CONSENSUS PROBLEMS IN SCALE-FREE NETWORK

2008 ◽  
Vol 22 (04) ◽  
pp. 435-445 ◽  
Author(s):  
ZHENGPING WU ◽  
ZHI-HONG GUAN
Keyword(s):  
Nearest Neighbor ◽  
Network Size ◽  
Average Degree ◽  
Consensus Problem ◽  
Scale Free Network ◽  
Scale Free ◽  
Free Network ◽  
Heterogeneity Parameter ◽  
Edge Failure ◽  
The Relationship

Recent advances in complex network research have stimulated increasing interest in understanding the relationship between the topology and dynamics of complex networks. In this paper, we investigate the consensus problem in a class of scale-free network with a heterogeneity parameter. It is found that, for a scale-free network, the time to reach a consensus is hundreds of times shorter than that of the nearest-neighbor coupled network with the same average degree and network size, and its robustness to the node-failure and edge-failure is increased at the same time. Furthermore, as the scale-free network becomes more homogenous, or its average degree becomes larger, the time to reach a consensus will become shorter, but not notably shorter. Therefore, the scale-free network with a larger exponent r and average degree k is a better choice to obtain a faster convergence speed in the consensus problem.

scholarly journals SCALE-FREE NETWORK THEORY IN STUDYING THE STRUCTURE OF THE ROAD NETWORK IN POLAND

2014 ◽  
Vol 26 (3) ◽  
pp. 235-242 ◽  
Author(s):  
Katarzyna KOCUR-BERA
Keyword(s):  
Statistical Analysis ◽  
Traffic Flow ◽  
Network Theory ◽  
Road Network ◽  
Scale Free Network ◽  
Scale Free ◽  
The Road ◽  
Normal Character ◽  
Free Network ◽  
The Relationship

This paper discusses the issue of statistical analysis of traffic flow in different regions of Poland. Such analysis allows us to identify “valuable (sensitive) areas” whose damage or blockage may provoke considerable disturbances or even a stoppage of traffic flow in the examined road network. The results of the studies indicate that the road network in Poland has the properties of a scale-free network. The distribution of the examined variables does not have a normal character, whereas the relationship between the number of nodes and the number of connections is a power-law feature. 

scholarly journals Quantitative Controllability Index of Complex Networks

2018 ◽  
Vol 2018 ◽  
pp. 1-9
Author(s):  
Lifu Wang ◽  
Yali Zhang ◽  
Jingxiao Han ◽  
Zhi Kong
Keyword(s):  
Complex Networks ◽  
Condition Number ◽  
Random Network ◽  
Small World ◽  
Scale Free Network ◽  
Scale Free ◽  
Network Topologies ◽  
Free Network ◽  
The Relationship ◽  
Controllability Index

In this paper, the controllability issue of complex network is discussed. A new quantitative index using knowledge of control centrality and condition number is constructed to measure the controllability of given networks. For complex networks with different controllable subspace dimensions, their controllability is mainly determined by the control centrality factor. For the complex networks that have the equal controllable subspace dimension, their different controllability is mostly determined by the condition number of subnetworks’ controllability matrix. Then the effect of this index is analyzed based on simulations on various types of network topologies, such as ER random network, WS small-world network, and BA scale-free network. The results show that the presented index could reflect the holistic controllability of complex networks. Such an endeavour could help us better understand the relationship between controllability and network topology.

scholarly journals Characterizing the intrinsic correlations of scale-free networks

2016 ◽  
Vol 27 (03) ◽  
pp. 1650024 ◽  
Author(s):  
J. B. de Brito ◽  
C. I. N. Sampaio Filho ◽  
A. A. Moreira ◽  
J. S. Andrade
Keyword(s):  
Extreme Values ◽  
Network Models ◽  
Network Size ◽  
Scale Free Network ◽  
Scale Free ◽  
Scale Free Networks ◽  
Free Network ◽  
Degree Correlations ◽  
Multiple Edges ◽  
Random Scale

When studying topological or dynamical properties of random scale-free networks, it is tacitly assumed that degree–degree correlations are not present. However, simple constraints, such as the absence of multiple edges and self-loops, can give rise to intrinsic correlations in these structures. In the same way that Fermionic correlations in thermodynamic systems are relevant only in the limit of low temperature, the intrinsic correlations in scale-free networks are relevant only when the extreme values for the degrees grow faster than the square root of the network size. In this situation, these correlations can significantly affect the dependence of the average degree of the nearest neighbors of a given vertex on this vertices degree. Here, we introduce an analytical approach that is capable to predict the functional form of this property. Moreover, our results indicate that random scale-free network models are not self-averaging, that is, the second moment of their degree distribution may vary orders of magnitude among different realizations. Finally, we argue that the intrinsic correlations investigated here may have profound impact on the critical properties of random scale-free networks.

On Link Density and Network Synchronization in Scale-Free Network

2013 ◽  
Vol 380-384 ◽  
pp. 2276-2279
Author(s):  
Wen Wei Liu ◽  
Dan Wang
Keyword(s):  
Network Size ◽  
Type I ◽  
Type Ii ◽  
Scale Free Network ◽  
Network Synchronization ◽  
Scale Free ◽  
Weighted Networks ◽  
Link Density ◽  
Free Network

The relations between link density and network synchronizability based on scale-free weighted networks is investigated. In this work, it shows that synchronizability of networks Type I decrease along with the increases of link density, when the netwrok size is fixed. While the synchronizability of networks Type II is remarkable decreased by enhancing the link density with different network size.

TIME-DELAY ROBUSTNESS OF CONSENSUS PROBLEMS IN REGULAR AND COMPLEX NETWORKS

2007 ◽  
Vol 18 (08) ◽  
pp. 1339-1350 ◽  
Author(s):  
ZHENGPING WU ◽  
ZHI-HONG GUAN
Keyword(s):  
Time Delay ◽  
Complex Networks ◽  
Nearest Neighbor ◽  
Small World ◽  
Node Degree ◽  
Small World Network ◽  
Scale Free Network ◽  
Star Network ◽  
Scale Free ◽  
Free Network

Recent advances in complex network research have stimulated increasing interests in understanding the relationship between the topology and dynamics of complex networks. Based on the theory of complex networks and computer simulation, we analyze the robustness to time-delay in linear consensus problem with different network topologies, such as global coupled network, star network, nearest-neighbor coupled network, small-world network, and scale-free network. It is found that global coupled network, star network, and scale-free network are vulnerable to time-delay, while nearest-neighbor coupled network and small-world network are robust to time-delay. And it is found that the maximum node degree of the network is a good predictor for time-delay robustness. And it is found that the robustness to time-delay can be improved significantly by a decoupling process to a small part of edges in scale-free network.

scholarly journals Evolution of Conformity Dynamics in Complex Social Networks

Symmetry ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 299 ◽  
Author(s):  
Yuhui Gong ◽  
Qian Yu
Keyword(s):  
Social Networks ◽  
Random Network ◽  
Small World ◽  
Network Size ◽  
Small World Network ◽  
Scale Free Network ◽  
Small World Networks ◽  
Dominant Group ◽  
Scale Free ◽  
Free Network

Conformity is a common phenomenon among people in social networks. In this paper, we focus on customers’ conformity behaviors in a symmetry market where customers are located in a social network. We establish a conformity model and analyze it in ring network, random network, small-world network, and scale-free network. Our simulations shown that topology structure, network size, and initial market share have significant effects on the evolution of customers’ conformity behaviors. The market will likely converge to a monopoly state in small-world networks but will form a duopoly market in scale networks. As the size of the network increases, there is a greater possibility of forming a dominant group of preferences in small-world network, and the market will converge to the monopoly of the product which has the initial selector in the market. Also, network density will become gradually significant in small-world networks.

Research on new evolution model of scale-free network

2009 ◽  
Vol 29 (5) ◽  
pp. 1230-1232
Author(s):  
Hao RAO ◽  
Chun YANG ◽  
Shao-hua TAO
Keyword(s):  
Evolution Model ◽  
Scale Free Network ◽  
Scale Free ◽  
Free Network
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