Design of the Small World Model by NS2

2014 ◽  
Vol 496-500 ◽  
pp. 2338-2341
Author(s):  
Jun Shang ◽  
Hao Qiang Liu ◽  
Qiang Liu ◽  
Zi Qi Liu
Keyword(s):  
Complex Network ◽  
Network Theory ◽  
Applied Research ◽  
Lower Cost ◽  
Small World ◽  
Scale Free Network ◽  
World Model ◽  
Complex Network Theory ◽  
Scale Free ◽  
Free Network

WSN is the network which is used mostly in the world nowadays, and it has the characteristics that lower cost and better functions than other kinds of the network, and the WSN network is built by the ordinary nodes and the super nodes.Theoretical study of the complex network is widely involved in the fields of computer networks, and the applied research becomes more and more important in the future. It has caused many academic attention about how to apply the complex network theory among the specific application in recent years. In the complex network theory, there has been a number of important research results about the use of the small-world network, scale-free network in the field of transportation.

scholarly journals Study on connectivity mechanism and robustness of three-dimensional pore network of sandstone based on complex network theory

2017 ◽  
Author(s):  
Guannan Liu ◽  
Xiaopeng Pei ◽  
Feng Gao ◽  
Xin Liang ◽  
Jianguo Wang ◽  
...  
Keyword(s):  
Complex Network ◽  
Network Theory ◽  
Structural Characteristics ◽  
Dominant Role ◽  
Three Dimensional ◽  
Scale Free Network ◽  
Complex Network Theory ◽  
Scale Free ◽  
Free Network ◽  
And Migration

Abstract. There are a large number of pores and throats inside the rock, with different magnitude and shape, whose connection is complex[1–3]. Based on the complex network theory, combined with X–ray CT scan and image processing technology, we used sandstone as an example to study the structural characteristics of rock network of different porosities. The experimental results show that the seepage network of sandstone is similar to the BA scale-free network in the structural characteristics. The average path length of sandstone generally increases with the increase of network magnitude. The average of number of edges of node plays a dominant role for the porosity of sandstone. It is inferred that in the large number of pores, few pores with a number of connections have an important role in the overall connectivity of the sandstone seepage network. At the same time, sandstone seepage network has better fault tolerance rate and robustness to external random attacks. The results of this paper may provide a new idea for the study of fluid storage and migration mechanisms in porous materials and the application of complex network theory in interdisciplinary fields.

Modeling and Simulation for Complex Network Based Military System-of-Systems (SoS)

2011 ◽  
Vol 145 ◽  
pp. 224-228 ◽  
Author(s):  
Xiao Song ◽  
Bing Cheng Liu ◽  
Guang Hong Gong
Keyword(s):  
Modeling And Simulation ◽  
Complex Network ◽  
Network Topology ◽  
Network Theory ◽  
Small World ◽  
System Of Systems ◽  
Statistical Parameters ◽  
Complex Network Theory ◽  
Scale Free ◽  
Topology Model

Military SoS increasingly shows its relation of complex network. According to complex network theory, we construct a SoS network topology model for network warfare simulation. Analyzing statistical parameters of the model, it is concluded that the topology model has small-world, high-aggregation and scale-free properties. Based on this model we mainly simulate and analyze vulnerability of the network. And this provides basis for analysis of the robustness and vulnerability of real battle SoS network.

scholarly journals Complex network theory, streamflow, and hydrometric monitoring system design

2015 ◽  
Vol 19 (7) ◽  
pp. 3301-3318 ◽  
Author(s):  
M. J. Halverson ◽  
S. W. Fleming
Keyword(s):  
Complex Network ◽  
Network Theory ◽  
Small World ◽  
Detection Algorithm ◽  
Clustering Coefficient ◽  
Network Stability ◽  
Meteorological Forcing ◽  
Complex Network Theory ◽  
Scale Free ◽  
Seasonal Flow

Abstract. Network theory is applied to an array of streamflow gauges located in the Coast Mountains of British Columbia (BC) and Yukon, Canada. The goal of the analysis is to assess whether insights from this branch of mathematical graph theory can be meaningfully applied to hydrometric data, and, more specifically, whether it may help guide decisions concerning stream gauge placement so that the full complexity of the regional hydrology is efficiently captured. The streamflow data, when represented as a complex network, have a global clustering coefficient and average shortest path length consistent with small-world networks, which are a class of stable and efficient networks common in nature, but the observed degree distribution did not clearly indicate a scale-free network. Stability helps ensure that the network is robust to the loss of nodes; in the context of a streamflow network, stability is interpreted as insensitivity to station removal at random. Community structure is also evident in the streamflow network. A network theoretic community detection algorithm identified separate communities, each of which appears to be defined by the combination of its median seasonal flow regime (pluvial, nival, hybrid, or glacial, which in this region in turn mainly reflects basin elevation) and geographic proximity to other communities (reflecting shared or different daily meteorological forcing). Furthermore, betweenness analyses suggest a handful of key stations which serve as bridges between communities and might be highly valued. We propose that an idealized sampling network should sample high-betweenness stations, small-membership communities which are by definition rare or undersampled relative to other communities, and index stations having large numbers of intracommunity links, while retaining some degree of redundancy to maintain network robustness.

scholarly journals Eigenvalue-based entropy in directed complex networks

PLoS ONE ◽  
2021 ◽  
Vol 16 (6) ◽  
pp. e0251993
Author(s):  
Yan Sun ◽  
Haixing Zhao ◽  
Jing Liang ◽  
Xiujuan Ma
Keyword(s):  
Complex Networks ◽  
Complex Network ◽  
Network Models ◽  
Small World ◽  
Laplacian Matrix ◽  
Directed Network ◽  
Small World Network ◽  
Scale Free Network ◽  
Scale Free ◽  
Free Network

Entropy is an important index for describing the structure, function, and evolution of network. The existing research on entropy is primarily applied to undirected networks. Compared with an undirected network, a directed network involves a special asymmetric transfer. The research on the entropy of directed networks is very significant to effectively quantify the structural information of the whole network. Typical complex network models include nearest-neighbour coupling network, small-world network, scale-free network, and random network. These network models are abstracted as undirected graphs without considering the direction of node connection. For complex networks, modeling through the direction of network nodes is extremely challenging. In this paper, based on these typical models of complex network, a directed network model considering node connection in-direction is proposed, and the eigenvalue entropies of three matrices in the directed network is defined and studied, where the three matrices are adjacency matrix, in-degree Laplacian matrix and in-degree signless Laplacian matrix. The eigenvalue-based entropies of three matrices are calculated in directed nearest-neighbor coupling, directed small world, directed scale-free and directed random networks. Through the simulation experiment on the real directed network, the result shows that the eigenvalue entropy of the real directed network is between the eigenvalue entropy of directed scale-free network and directed small-world network.

A New Energy-Efficient and Fault-Tolerant Evolution Model for Large-Scale Wireless Sensor Networks Based on Complex Network Theory

2019 ◽  
Vol 10 (3) ◽  
pp. 21-36 ◽  
Author(s):  
Xiaobo Tan ◽  
Ji Tang ◽  
Liting Yu ◽  
Jialu Wang
Keyword(s):  
Network Theory ◽  
Energy Efficient ◽  
Large Scale ◽  
Fault Tolerant ◽  
Evolution Model ◽  
Scale Free Network ◽  
Complex Network Theory ◽  
Network Characteristics ◽  
Scale Free ◽  
Free Network

In this article, the authors present a new novel energy-efficient and fault-tolerant evolution model for large-scale wireless sensor networks based on complex network theory. In the evolution model, not only is the residual energy of each node considered, but also the constraint of links is introduced, which makes the energy consumption of the whole network more balanced. Furthermore, both preferential attachment and random attachment to the evolution model are introduced, which reduces the proportion of the nodes with high degree while keeping scale-free network characteristics to some extent. Theoretical analysis shows that the new model is an extension of the BA model, which is a mixed model between a BA model and a stochastic model. Simulation results show that EFEM has better stochastic network characteristics while keeping scale-free network characteristics if the value of random probability is near 0.2 and it can help to construct a high survivability network for large-scale WSNs.

Pinning Control of Enterprise Marketing Network Based on Complex Network Theory

2014 ◽  
Vol 533 ◽  
pp. 491-494
Author(s):  
Xiao Hong Qin ◽  
Wei Ge
Keyword(s):  
Network Topology ◽  
Control Strategy ◽  
Network Theory ◽  
Large Scale ◽  
Pinning Control ◽  
Scale Free Network ◽  
Complex Network Theory ◽  
Scale Free ◽  
Free Network ◽  
Marketing Network

Complex enterprise marketing network is typical scale-free network. Based on the non-uniformity of enterprise marketing network topology, we select pinning control strategy. There are network members for selection a certain percentage to exercise control, to use of virtual control action associated with the coupling between network members, making large-scale enterprise marketing network reaches a steady state. Paper showed that pinning control is effectiveness to control of enterprise marketing for network.

scholarly journals Analysis on Invulnerability of Wireless Sensor Network towards Cascading Failures Based on Coupled Map Lattice

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-14 ◽  
Author(s):  
Xiuwen Fu ◽  
Yongsheng Yang ◽  
Haiqing Yao
Keyword(s):  
Random Network ◽  
Small World ◽  
Coupled Map Lattice ◽  
Wireless Sensor ◽  
Cascading Failures ◽  
Scale Free Network ◽  
Scale Free ◽  
Network Topologies ◽  
Free Network ◽  
Entire Network

Previous research of wireless sensor networks (WSNs) invulnerability mainly focuses on the static topology, while ignoring the cascading process of the network caused by the dynamic changes of load. Therefore, given the realistic features of WSNs, in this paper we research the invulnerability of WSNs with respect to cascading failures based on the coupled map lattice (CML). The invulnerability and the cascading process of four types of network topologies (i.e., random network, small-world network, homogenous scale-free network, and heterogeneous scale-free network) under various attack schemes (i.e., random attack, max-degree attack, and max-status attack) are investigated, respectively. The simulation results demonstrate that the rise of interference R and coupling coefficient ε will increase the risks of cascading failures. Cascading threshold values Rc and εc exist, where cascading failures will spread to the entire network when R>Rc or ε>εc. When facing a random attack or max-status attack, the network with higher heterogeneity tends to have a stronger invulnerability towards cascading failures. Conversely, when facing a max-degree attack, the network with higher uniformity tends to have a better performance. Besides that, we have also proved that the spreading speed of cascading failures is inversely proportional to the average path length of the network and the increase of average degree k can improve the network invulnerability.

scholarly journals SCALE-FREE NETWORK THEORY IN STUDYING THE STRUCTURE OF THE ROAD NETWORK IN POLAND

2014 ◽  
Vol 26 (3) ◽  
pp. 235-242 ◽  
Author(s):  
Katarzyna KOCUR-BERA
Keyword(s):  
Statistical Analysis ◽  
Traffic Flow ◽  
Network Theory ◽  
Road Network ◽  
Scale Free Network ◽  
Scale Free ◽  
The Road ◽  
Normal Character ◽  
Free Network ◽  
The Relationship

This paper discusses the issue of statistical analysis of traffic flow in different regions of Poland. Such analysis allows us to identify “valuable (sensitive) areas” whose damage or blockage may provoke considerable disturbances or even a stoppage of traffic flow in the examined road network. The results of the studies indicate that the road network in Poland has the properties of a scale-free network. The distribution of the examined variables does not have a normal character, whereas the relationship between the number of nodes and the number of connections is a power-law feature. 

scholarly journals HIERARCHICAL AND MIXING PROPERTIES OF STATIC COMPLEX NETWORKS EMERGING FROM FLUCTUATING CLASSICAL RANDOM GRAPHS

2006 ◽  
Vol 17 (09) ◽  
pp. 1303-1311 ◽  
Author(s):  
SUMIYOSHI ABE ◽  
STEFAN THURNER
Keyword(s):  
Complex Network ◽  
Preferential Attachment ◽  
Hierarchical Organization ◽  
Scale Free Network ◽  
Mixing Properties ◽  
Scale Free ◽  
Free Network ◽  
Growing Network ◽  
Arbitrary Connectivity

The Erdös–Rényi classical random graph is characterized by a fixed linking probability for all pairs of vertices. Here, this concept is generalized by drawing the linking probability from a certain distribution. Such a procedure is found to lead to a static complex network with an arbitrary connectivity distribution. In particular, a scale-free network with the hierarchical organization is constructed without assuming any knowledge about the global linking structure, in contrast to the preferential attachment rule for a growing network. The hierarchical and mixing properties of the static scale-free network thus constructed are studied. The present approach establishes a bridge between a scalar characterization of individual vertices and topology of an emerging complex network. The result may offer a clue for understanding the origin of a few abundance of connectivity distributions in a wide variety of static real-world networks.

EXPRESS PASSENGER TRANSPORT SYSTEM AS A SCALE-FREE NETWORK

2006 ◽  
Vol 20 (27) ◽  
pp. 1755-1761 ◽  
Author(s):  
BAIBAI FU ◽  
ZIYOU GAO ◽  
FASHENG LIU ◽  
XIANJUAN KONG
Keyword(s):  
Transport System ◽  
Network Topology ◽  
Small World ◽  
Power Exponent ◽  
Scale Free Network ◽  
Passenger Transport ◽  
Scale Free ◽  
Scale Free Networks ◽  
Highway Network ◽  
Free Network

An express highway itself is not a scale-free network, while the Express Passenger Transport System (EPTS) on the express highway network has the properties of a small-world and scale-free network. Data analysis based on the observation of the EPTS in Shandong province, China, shows that the EPTS has the properties of scale-free networks and the power exponent λ of the distribution is equal to about 2.1. Based on the scale-free network topology structure of the EPTS network, the construction of the EPTS network will be more efficient and robust.

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