scholarly journals Small-World and Scale-Free Network Models for IoT Systems

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Insoo Sohn
Keyword(s):  
Graph Theory ◽  
Complex Network ◽  
Network Topology ◽  
Network Models ◽  
Small World ◽  
Small World Networks ◽  
Scale Free ◽  
Scale Free Networks ◽  
Massive Number ◽  
Complex Network Models

It is expected that Internet of Things (IoT) revolution will enable new solutions and business for consumers and entrepreneurs by connecting billions of physical world devices with varying capabilities. However, for successful realization of IoT, challenges such as heterogeneous connectivity, ubiquitous coverage, reduced network and device complexity, enhanced power savings, and enhanced resource management have to be solved. All these challenges are heavily impacted by the IoT network topology supported by massive number of connected devices. Small-world networks and scale-free networks are important complex network models with massive number of nodes and have been actively used to study the network topology of brain networks, social networks, and wireless networks. These models, also, have been applied to IoT networks to enhance synchronization, error tolerance, and more. However, due to interdisciplinary nature of the network science, with heavy emphasis on graph theory, it is not easy to study the various tools provided by complex network models. Therefore, in this paper, we attempt to introduce basic concepts of graph theory, including small-world networks and scale-free networks, and provide system models that can be easily implemented to be used as a powerful tool in solving various research problems related to IoT.

scholarly journals On the Distributions of Subgraph Centralities in Complex Networks

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Faxu Li ◽  
Liang Wei ◽  
Haixing Zhao ◽  
Feng Hu
Keyword(s):  
Complex Networks ◽  
Probability Distributions ◽  
Network Connectivity ◽  
Network Models ◽  
Small World ◽  
Small World Networks ◽  
Power Law Distribution ◽  
Scale Free ◽  
Scale Free Networks ◽  
Complex Network Models

Subgraph centrality measure characterizes the participation of each node in all subgraphs in a network. Smaller subgraphs are given more weight than large ones, which makes this measure appropriate for characterizing network motifs. This measure is better in being able to discriminate the nodes of a network than alternate measures. In this paper, the important issue of subgraph centrality distributions is investigated through theory-guided extensive numerical simulations, for three typical complex network models, namely, the ER random-graph networks, WS small-world networks, and BA scale-free networks. It is found that these three very different types of complex networks share some common features, particularly that the subgraph centrality distributions in increasing order are all insensitive to the network connectivity characteristics, and also found that the probability distributions of subgraph centrality of the ER and of the WS models both follow the gamma distribution, and the BA scale-free networks exhibit a power-law distribution with an exponential cutoff.

scholarly journals Resilience of Interbank Market Networks to Shocks

2011 ◽  
Vol 2011 ◽  
pp. 1-12 ◽  
Author(s):  
Shouwei Li ◽  
Jianmin He
Keyword(s):  
Network Models ◽  
Small World ◽  
Interbank Market ◽  
Small World Networks ◽  
Scale Free ◽  
Scale Free Networks ◽  
Tiered Networks ◽  
The Stability ◽  
Random Shocks ◽  
Market Networks

This paper first constructs a tiered network model of the interbank market. Then, from the perspective of contagion risk, it studies numerically the resilience of four types of interbank market network models to shocks, namely, tiered networks, random networks, small-world networks, and scale-free networks. This paper studies the interbank market with homogeneous and heterogeneous banks and analyzes random shocks and selective shocks. The study reveals that tiered interbank market networks and random interbank market networks are basically more vulnerable against selective shocks, while small-world interbank market networks and scale-free interbank market networks are generally more vulnerable against random shocks. Besides, the results indicate that, in the four types of interbank market networks, scale-free networks have the highest stability against shocks, while small-world networks are the most vulnerable. When banks are homogeneous, faced with selective shocks, the stability of the tiered interbank market networks is slightly lower than that of random interbank market networks, whereas, in other cases, the stability of the tiered interbank market networks is basically between that of random interbank market networks and that of scale-free interbank market networks.

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.

Information Networks as Complex Systems

2011 ◽  
pp. 43-58
Author(s):  
Yoshiteru Ishida
Keyword(s):  
Complex Systems ◽  
Complex Network ◽  
Normal State ◽  
Small World ◽  
Information Networks ◽  
Small World Networks ◽  
Scale Free ◽  
Abnormal State ◽  
Scale Free Networks ◽  
Spatial Prisoner’S Dilemma

Complex network such as scale-free networks and small-world networks have been studied with the dynamics when the information percolates through the networks. This chapter reports the problem of spreading the normal state (rather than spreading of the abnormal state) that is formalized as cleaning a contaminated network by mutual copying. Repairing by copying is the “double edged sword” that could spread contamination when properly used. A framework for controlling copying involving a spatial Prisoner’s Dilemma is introduced. Adaptive character to the network environment has been observed.

scholarly journals Quantitative method for resilience assessment framework of airport network during COVID-19

PLoS ONE ◽  
2021 ◽  
Vol 16 (12) ◽  
pp. e0260940
Author(s):  
Jiuxia Guo ◽  
Yang Li ◽  
Zongxin Yang ◽  
Xinping Zhu
Keyword(s):  
Complex Network ◽  
Small World ◽  
Global Scale ◽  
Assessment Framework ◽  
Small World Networks ◽  
Scale Free ◽  
Global Pandemic ◽  
Network Metrics ◽  
Resilience Assessment

The resilience and vulnerability of airport networks are significant challenges during the COVID-19 global pandemic. Previous studies considered node failure of networks under natural disasters and extreme weather. Herein, we propose a complex network methodology combined with data-driven to assess the resilience of airport networks toward global-scale disturbance using the Chinese airport network (CAN) and the European airport network (EAN) as a case study. The assessment framework includes vulnerability and resilience analyses from the network- and node-level perspectives. Subsequently, we apply the framework to analyze the airport networks in China and Europe. Specifically, real air traffic data for 232 airports in China and 82 airports in Europe are selected to form the CAN and EAN, respectively. The complex network analysis reveals that the CAN and the EAN are scale-free small-world networks, that are resilient to random attacks. However, the connectivity and vulnerability of the CAN are inferior to those of the EAN. In addition, we select the passenger throughput from the top-50 airports in China and Europe to perform a comparative analysis. By comparing the resilience evaluation of individual airports, we discovered that the factors of resilience assessment of an airport network for global disturbance considers the network metrics and the effect of government policy in actual operations. Additionally, this study also proves that a country’s emergency response-ability towards the COVID-19 has a significantly affectes the recovery of its airport network.

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.

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.

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.

Propagation and stability in software: A complex network perspective

2015 ◽  
Vol 26 (05) ◽  
pp. 1550052 ◽  
Author(s):  
Lei Wang ◽  
Ping Wang
Keyword(s):  
Software Engineering ◽  
Complex Networks ◽  
Large Scale ◽  
Structural Difference ◽  
Small World ◽  
Change Propagation ◽  
Small World Networks ◽  
Typical Structure ◽  
Scale Free ◽  
Scale Free Networks

In this paper, we attempt to understand the propagation and stability feature of large-scale complex software from the perspective of complex networks. Specifically, we introduced the concept of "propagation scope" to investigate the problem of change propagation in complex software. Although many complex software networks exhibit clear "small-world" and "scale-free" features, we found that the propagation scope of complex software networks is much lower than that of small-world networks and scale-free networks. Furthermore, because the design of complex software always obeys the principles of software engineering, we introduced the concept of "edge instability" to quantify the structural difference among complex software networks, small-world networks and scale-free networks. We discovered that the edge instability distribution of complex software networks is different from that of small-world networks and scale-free networks. We also found a typical structure that contributes to the edge instability distribution of complex software networks. Finally, we uncovered the correlation between propagation scope and edge instability in complex networks by eliminating the edges with different instability ranges.

Complex networks

2018 ◽  
Author(s):  
Graziano Vernizzi ◽  
Henri Orland
Keyword(s):  
Complex Networks ◽  
Small World ◽  
Laplacian Matrix ◽  
Square Lattice ◽  
Small World Networks ◽  
Scale Free ◽  
Scale Free Networks ◽  
Free Network ◽  
Scale Free Graphs ◽  
Regular Networks

This article deals with complex networks, and in particular small world and scale free networks. Various networks exhibit the small world phenomenon, including social networks and gene expression networks. The local ordering property of small world networks is typically associated with regular networks such as a 2D square lattice. The small world phenomenon can be observed in most scale free networks, but few small world networks are scale free. The article first provides a brief background on small world networks and two models of scale free graphs before describing the replica method and how it can be applied to calculate the spectral densities of the adjacency matrix and Laplacian matrix of a scale free network. It then shows how the effective medium approximation can be used to treat networks with finite mean degree and concludes with a discussion of the local properties of random matrices associated with complex networks.

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