters of the Kleinberg model, namely, the distance of neighbors, the number of edge-adding, and the edge-adding probability, are analyzed for their impacts on its synchronizability and average path length. It can be deduced that the synchronizability becomes stronger as the edge-adding probability increases, and the increasing edge-adding probability could make the average path length of the Kleinberg small-world network go smaller. Moreover, larger distance among neighbors and more edges to be added could play positive roles in enhancing the synchronizability of the Kleinberg model. The lorentz oscillators are employed to verify the conclusions numerically.

Determining average path length and average trapping time on generalized dual dendrimer

2015 ◽  
Vol 29 (12) ◽  
pp. 1550072 ◽  
Author(s):  
Ling Li ◽  
Jihong Guan
Keyword(s):  
Path Length ◽  
Small World ◽  
Network Size ◽  
Average Path Length ◽  
Trapping Efficiency ◽  
Trapping Time ◽  
Coordination Numbers ◽  
Central Node ◽  
Trapping Problem ◽  
Structure Properties

Dendrimer has wide number of important applications in various fields. In some cases during transport or diffusion process, it transforms into its dual structure named Husimi cactus. In this paper, we study the structure properties and trapping problem on a family of generalized dual dendrimer with arbitrary coordination numbers. We first calculate exactly the average path length (APL) of the networks. The APL increases logarithmically with the network size, indicating that the networks exhibit a small-world effect. Then we determine the average trapping time (ATT) of the trapping process in two cases, i.e., the trap placed on a central node and the trap is uniformly distributed in all the nodes of the network. In both case, we obtain explicit solutions of ATT and show how they vary with the networks size. Besides, we also discuss the influence of the coordination number on trapping efficiency.

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.

Analysis of Oncogene Protein Structure Using Small World Network Concept

2020 ◽  
Vol 15 (7) ◽  
pp. 732-740
Author(s):  
Neetu Kumari ◽  
Anshul Verma
Keyword(s):  
Amino Acids ◽  
Protein Structure ◽  
Degree Distribution ◽  
Protein Structures ◽  
Small World ◽  
Extreme Condition ◽  
Centrality Measures ◽  
Small World Network ◽  
Network Concept ◽  
Oncogene Protein

Background: The basic building block of a body is protein which is a complex system whose structure plays a key role in activation, catalysis, messaging and disease states. Therefore, careful investigation of protein structure is necessary for the diagnosis of diseases and for the drug designing. Protein structures are described at their different levels of complexity: primary (chain), secondary (helical), tertiary (3D), and quaternary structure. Analyzing complex 3D structure of protein is a difficult task but it can be analyzed as a network of interconnection between its component, where amino acids are considered as nodes and interconnection between them are edges. Objective: Many literature works have proven that the small world network concept provides many new opportunities to investigate network of biological systems. The objective of this paper is analyzing the protein structure using small world concept. Methods: Protein is analyzed using small world network concept, specifically where extreme condition is having a degree distribution which follows power law. For the correct verification of the proposed approach, dataset of the Oncogene protein structure is analyzed using Python programming. Results: Protein structure is plotted as network of amino acids (Residue Interaction Graph (RIG)) using distance matrix of nodes with given threshold, then various centrality measures (i.e., degree distribution, Degree-Betweenness correlation, and Betweenness-Closeness correlation) are calculated for 1323 nodes and graphs are plotted. Conclusion: Ultimately, it is concluded that there exist hubs with higher centrality degree but less in number, and they are expected to be robust toward harmful effects of mutations with new functions.

scholarly journals The structure of co-publications multilayer network

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Ghislain Romaric Meleu ◽  
Paulin Yonta Melatagia
Keyword(s):  
Power Law ◽  
Degree Distribution ◽  
Preferential Attachment ◽  
Small World ◽  
Generation Model ◽  
Small World Network ◽  
Power Law Distribution ◽  
Multilayer Networks ◽  
Multilayer Network ◽  
Scientific Papers

AbstractUsing the headers of scientific papers, we have built multilayer networks of entities involved in research namely: authors, laboratories, and institutions. We have analyzed some properties of such networks built from data extracted from the HAL archives and found that the network at each layer is a small-world network with power law distribution. In order to simulate such co-publication network, we propose a multilayer network generation model based on the formation of cliques at each layer and the affiliation of each new node to the higher layers. The clique is built from new and existing nodes selected using preferential attachment. We also show that, the degree distribution of generated layers follows a power law. From the simulations of our model, we show that the generated multilayer networks reproduce the studied properties of co-publication networks.

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