TOLERANCE OF SCALE-FREE NETWORKS UNDER DEGREE SEGMENT PROTECTION AND REMOVAL

2012 ◽  
Vol 26 (24) ◽  
pp. 1250156
Author(s):  
TAO FU ◽  
BO XU ◽  
YONG-AN ZHANG ◽  
YINI CHEN
Keyword(s):  
Power Law ◽  
Percolation Theory ◽  
Power Law Distribution ◽  
Degree Sum ◽  
Scale Free ◽  
Critical Node ◽  
Scale Free Networks ◽  
Node Protection ◽  
Node Removal ◽  
Removal Fraction

We study the tolerance of scale-free networks (following a power-law distribution P(k) = c⋅kα) under degree segment protection and removal. We use percolation theory to examine analytically and numerically the critical node removal fraction pc required for the disintegration of the network as well as the critical node protection fraction ppc necessary to immunize the network against the disintegration. We show that when degree segment protection is prior to degree segment removal and 2 ≤ α ≤3, scale-free networks are quite robust due to the extremely low value of ppc. Meanwhile, if we protect a degree segment with a fixed fraction of nodes, the threshold pc has a generally downward trend as the degree sum of the segment decreases, but it is not strictly monotonic.

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 The use of the power law for designing wireless networks

2018 ◽  
Vol 21 ◽  
pp. 00012
Author(s):  
Andrzej Paszkiewicz
Keyword(s):  
Wireless Networks ◽  
Power Law ◽  
Degree Distribution ◽  
Limited Resources ◽  
Random Networks ◽  
New Approach ◽  
Available Bandwidth ◽  
Scale Free ◽  
Scale Free Networks ◽  
Node Removal

The paper concerns the use of the scale-free networks theory and the power law in designing wireless networks. An approach based on generating random networks as well as on the classic Barabási-Albert algorithm were presented. The paper presents a new approach taking the limited resources for wireless networks into account, such as available bandwidth. In addition, thanks to the introduction of opportunities for dynamic node removal it was possible to realign processes occurring in wireless networks. After introduction of these modifications, the obtained results were analyzed in terms of a power law and the degree distribution of each node.

Second-order centrality correlation in scale-free networks

2015 ◽  
Vol 26 (10) ◽  
pp. 1550116 ◽  
Author(s):  
Meilei Lv ◽  
Xinling Guo ◽  
Jiaquan Chen ◽  
Zhe-Ming Lu ◽  
Tingyuan Nie
Keyword(s):  
Second Order ◽  
Degree Centrality ◽  
Apparent Difference ◽  
Power Law Distribution ◽  
Scale Free ◽  
Degree Correlation ◽  
Critical Nodes ◽  
Scale Free Networks ◽  
Node Removal ◽  
Assortative Network

Scale-free networks in which the degree displays a power-law distribution can be classified into assortative, disassortative, and neutral networks according to their degree–degree correlation. The second-order centrality proposed in a distributed computation manner is quick-calculated and accurate to identify critical nodes. We explore the second-order centrality correlation (SOC) for each type of the scale-free networks. The SOC–SOC correlation in assortative network and neutral network behaves similarly to the degree–degree correlation, while it behaves an apparent difference in disassortative networks. Experiments show that the invulnerability of most of scale-free networks behaves similarly under the node removal ordering by SOC centrality and degree centrality, respectively. The netscience network and the Yeast network behave a little differently because they are native disconnecting networks.

scholarly journals Scale-free networks with the power-law exponent between 1 and 3

2007 ◽  
Vol 56 (10) ◽  
pp. 5635
Author(s):  
Guo Jin-Li ◽  
Wang Li-Na
Keyword(s):  
Power Law ◽  
Scale Free ◽  
Power Law Exponent ◽  
Scale Free Networks

scholarly journals Modeling and Analysis of New Products Diffusion on Heterogeneous Networks

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Shuping Li ◽  
Zhen Jin
Keyword(s):  
Decision Making ◽  
Numerical Analysis ◽  
Power Law ◽  
Heterogeneous Networks ◽  
New Products ◽  
Positive Equilibrium ◽  
Modeling And Analysis ◽  
Scale Free ◽  
Scale Free Networks ◽  
Law Degree

We present a heterogeneous networks model with the awareness stage and the decision-making stage to explain the process of new products diffusion. If mass media is neglected in the decision-making stage, there is a threshold whether the innovation diffusion is successful or not, or else it is proved that the network model has at least one positive equilibrium. For networks with the power-law degree distribution, numerical simulations confirm analytical results, and also at the same time, by numerical analysis of the influence of the network structure and persuasive advertisements on the density of adopters, we give two different products propagation strategies for two classes of nodes in scale-free networks.

Effect of connection on transport between scale free networks

2017 ◽  
Vol 28 (05) ◽  
pp. 1750064 ◽  
Author(s):  
A. Ould Baba ◽  
O. Bamaarouf ◽  
A. Rachadi ◽  
H. Ez-Zahraouy
Keyword(s):  
Numerical Simulations ◽  
Power Law ◽  
Preferential Attachment ◽  
Electrical Conductance ◽  
Global Network ◽  
Scale Free ◽  
Scale Free Networks ◽  
Conductance Distribution

Using numerical simulations, we investigate the effects of the connectivity and topologies of network on the quality of transport between connected scale free networks. Hence, the flow as the electrical conductance between connected networks is calculated. It is found that the conductance distribution between networks follow a power law [Formula: see text] where [Formula: see text] is the exponent of the global Network of network, we show that the transport in the symmetric growing preferential attachment connection is more efficient than the symmetric static preferential attachment connection. Furthermore, the differences of transport and networks communications properties in the different cases are discussed.

Priority Weighted Fitness Model in Networks

2012 ◽  
Vol 229-231 ◽  
pp. 1854-1857
Author(s):  
Xin Yi Chen
Keyword(s):  
World Wide Web ◽  
Power Law ◽  
Common Property ◽  
World Wide ◽  
Genetic Networks ◽  
Power Law Distribution ◽  
Large Networks ◽  
Scale Free ◽  
The World ◽  
Complex Topology

Systems as diverse as genetic networks or the World Wide Web are best described as networks with complex topology. A common property of many large networks is that the vertex connectivities follow a power-law distribution. This feature was found to be a consequence of three generic mechanisms: (i) networks expand continuously by the addition of new vertices, (ii) new vertex with priority selected different edges of weighted selected that connected to different vertices in the system, and (iii) by the fitness probability that a new vertices attach preferentially to sites that are already well connected. A model based on these ingredients reproduces the observed stationary scale-free distributions, which indicates that the development of large networks is governed by robust self-organizing phenomena. Experiment results show that the model is more close to the actual Internet network.

scholarly journals SYNCHRONIZABILITY AND SYNCHRONIZATION DYNAMICS OF WEIGHED AND UNWEIGHED SCALE FREE NETWORKS WITH DEGREE MIXING

2007 ◽  
Vol 17 (07) ◽  
pp. 2419-2434 ◽  
Author(s):  
FRANCESCO SORRENTINO ◽  
MARIO DI BERNARDO ◽  
FRANCO GAROFALO
Keyword(s):  
Power Law ◽  
Biological Networks ◽  
Optimization Strategy ◽  
Power Law Distribution ◽  
Scale Free ◽  
Degree Correlation ◽  
Topological Features ◽  
Low Degree ◽  
Correlation Properties ◽  
Law Degree

We study the synchronizability and the synchronization dynamics of networks of nonlinear oscillators. We investigate how the synchronization of the network is influenced by some of its topological features such as variations of the power law degree distribution exponent γ and the degree correlation coefficient r. Using an appropriate construction algorithm based on clustering the network vertices in p classes according to their degrees, we construct networks with an assigned power law distribution but changing degree correlation properties. We find that the network synchronizability improves when the network becomes disassortative, i.e. when nodes with low degree are more likely to be connected to nodes with higher degree. We consider the case of both weighed and unweighed networks. The analytical results reported in the paper are then confirmed by a set of numerical observations obtained on weighed and unweighed networks of nonlinear Rössler oscillators. Using a nonlinear optimization strategy we also show that negative degree correlation is an emerging property of networks when synchronizability is to be optimized. This suggests that negative degree correlation observed experimentally in a number of physical and biological networks might be motivated by their need to synchronize better.

scholarly journals Ultra-small scale-free geometric networks

2006 ◽  
Vol 43 (3) ◽  
pp. 665-677 ◽  
Author(s):  
J. E. Yukich
Keyword(s):  
Long Range ◽  
Power Law ◽  
Degree Distribution ◽  
Small Scale ◽  
Graph Distance ◽  
Power Law Distribution ◽  
Scale Free

We consider a family of long-range percolation models (Gp)p>0on ℤdthat allow dependence between edges and have the following connectivity properties forp∈ (1/d, ∞): (i) the degree distribution of vertices inGphas a power-law distribution; (ii) the graph distance between pointsxandyis bounded by a multiple of logpdlogpd|x-y| with probability 1 -o(1); and (iii) an adversary can delete a relatively small number of nodes fromGp(ℤd∩ [0,n]d), resulting in two large, disconnected subgraphs.

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