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 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.

scholarly journals The Evolution of Price Competition Game on Complex Networks

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-13
Author(s):  
Feng Jie Xie ◽  
Jing Shi
Keyword(s):  
Complex Networks ◽  
Real World ◽  
Price Competition ◽  
Small World ◽  
Square Lattice ◽  
Small World Network ◽  
Scale Free Network ◽  
The Real ◽  
Scale Free ◽  
Free Network

The well-known “Bertrand paradox” describes a price competition game in which two competing firms reach an outcome where both charge a price equal to the marginal cost. The fact that the Bertrand paradox often goes against empirical evidences has intrigued many researchers. In this work, we study the game from a new theoretical perspective—an evolutionary game on complex networks. Three classic network models, square lattice, WS small-world network, and BA scale-free network, are used to describe the competitive relations among the firms which are bounded rational. The analysis result shows that full price keeping is one of the evolutionary equilibriums in a well-mixed interaction situation. Detailed experiment results indicate that the price-keeping phenomenon emerges in a square lattice, small-world network and scale-free network much more frequently than in a complete network which represents the well-mixed interaction situation. While the square lattice has little advantage in achieving full price keeping, the small-world network and the scale-free network exhibit a stronger capability in full price keeping than the complete network. This means that a complex competitive relation is a crucial factor for maintaining the price in the real world. Moreover, competition scale, original price, degree of cutting price, and demand sensitivity to price show a significant influence on price evolution on a complex network. The payoff scheme, which describes how each firm’s payoff is calculated in each round game, only influences the price evolution on the scale-free network. These results provide new and important insights for understanding price competition in the real world.

scholarly journals Eigenvalue-based entropy in directed complex networks

PLoS ONE ◽  
2021 ◽  
Vol 16 (6) ◽  
pp. e0251993
Author(s):  
Yan Sun ◽  
Haixing Zhao ◽  
Jing Liang ◽  
Xiujuan Ma
Keyword(s):  
Complex Networks ◽  
Complex Network ◽  
Network Models ◽  
Small World ◽  
Laplacian Matrix ◽  
Directed Network ◽  
Small World Network ◽  
Scale Free Network ◽  
Scale Free ◽  
Free Network

Entropy is an important index for describing the structure, function, and evolution of network. The existing research on entropy is primarily applied to undirected networks. Compared with an undirected network, a directed network involves a special asymmetric transfer. The research on the entropy of directed networks is very significant to effectively quantify the structural information of the whole network. Typical complex network models include nearest-neighbour coupling network, small-world network, scale-free network, and random network. These network models are abstracted as undirected graphs without considering the direction of node connection. For complex networks, modeling through the direction of network nodes is extremely challenging. In this paper, based on these typical models of complex network, a directed network model considering node connection in-direction is proposed, and the eigenvalue entropies of three matrices in the directed network is defined and studied, where the three matrices are adjacency matrix, in-degree Laplacian matrix and in-degree signless Laplacian matrix. The eigenvalue-based entropies of three matrices are calculated in directed nearest-neighbor coupling, directed small world, directed scale-free and directed random networks. Through the simulation experiment on the real directed network, the result shows that the eigenvalue entropy of the real directed network is between the eigenvalue entropy of directed scale-free network and directed small-world network.

CONGESTION AND EFFICIENCY IN COMPLEX TRAFFIC NETWORKS

2013 ◽  
Vol 24 (10) ◽  
pp. 1350072 ◽  
Author(s):  
JIAN-FENG ZHENG ◽  
ZHI-HONG ZHU ◽  
HAO-MING DU ◽  
ZI-YOU GAO
Keyword(s):  
Complex Networks ◽  
Small World ◽  
Traffic Networks ◽  
Flow State ◽  
Traffic Demand ◽  
Scale Free ◽  
Link Cost ◽  
Network Topologies ◽  
The Impact ◽  
The Relationship

This paper investigates the degree of congestion and efficiency in complex traffic networks, by introducing congestion effects, which can be described by flow-based link cost functions. Different network topologies including random networks, small-world networks and scale-free networks are explored. The impact of different distributions of capacity and origin-destination traffic demand on the degree of congestion and efficiency in complex networks is mainly studied. A phase transition from free flow state to traffic jams can be uncovered. The relationship between congestion and efficiency in complex networks is also discussed.

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.

RISK ASSESSMENT OF ATTACK-INDUCED CASCADE IN COMPLEX NETWORKS

2011 ◽  
Vol 22 (08) ◽  
pp. 765-773
Author(s):  
ZHE-JING BAO ◽  
WEN-JUN YAN ◽  
CHUANG-XIN GUO
Keyword(s):  
Risk Assessment ◽  
Complex Networks ◽  
Quantitative Evaluation ◽  
Small World ◽  
Random Networks ◽  
Small World Network ◽  
Scale Free Network ◽  
Scale Free ◽  
Probability Of Occurrence ◽  
Free Network

For the complex networks, including scale-free, small-world, local-world and random networks, the global quantitative evaluation of attack-induced cascade is investigated in this paper by introducing the risk assessment, which integrates the probability of occurrence with the damage size of attacks on nodes. It is discovered by simulations, among the several kinds of networks, that the small-world network has the largest risk assessment of attack-induced cascade; the risk assessment of three other networks are all very low and the most protection against attack should be given to the small-world network accordingly. Furthermore, the percentage of the most fragile nodes in the scale-free network is very low, compared with that in the small-world network.

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.

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