ENHANCING THE SYNCHRONIZABILITY OF SCALE-FREE NETWORKS BY ADDING EDGES

2010 ◽  
Vol 21 (01) ◽  
pp. 67-77 ◽  
Author(s):  
SHENG-JUN WANG ◽  
ZHI-XI WU ◽  
HAI-RONG DONG ◽  
GUANRONG CHEN
Keyword(s):  
Nearest Neighbors ◽  
Laplacian Matrix ◽  
New Method ◽  
Scale Free Network ◽  
Largest Eigenvalue ◽  
Scale Free ◽  
Scale Free Networks ◽  
Free Network ◽  
The Largest Eigenvalue

To efficiently enhance the synchronizability of a scale-free network by adding some edges, we numerically study the effect of edge-adding on the spectrum of the network Laplacian matrix. Based on the relation between the largest eigenvalue of the Laplacian matrix and the largest degree of the scale-free network, we show that adding a new edge to the node of largest degree will generally weaken the synchronizability of a scale-free network. We consequently propose a method to effectively enhance the network synchronizability by attaching the new edge to a node whose nearest-neighbors have small degrees. The effect of the new method is analyzed and demonstrated with comparisons.

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 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.

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.

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.

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.

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.

scholarly journals Designing efficient hybrid strategies for information spreading in scale-free networks

2018 ◽  
Vol 5 (8) ◽  
pp. 180117 ◽  
Author(s):  
Shuangyan Wang ◽  
Wuyi Cheng ◽  
Yang Hao
Keyword(s):  
Large Degree ◽  
Small Degree ◽  
Network Structures ◽  
Scale Free Network ◽  
Scale Free ◽  
Monte Carlo Experiments ◽  
Scale Free Networks ◽  
Critical Issues ◽  
Free Network ◽  
Information Spreading

Designing a spreading strategy is one of the critical issues strongly affecting spreading efficiency in complex networks. In this paper, to improve the efficiency of information spreading in scale-free networks, we propose four hybrid strategies by combining two basic strategies, i.e. (i) the LS (in which information is preferentially spread from the large-degree vertices to the small-degree ones), and (ii) the SL (in which information is preferentially spread from the small-degree vertices to the large-degree ones). The objective in combining the two basic LS and SL strategies is to fully exploit the advantages of both strategies. To evaluate the spreading efficiency of the proposed four hybrid strategies, we first propose an information spreading model. Then, we introduce the details of the proposed hybrid strategies that are formulated by combining LS and SL. Third, we build a set of scale-free network structures by differently configuring the relevant parameters. In addition, finally, we conduct various Monte Carlo experiments to examine the spreading efficiency of the proposed hybrid strategies in different scale-free network structures. Experimental results indicate that the proposed hybrid strategies are effective and efficient for spreading information in scale-free networks.

scholarly journals Exact Solutions of a Generalized Weighted Scale Free Network

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Li Tan ◽  
Dingyou Lei
Keyword(s):  
Random Processes ◽  
Analytic Solutions ◽  
Strength Distribution ◽  
Edge Weight ◽  
Scale Free Network ◽  
Scale Free ◽  
Scale Free Networks ◽  
Free Network ◽  
Vertex Degrees ◽  
Power Law Distributions

We investigate a class of generalized weighted scale-free networks, where the new vertex connects tompairs of vertices selected preferentially. The key contribution of this paper is that, from the standpoint of random processes, we provide rigorous analytic solutions for the steady state distributions, including the vertex degree distribution, the vertex strength distribution and the edge weight distribution. Numerical simulations indicate that this network model yields three power law distributions for the vertex degrees, vertex strengths and edge weights, respectively.

scholarly journals Bipartite subgraphs and the signless Laplacian matrix

2011 ◽  
Vol 5 (1) ◽  
pp. 1-13 ◽  
Author(s):  
Steve Kirkland ◽  
Debdas Paul
Keyword(s):  
Laplacian Matrix ◽  
Rayleigh Quotient ◽  
Scale Free Network ◽  
Power Law Distribution ◽  
Laplacian Eigenvalue ◽  
Scale Free ◽  
Protein Protein Interaction ◽  
Signless Laplacian Matrix ◽  
Signless Laplacian ◽  
Free Network

For a connected graph G, we derive tight inequalities relating the smallest signless Laplacian eigenvalue to the largest normalized Laplacian eigenvalue. We investigate how vectors yielding small values of the Rayleigh quotient for the signless Laplacian matrix can be used to identify bipartite subgraphs. Our results are applied to some graphs with degree sequences approximately following a power law distribution with exponent value 2:1 (scale-free networks), and to a scale-free network arising from protein-protein interaction.

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