scholarly journals Dynamical Recovery of Complex Networks under a Localised Attack

Algorithms ◽  
2021 ◽  
Vol 14 (9) ◽  
pp. 274
Author(s):  
Fan Wang ◽  
Gaogao Dong ◽  
Lixin Tian
Keyword(s):  
Complex Networks ◽  
Recovery Process ◽  
Local Failure ◽  
Network Activity ◽  
Scale Free ◽  
Failure Propagation ◽  
Free Network ◽  
Memory Characteristic ◽  
Dynamical Recovery ◽  
Insight Into

In real systems, some damaged nodes can spontaneously become active again when recovered from themselves or their active neighbours. However, the spontaneous dynamical recovery of complex networks that suffer a local failure has not yet been taken into consideration. To model this recovery process, we develop a framework to study the resilience behaviours of the network under a localised attack (LA). Since the nodes’ state within the network affects the subsequent dynamic evolution, we study the dynamic behaviours of local failure propagation and node recoveries based on this memory characteristic. It can be found that the fraction of active nodes switches back and forth between high network activity and low network activity, which leads to the spontaneous emergence of phase-flipping phenomena. These behaviours can be found in a random regular network, Erdős-Rényi network and Scale-free network, which shows that these three types of networks have the same or different resilience behaviours under an LA and random attack. These results will be helpful for studying the spontaneous recovery real systems under an LA. Our work provides insight into understanding the recovery process and a protection strategy of various complex systems from the perspective of damaged memory.

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.

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 SZNAJD MODEL WITH SYNCHRONOUS UPDATING ON COMPLEX NETWORKS

2005 ◽  
Vol 16 (07) ◽  
pp. 1149-1161 ◽  
Author(s):  
YU-SONG TU ◽  
A. O. SOUSA ◽  
LING-JIANG KONG ◽  
MU-REN LIU
Keyword(s):  
Complex Networks ◽  
Small World ◽  
System Size ◽  
The State ◽  
Clustering Coefficient ◽  
Square Lattice ◽  
Node Degree ◽  
Scale Free ◽  
Free Network ◽  
Formation Step

We analyze the evolution of Sznajd Model with synchronous updating in several complex networks. Similar to the model on square lattice, we have found a transition between the state with nonconsensus and the state with complete consensus in several complex networks. Furthermore, by adjusting the network parameters, we find that a large clustering coefficient does not favor development of a consensus. In particular, in the limit of large system size with the initial concentration p =0.5 of opinion +1, a consensus seems to be never reached for the Watts–Strogatz small-world network, when we fix the connectivity k and the rewiring probability ps; nor for the scale-free network, when we fix the minimum node degree m and the triad formation step probability pt.

A FAST ESTIMATION ALGORITHM OF COMMUNITY NUMBER IN LARGE SCALE-FREE COMPLEX NETWORKS

2014 ◽  
Vol 28 (04) ◽  
pp. 1450039 ◽  
Author(s):  
PEIHUA FU ◽  
SHAN'AN ZHU ◽  
ANDING ZHU ◽  
XIAO DONG
Keyword(s):  
Complex Networks ◽  
Large Scale ◽  
Optimal Parameter ◽  
Estimation Algorithm ◽  
Large Degree ◽  
Terminal Condition ◽  
Scale Free Network ◽  
Scale Free ◽  
Core Node ◽  
Free Network

In conventional community detecting algorithms, the community number is always a bypass product and cannot be estimated before partitioning. Since partitioning large scale and dynamic complex networks takes exhausting computation, the community number sometimes can be a terminal condition of iterations or a preset optimal parameter for speeding up partitioning algorithms. This paper assumes that communities are organized around the center of core nodes in a scale-free network. A separability function is built to dichotomize nodes into two classes and the class of large degree nodes is selected as the core node candidate set. An improved shortest path seeking algorithm is applied to remove the closest neighbors of a specific core node. The number of remaining core nodes is then the estimated number of communities. Experiments of real world scale-free networks and computer generated networks show that the results are very close to the well-proven results.

The Dynamics on Single Networks

2018 ◽  
Author(s):  
Ginestra Bianconi
Keyword(s):  
Complex Networks ◽  
Diffusion Processes ◽  
Network Dynamics ◽  
Dynamical Behaviour ◽  
Emergent Properties ◽  
Epidemic Spreading ◽  
Scale Free ◽  
Free Network ◽  
The Rich ◽  
And Function

This chapter provides the relevant background on the network dynamics of complex networks formed by just one layer (single networks). Emergent properties of network dynamics are characterized using the framework of phase transitions. The major results on robustness of complex networks, percolation theory and epidemic spreading are presented, revealing the rich interplay between network structure and function. In this context particular emphasis is given to the implications of the scale-free network topology on these dynamical processes. Diffusion processes and synchronization and controllability are characterized on networks, revealing the relevance of spectral properties and peripheral nodes for determining their dynamical behaviour.

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 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.

Node influence identification via resource allocation dynamics

2014 ◽  
Vol 25 (11) ◽  
pp. 1450065 ◽  
Author(s):  
Shu-Jiao Ma ◽  
Zhuo-Ming Ren ◽  
Chun-Ming Ye ◽  
Qiang Guo ◽  
Jian-Guo Liu
Keyword(s):  
Resource Allocation ◽  
Complex Networks ◽  
Network Structure ◽  
Decomposition Method ◽  
Scale Free Network ◽  
Improved Method ◽  
Exponential Form ◽  
Ranking List ◽  
Scale Free ◽  
Free Network

Identifying the node influence in complex networks is an important task to optimally use the network structure and ensure the more efficient spreading in information. In this paper, by taking into account the resource allocation dynamics (RAD) and the k-shell decomposition method, we present an improved method namely RAD to generate the ranking list to evaluate the node influence. First, comparing with the epidemic process results for four real networks, the RAD method could identify the node influence more accurate than the ones generated by the topology-based measures including the degree, k-shell, closeness and the betweenness. Then, a growing scale-free network model with tunable assortative coefficient is introduced to analyze the effect of the assortative coefficient on the accuracy of the RAD method. Finally, the positive correlation is found between the RAD method and the k-shell values which display an exponential form. This work would be helpful for deeply understanding the node influence of a network.

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.

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.

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