scholarly journals Network rewiring dynamics with convergence towards a star network

2016 ◽  
Vol 472 (2194) ◽  
pp. 20160236 ◽  
Author(s):  
P. A. Whigham ◽  
G. Dick ◽  
M. Parry
Keyword(s):  
Infectious Disease ◽  
Random Network ◽  
Small World ◽  
Fixation Time ◽  
Fixed Size ◽  
Star Network ◽  
Scale Free ◽  
Link Type ◽  
Scale Free Networks ◽  
Network Rewiring

Network rewiring as a method for producing a range of structures was first introduced in 1998 by Watts & Strogatz ( Nature 393 , 440–442. ( doi:10.1038/30918 )). This approach allowed a transition from regular through small-world to a random network. The subsequent interest in scale-free networks motivated a number of methods for developing rewiring approaches that converged to scale-free networks. This paper presents a rewiring algorithm (RtoS) for undirected, non-degenerate, fixed size networks that transitions from regular, through small-world and scale-free to star-like networks. Applications of the approach to models for the spread of infectious disease and fixation time for a simple genetics model are used to demonstrate the efficacy and application of the approach.

STABILITY OF TWO TYPICAL COMPLEX DYNAMICAL NETWORKS

2008 ◽  
Vol 22 (05) ◽  
pp. 553-560 ◽  
Author(s):  
WU-JIE YUAN ◽  
XIAO-SHU LUO ◽  
PIN-QUN JIANG ◽  
BING-HONG WANG ◽  
JIN-QING FANG
Keyword(s):  
Numerical Simulation ◽  
Dissipative System ◽  
Small World ◽  
Complex Dynamical Networks ◽  
Dynamical Networks ◽  
Scale Free ◽  
Scale Free Networks ◽  
General Complex ◽  
The Stability ◽  
Theoretical Results

When being constructed, complex dynamical networks can lose stability in the sense of Lyapunov (i. s. L.) due to positive feedback. Thus, there is much important worthiness in the theory and applications of complex dynamical networks to study the stability. In this paper, according to dissipative system criteria, we give the stability condition in general complex dynamical networks, especially, in NW small-world and BA scale-free networks. The results of theoretical analysis and numerical simulation show that the stability i. s. L. depends on the maximal connectivity of the network. Finally, we show a numerical example to verify our theoretical results.

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.

sispread: A Software to Simulate Infectious Diseases Spreading on Contact Networks

2007 ◽  
Vol 46 (01) ◽  
pp. 19-26 ◽  
Author(s):  
P. Crépey ◽  
M. Barthélemy ◽  
A.-J. Valleron ◽  
F.P. Alvarez
Keyword(s):  
Infectious Disease ◽  
Infectious Agent ◽  
Small World ◽  
Simulation Software ◽  
Third Party ◽  
Contact Networks ◽  
Scale Free ◽  
Multiple Networks ◽  
New Strategies ◽  
Epidemiological Parameters

Summary Objectives: We present a simulation software which allows studying the dynamics of a hypothetic infectious disease within a network of connected people. The software is aimed to facilitate the discrimination of stochastic factors governing the evolution of an infection in a network. In order to do this it provides simple tools to create networks of individuals and to set the epidemiological parameters of the outbreaks. Methods: Three popular models of infectious disease can be used (SI, SIS, SIR). The simulated networks are either the algorithm-based included ones (scale free, small-world, and random homogeneous networks), or provided by third party software. Results: It allows the simulation of a single or many outbreaks over a network, or outbreaks over multiple networks (with identical properties). Standard outputs are the evolution of the prevalence of the disease, on a single outbreak basis or by averaging many outbreaks. The user can also obtain customized outputs which address in detail different possible epidemiological questions about the spread of an infectious agent in a community. Conclusions: The presented software introduces sources of stochasticity present in real epidemics by simulating outbreaks on contact networks of individuals. This approach may help to understand the paths followed by outbreaks in a given community and to design new strategies for preventing and controlling them.

scholarly journals EPIDEMIC DYNAMICS ON RANDOM AND SCALE-FREE NETWORKS

2012 ◽  
Vol 54 (1-2) ◽  
pp. 3-22 ◽  
Author(s):  
J. BARTLETT ◽  
M. J. PLANK
Keyword(s):  
Random Network ◽  
Infectious Agent ◽  
Mixed Population ◽  
Random Networks ◽  
Scale Free Network ◽  
Final Size ◽  
Scale Free ◽  
Epidemic Dynamics ◽  
Scale Free Networks ◽  
Free Network

AbstractRandom networks were first used to model epidemic dynamics in the 1950s, but in the last decade it has been realized that scale-free networks more accurately represent the network structure of many real-world situations. Here we give an analytical and a Monte Carlo method for approximating the basic reproduction number ${R}_{0} $ of an infectious agent on a network. We investigate how final epidemic size depends on ${R}_{0} $ and on network density in random networks and in scale-free networks with a Pareto exponent of 3. Our results show that: (i) an epidemic on a random network has the same average final size as an epidemic in a well-mixed population with the same value of ${R}_{0} $; (ii) an epidemic on a scale-free network has a larger average final size than in an equivalent well-mixed population if ${R}_{0} \lt 1$, and a smaller average final size than in a well-mixed population if ${R}_{0} \gt 1$; (iii) an epidemic on a scale-free network spreads more rapidly than an epidemic on a random network or in a well-mixed population.

EFFECTS OF CONFIDENCE SCALE AND NETWORK STRUCTURE ON MINORITY OPINION SPREADING

2010 ◽  
Vol 21 (08) ◽  
pp. 1001-1010 ◽  
Author(s):  
BO SHEN ◽  
YUN LIU
Keyword(s):  
Simple Model ◽  
Network Structure ◽  
Random Network ◽  
Random Networks ◽  
Scale Free Network ◽  
Opinion Formation ◽  
Scale Free ◽  
Scale Free Networks ◽  
Free Network ◽  
Confidence Scale

We study the dynamics of minority opinion spreading using a proposed simple model, in which the exchange of views between agents is determined by a quantity named confidence scale. To understand what will promote the success of minority, two types of networks, random network and scale-free network are considered in opinion formation. We demonstrate that the heterogeneity of networks is advantageous to the minority and exchanging views between more agents will reduce the opportunity of minority's success. Further, enlarging the degree that agents trust each other, i.e. confidence scale, can increase the probability that opinions of the minority could be accepted by the majority. We also show that the minority in scale-free networks are more sensitive to the change of confidence scale than that in random 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.

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.

scholarly journals The network structure affects the fixation probability when it couples to the birth-death dynamics in finite population

2021 ◽  
Vol 17 (10) ◽  
pp. e1009537
Author(s):  
Mohammad Ali Dehghani ◽  
Amir Hossein Darooneh ◽  
Mohammad Kohandel
Keyword(s):  
Network Structure ◽  
Evolutionary Dynamics ◽  
Finite Population ◽  
Small World ◽  
Fixation Time ◽  
Fixation Probability ◽  
Neutral Drift ◽  
Scale Free ◽  
Wide Range ◽  
And Mathematics

The study of evolutionary dynamics on graphs is an interesting topic for researchers in various fields of science and mathematics. In systems with finite population, different model dynamics are distinguished by their effects on two important quantities: fixation probability and fixation time. The isothermal theorem declares that the fixation probability is the same for a wide range of graphs and it only depends on the population size. This has also been proved for more complex graphs that are called complex networks. In this work, we propose a model that couples the population dynamics to the network structure and show that in this case, the isothermal theorem is being violated. In our model the death rate of a mutant depends on its number of neighbors, and neutral drift holds only in the average. We investigate the fixation probability behavior in terms of the complexity parameter, such as the scale-free exponent for the scale-free network and the rewiring probability for the small-world network.

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