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.

Traffic dynamics on multilayer networks with two logical layers

2021 ◽  
pp. 2150109
Author(s):  
Jinlong Ma ◽  
Zhichao Sun ◽  
Yongqiang Zhang ◽  
Xiangyang Xu ◽  
Ruimei Zhao ◽  
...  
Keyword(s):  
Network Model ◽  
Random Network ◽  
Physical Layer ◽  
Random Networks ◽  
Scale Free Network ◽  
Multilayer Networks ◽  
Traffic Dynamics ◽  
Scale Free ◽  
Traffic Capacity ◽  
Free Network

In order to study traffic dynamics on multilayer networks, it is of great significance to build a network model which can more exactly reflect the actual network layered structure characteristics. In this paper, a three-layer network model in which two logical layers are mapped on one physical layer is established, and the traffic capacities of three kinds of multilayer networks with different combinations of logical layers are compared. Simulation results show that when the physical layer is the same random network, the network whose logical layers are two random networks has the optimal traffic capacity, the network with one random network and one scale-free network in the logical layers has the better traffic capacity than the network whose logical layers are two scale-free networks.

scholarly journals Network Entropy and Systemic Risk in Dynamic Banking Systems

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-7 ◽  
Author(s):  
Liang He ◽  
Shouwei Li
Keyword(s):  
Systemic Risk ◽  
Random Network ◽  
Small World ◽  
Random Networks ◽  
Scale Free Network ◽  
Small World Networks ◽  
Scale Free ◽  
Banking Systems ◽  
Free Network ◽  
Network Entropy

We investigate network entropy of dynamic banking systems, where interbank networks analyzed include random networks, small-world networks, and scale-free networks. We find that network entropy is positively correlated with the effect of systemic risk in the three kinds of interbank networks and that network entropy in the small-world network is the largest, followed by those in the random network and the scale-free 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.

Scale-Free Networks Based on the Value of Interest

2013 ◽  
Vol 753-755 ◽  
pp. 2959-2962
Author(s):  
Jun Tao Yang ◽  
Hui Wen Deng
Keyword(s):  
Network Model ◽  
Power Law ◽  
Scale Free Network ◽  
Power Law Distribution ◽  
Scale Free ◽  
Distribution Property ◽  
Scale Free Networks ◽  
Free Model ◽  
Free Network ◽  
Interest Model

Assigning the value of interest to each node in the network, we give a scale-free network model. The value of interest is related to the fitness and the degree of the node. Experimental results show that the interest model not only has the characteristics of the BA scale-free model but also has the characteristics of fitness model, and the network has a power-law distribution property.

scholarly journals OPTIMIZATION OF ROBUSTNESS OF SCALE-FREE NETWORK TO RANDOM AND TARGETED ATTACKS

2005 ◽  
Vol 19 (16) ◽  
pp. 785-792 ◽  
Author(s):  
JIAN-GUO LIU ◽  
ZHONG-TUO WANG ◽  
YAN-ZHONG DANG
Keyword(s):  
Network Design ◽  
Scale Free Network ◽  
Design Guideline ◽  
Scale Free ◽  
Targeted Attacks ◽  
Maximum Value ◽  
Scale Free Networks ◽  
Free Network ◽  
Random Failures ◽  
Connectivity Distribution

Scale-free networks, having connectivity distribution P(k)~k-α (where k is the site connectivity), are very resilient to random failures but are fragile to intentional attacks. The purpose of this paper is to find the network design guideline which can make the robustness of the network to both random failures and intentional attacks maximum while keeping the average connectivity <k> per node constant. We find that when <k> = 3 the robustness of the scale-free networks reach its maximum value if the minimal connectivity m = 1, but when <k> is larger than four, the networks will become more robust to random failures and targeted attacks as the minimal connectivity m gets larger.

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.

scholarly journals Effects of Resource Limitations and Cost Influences on Computer Virus Epidemic Dynamics and Tipping Points

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Chung-Yuan Huang ◽  
Chuen-Tsai Sun
Keyword(s):  
Computer Virus ◽  
Tipping Point ◽  
Tipping Points ◽  
Scale Free Network ◽  
Virus Infections ◽  
Scale Free ◽  
Epidemic Dynamics ◽  
Resource Limitations ◽  
Free Network ◽  
Network Power

One of the most important assessment indicators of computer virus infections is epidemic tipping point. Although many researchers have focused on the effects of scale-free network power-law connectivity distributions on computer virus epidemic dynamics and tipping points, few have comprehensively considered resource limitations and costs. Our goals for this paper are to show that (a) opposed to the current consensus, a significant epidemic tipping point does exist when resource limitations and costs are considered and (b) it is possible to control the spread of a computer virus in a scale-free network if resources are restricted and if costs associated with infection events are significantly increased.

The evolution of donations on scale-free networks during a COVID-19 breakout

2021 ◽  
Author(s):  
Xian-jia wang ◽  
Lin-lin wang
Keyword(s):  
Steady State ◽  
Public Goods ◽  
Scale Free Network ◽  
Initial State ◽  
Scale Free ◽  
The Public ◽  
Scale Free Networks ◽  
Population Sizes ◽  
Free Network ◽  
Selection Strength

Abstract Having a large number of timely donations during the early stages of a COVID-19 breakout would normally be considered rare. Donation is a special public goods game with zero yield, and it has the characteristics of prisoners’ dilemma. This paper discusses why timely donations in the early stages of COVID-19 occur. Based on the idea that donation is a strategy adopted by interconnected players on account of their understanding of the environment, donation-related populations are placed in social networks and the inter-correlation structure in the population is described by scale-free networks. Players in donation-related groups are of four types: donors, illegal beneficiaries, legal beneficiaries, and inactive people. We model the evolutionary game of donation on a scale-free network. Donors, illegal beneficiaries and inactive people learn and update strategies under the Fermi Update Rule, whereas the conversion between the legal beneficiaries and the other three strategies is determined by the environment surrounding the players. We study the evolution of cooperative action when the agglomeration coefficient, the parameters in the utility function, the selection strength parameter, the utility discount coefficient, the public goods discount coefficient and the initial state of the population in the scale-free network change. For population sizes of 50,100,150 and 200, we give the utility functions and the agglomeration coefficients for promoting cooperation. And we study the corresponding steady state and structural characteristics of the population. We identify the best ranges of selection strength K, the public goods discount coefficient α and the utility discount coefficient β for promoting cooperation at different population sizes. Furthermore, with an increase of the population size, the Donor Trap are found. At the same time, it is discovered that the initial state of the population has a great impact on the steady state; thus the Upper and Lower Triangle Phenomena are proposed. We also find that population size itself is also an important factor for promoting donation, pointing out the direction of efforts to further promote donation and achieve better social homeostasis under the donation model.

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