scholarly journals Topological Properties of a 3-Regular Small World Network

2014 ◽  
Vol 2014 ◽  
pp. 1-4
Author(s):  
Huanshen Jia ◽  
Guona Hu ◽  
Haixing Zhao
Keyword(s):  
Complex Networks ◽  
Network Model ◽  
Spanning Trees ◽  
Small World ◽  
Clustering Coefficient ◽  
Deterministic Models ◽  
Engineering Technology ◽  
Research Fields ◽  
Potential Applications ◽  
Regular Network

Complex networks have seen much interest from all research fields and have found many potential applications in a variety of areas including natural, social, biological, and engineering technology. The deterministic models for complex networks play an indispensable role in the field of network model. The construction of a network model in a deterministic way not only has important theoretical significance, but also has potential application value. In this paper, we present a class of 3-regular network model with small world phenomenon. We determine its relevant topological characteristics, such as diameter and clustering coefficient. We also give a calculation method of number of spanning trees in the 3-regular network and derive the number and entropy of spanning trees, respectively.

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.

Network model of bilateral power markets based on complex networks

2014 ◽  
Vol 28 (22) ◽  
pp. 1450144 ◽  
Author(s):  
Yang Wu ◽  
Junyong Liu ◽  
Furong Li ◽  
Zhanxin Yan ◽  
Li Zhang
Keyword(s):  
Complex Networks ◽  
Network Model ◽  
Simulation Analysis ◽  
Electric Power Industry ◽  
Clustering Coefficient ◽  
Power Markets ◽  
Cascading Failure ◽  
Topological Stability ◽  
Market Organization ◽  
Topological Robustness

The bilateral power transaction (BPT) mode becomes a typical market organization with the restructuring of electric power industry, the proper model which could capture its characteristics is in urgent need. However, the model is lacking because of this market organization's complexity. As a promising approach to modeling complex systems, complex networks could provide a sound theoretical framework for developing proper simulation model. In this paper, a complex network model of the BPT market is proposed. In this model, price advantage mechanism is a precondition. Unlike other general commodity transactions, both of the financial layer and the physical layer are considered in the model. Through simulation analysis, the feasibility and validity of the model are verified. At same time, some typical statistical features of BPT network are identified. Namely, the degree distribution follows the power law, the clustering coefficient is low and the average path length is a bit long. Moreover, the topological stability of the BPT network is tested. The results show that the network displays a topological robustness to random market member's failures while it is fragile against deliberate attacks, and the network could resist cascading failure to some extent. These features are helpful for making decisions and risk management in BPT markets.

A NOVEL SMALL-WORLD NETWORK MODEL: KEEPING CONNECTIVITY WITHOUT ADDING EDGES

2008 ◽  
Vol 22 (29) ◽  
pp. 5229-5234 ◽  
Author(s):  
XUHUA YANG ◽  
BO WANG ◽  
WANLIANG WANG ◽  
YOUXIAN SUN
Keyword(s):  
Network Model ◽  
Regular Ring ◽  
Nearest Neighbor ◽  
Small World ◽  
Clustering Coefficient ◽  
The Novel ◽  
Small World Network ◽  
Characteristic Path Length ◽  
Large N ◽  
Novel Model

Considering the problems of potentially generating a disconnected network in the WS small-world network model [Watts and Strogatz, Nature393, 440 (1998)] and of adding edges in the NW small-world network model [Newman and Watts, Phys. Lett. A263, 341 (1999)], we propose a novel small-world network model. First, generate a regular ring lattice of N vertices. Second, randomly rewire each edge of the lattice with probability p. During the random rewiring procedure, keep the edges between the two nearest neighbor vertices, namely, always keep a connected ring. This model need not add edges and can maintain connectivity of the network at all times in the random rewiring procedure. Simulation results show that the novel model has the typical small-world properties which are small characteristic path length and high clustering coefficient. For large N, the model is approximately equal to the WS model. For large N and small p, the model is approximately equal to the WS model or the NW model.

SMALL-WORLD EFFECT IN GEOGRAPHICAL ATTACHMENT NETWORKS

2019 ◽  
pp. 1-21
Author(s):  
Qunqiang Feng ◽  
Yongkang Wang ◽  
Zhishui Hu
Keyword(s):  
Network Model ◽  
Degree Distribution ◽  
Small World ◽  
Clustering Coefficient ◽  
Probabilistic Methods ◽  
Small World Network ◽  
Computational Simulations ◽  
Physical Literature

AbstractIn this work, we use rigorous probabilistic methods to study the asymptotic degree distribution, clustering coefficient, and diameter of geographical attachment networks. As a type of small-world network model, these networks were first proposed in the physical literature, where they were analyzed only with heuristic arguments and computational simulations.

Building Complex Network Similar to Facebook

2014 ◽  
Vol 513-517 ◽  
pp. 909-913
Author(s):  
Dong Wei Guo ◽  
Xiang Yan Meng ◽  
Cai Fang Hou
Keyword(s):  
Social Networks ◽  
Social Network ◽  
Complex Networks ◽  
Complex Network ◽  
Network Model ◽  
Clustering Coefficient ◽  
Network Characteristics ◽  
Modeling Methods ◽  
Community Strength ◽  
Strength Based

Social networks have been developed rapidly, especially for Facebook which is very popular with 10 billion users. It is a considerable significant job to build complex network similar to Facebook. There are many modeling methods of complex networks but which cant describe characteristics similar to Facebook. This paper provide a building method of complex networks with tunable clustering coefficient and community strength based on BA network model to imitate Facebook. The strategies of edge adding based on link-via-triangular, link-via-BA and link-via-type are used to build a complex network with tunable clustering coefficient and community strength. Under different parameters, statistical properties of the complex network model are analyzed. The differences and similarities are studied among complex network model proposed by this paper and real social network on Facebook. It is found that the network characteristics of the network model and real social network on Facebook are similar under some specific parameters. It is proved that the building method of complex networks is feasible.

scholarly journals SZNAJD MODEL WITH SYNCHRONOUS UPDATING ON COMPLEX NETWORKS

2005 ◽  
Vol 16 (07) ◽  
pp. 1149-1161 ◽  
Author(s):  
YU-SONG TU ◽  
A. O. SOUSA ◽  
LING-JIANG KONG ◽  
MU-REN LIU
Keyword(s):  
Complex Networks ◽  
Small World ◽  
System Size ◽  
The State ◽  
Clustering Coefficient ◽  
Square Lattice ◽  
Node Degree ◽  
Scale Free ◽  
Free Network ◽  
Formation Step

We analyze the evolution of Sznajd Model with synchronous updating in several complex networks. Similar to the model on square lattice, we have found a transition between the state with nonconsensus and the state with complete consensus in several complex networks. Furthermore, by adjusting the network parameters, we find that a large clustering coefficient does not favor development of a consensus. In particular, in the limit of large system size with the initial concentration p =0.5 of opinion +1, a consensus seems to be never reached for the Watts–Strogatz small-world network, when we fix the connectivity k and the rewiring probability ps; nor for the scale-free network, when we fix the minimum node degree m and the triad formation step probability pt.

A NETWORK MODEL GENERATED FROM THE RECURSIVE GRAPH BASED ON POLYGON

2013 ◽  
Vol 24 (09) ◽  
pp. 1350062 ◽  
Author(s):  
YUANYUAN SUN ◽  
KAINING HOU ◽  
YUJIE ZHAO
Keyword(s):  
Real Life ◽  
Network Models ◽  
Small World ◽  
Mapping Method ◽  
Clustering Coefficient ◽  
Research Fields ◽  
Network Diameter ◽  
Degree Correlations ◽  
New Perspective ◽  
Small World Property

The study of network models is one of the most challenging research fields among the studies of complex networks, which have been the hot research topics in recent decades. In this paper, we construct a deterministic network by a mapping method based on a recursive graph, and analyze its topological characteristics, including degree distribution, clustering coefficient, network diameter, average path length and degree correlations. We obtain that this network has the small-world property and positive correlation. The network modeling as we present gives a new perspective on networks, and helps to understand better the evolutions of the real-life systems, making it possible to explore the complexity of complex systems.

scholarly journals CONTOUR POLYGONAL APPROXIMATION USING THE SHORTEST PATH IN NETWORKS

2014 ◽  
Vol 25 (02) ◽  
pp. 1350090 ◽  
Author(s):  
ANDRÉ RICARDO BACKES ◽  
DALCIMAR CASANOVA ◽  
ODEMIR MARTINEZ BRUNO
Keyword(s):  
Complex Networks ◽  
Shortest Path ◽  
Small World ◽  
Approximation Methods ◽  
Geodesic Path ◽  
Polygonal Approximation ◽  
Line Segments ◽  
Network Properties ◽  
Novel Method ◽  
Regular Network

Contour polygonal approximation is a simplified representation of a contour by line segments so that the main characteristics of the contour remain in a small number of line segments. This paper presents a novel method for polygonal approximation based on the Complex Networks theory. We convert each point of the contour into a vertex so that a regular network can be modeled. Then we transform this network into a Small-World Complex Network by applying some transformations over its edges. We compute the polygonal approximation analyzing the network properties, especially the geodesic path. The paper presents the main characteristics of the method, as well as its functionality. We evaluate the proposed method using benchmark contours and compare its results with other polygonal approximation methods.

Research on Edge-Growing Models Related with Scale-Free Small-World Networks

2014 ◽  
Vol 513-517 ◽  
pp. 2444-2448 ◽  
Author(s):  
Bing Yao ◽  
Ming Yao ◽  
Xiang En Chen ◽  
Xia Liu ◽  
Wan Jia Zhang
Keyword(s):  
Complex Networks ◽  
Topological Structure ◽  
Spanning Trees ◽  
Network Models ◽  
Small World ◽  
Small World Networks ◽  
Scale Free ◽  
Scale Free Networks ◽  
Growing Network

Understanding the topological structure of scale-free networks or small world networks is required and useful for investigation of complex networks. We will build up a class of edge-growing network models and provide an algorithm for finding spanning trees of edge-growing network models in this article.

scholarly journals Complex network dynamics of the topological structure in a geochemical field from the Nanling area in South China

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Nian Peng ◽  
Xiaoyan Zhu ◽  
Yongshun Liu ◽  
Baofeng Nie ◽  
Ying Cui ◽  
...  
Keyword(s):  
Complex Networks ◽  
South China ◽  
Control Parameter ◽  
Small World ◽  
Coarse Graining ◽  
Clustering Coefficient ◽  
Topological Classification ◽  
Correlation Structures ◽  
Geochemical Elements

AbstractThe topological classification of geochemical elements is widely used as a reference for regional prospecting prediction. In this study, we analyze the topological correlation structures of 39 representative geochemical elements from the Nanling area of South China by implementing the complex networks theory. The topological correlation structures of geochemical elements have a high clustering coefficient (0.8120–0.8880), but the magnitude of the shortest path (1.2950–2.3600) is small. In combination with the analysis of complex networks characteristics, we report that the topological correlation structures of the geochemical elements in this area have small-world characteristics, which reveals the self-organized criticality. As shown in the topological network, two random elements have some level of associations, which present a specific community feature. Our preliminary result shows that with changing the control parameter (k) of “coarse-graining”, the topological correlation structures undergo two critical phase transitions. As the control parameter (k) reaches 0.44, the entire element system evolves into two parts. When the control parameter (k) reaches 0.63, the system forms three “communities”. It is worth noting that the three “communities” are basically consistent with the Goldschmidt’s geochemical classification of the elements, which are lithophile, siderophile, and chalcophile groups, respectively. In these “communities”, we also found that a small level of component units is nested.

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