CASCADING FAILURES IN BARABÁSI–ALBERT SCALE-FREE NETWORKS WITH A BREAKDOWN PROBABILITY

2009 ◽  
Vol 20 (04) ◽  
pp. 585-595 ◽  
Author(s):  
JIAN-WEI WANG ◽  
LI-LI RONG
Keyword(s):  
Theoretical Analysis ◽  
Numerical Simulations ◽  
Cascading Failures ◽  
Scale Free ◽  
Scale Free Networks ◽  
Initial Load ◽  
Breakdown Probability ◽  
Proportional Relationship ◽  
Simulation Results ◽  
Failed Node

In this paper, adopting the initial load of a node j to be [Formula: see text], where kj is the degree of the node j and α is a tunable parameter that controls the strength of the initial load of a node, we propose a cascading model with a breakdown probability and explore cascading failures on a typical network, i.e., the Barabási–Albert (BA) network with scale-free property. Assume that a failed node leads only to a redistribution of the load passing through it to its neighboring nodes. According to the simulation results, we find that BA networks reach the strongest robustness level against cascading failures when α = 1 and the robustness of networks has a positive correlation with the average degree 〈k〉, not relating to the different breakdown probabilities. In addition, it is found that the robustness against cascading failures has an inversely proportional relationship with the breakdown probability of an overload node. Finally, the numerical simulations are verified by the theoretical analysis.

VULNERABILITY OF EFFECTIVE ATTACK ON EDGES IN SCALE-FREE NETWORKS DUE TO CASCADING FAILURES

2009 ◽  
Vol 20 (08) ◽  
pp. 1291-1298 ◽  
Author(s):  
JIAN-WEI WANG ◽  
LI-LI RONG
Keyword(s):  
Theoretical Prediction ◽  
Numerical Simulations ◽  
Real Life ◽  
Network Robustness ◽  
Critical Threshold ◽  
Cascading Failure ◽  
Cascading Failures ◽  
Scale Free ◽  
Scale Free Networks ◽  
Initial Load

Assume the initial load of an edge ij in a network to be Lij =[(ki ∑a ∈ Γi ka)(kj ∑b ∈ Γj kb)]α with ki and kj being the degrees of the nodes connected by the edge, where α is a tunable parameter which controls the strength of the edge initial load, and Γi and Γj are the sets of neighboring nodes of i and j, respectively. We investigate the cascading phenomenon of uncorrelated scale-free networks subject to two different attacking strategies on edges, i.e. attacking on the edges with the highest loads or the lowest loads (LL). By the critical threshold of edge capacity quantifying the network robustness, we numerically discuss the effects of two attacks for the network vulnerability. Interestingly, it is found that the attack on the edge with the LL is highly effective in disrupting the structure of the attacked network when α < 0.5. In the case of α = 0.5, the effects of two attacks for the network robustness against cascading failures are almost identical. We furthermore provide the theoretical prediction support for the numerical simulations. These results may be very helpful for real-life networks to protect the key edges selected effectively to avoid cascading-failure-induced disasters.

scholarly journals Modelling cascading failures in networks with the harmonic closeness

PLoS ONE ◽  
2021 ◽  
Vol 16 (1) ◽  
pp. e0243801
Author(s):  
Yucheng Hao ◽  
Limin Jia ◽  
Yanhui Wang ◽  
Zhichao He
Keyword(s):  
Small World ◽  
Adjustable Parameter ◽  
Cascading Failures ◽  
Small World Networks ◽  
Scale Free ◽  
Low Load ◽  
Scale Free Networks ◽  
Initial Load ◽  
The Impact ◽  
Valuable Result

Many studies on cascading failures adopt the degree or the betweenness of a node to define its load. From a novel perspective, we propose an approach to obtain initial loads considering the harmonic closeness and the impact of neighboring nodes. Based on simulation results for different adjustable parameter θ, local parameter δ and proportion of attacked nodes f, it is found that in scale-free networks (SF networks), small-world networks (SW networks) and Erdos-Renyi networks (ER networks), there exists a negative correlation between optimal θ and δ. By the removal of the low load node, cascading failures are more likely to occur in some cases. In addition, we find a valuable result that our method yields better performance compared with other methods in SF networks with an arbitrary f, SW and ER networks with large f. Moreover, the method concerning the harmonic closeness makes these three model networks more robust for different average degrees. Finally, we perform the simulations on twenty real networks, whose results verify that our method is also effective to distribute the initial load in different real networks.

Robustness of complex networks with both unidirectional and bidirectional links against cascading failures

2017 ◽  
Vol 31 (27) ◽  
pp. 1750252 ◽  
Author(s):  
Lin Ding ◽  
Victor C. M. Leung ◽  
Min-Sheng Tan
Keyword(s):  
Complex Networks ◽  
Low Cost ◽  
Small World ◽  
Network Robustness ◽  
Cascading Failures ◽  
Small World Networks ◽  
Scale Free ◽  
Scale Free Networks ◽  
Simulation Results ◽  
Direction Determining

The robustness of complex networks against cascading failures has been of great interest, while most of the researchers have considered undirected networks. However, to be more realistic, a part of links of many real systems should be described as unidirectional. In this paper, by applying three link direction-determining (DD) strategies, the tolerance of cascading failures is investigated in various networks with both unidirectional and bidirectional links. By extending the utilization of a classical global betweenness method, we propose a new cascading model, taking into account the weights of nodes and the directions of links. Then, the effects of unidirectional links on the network robustness against cascaded attacks are examined under the global load-based distribution mechanism. The simulation results show that the link-directed methods could not always lead to the decrease of the network robustness as indicated in the previous studies. For small-world networks, these methods certainly make the network weaker. However, for scale-free networks, the network robustness can be significantly improved by the link-directed method, especially for the method with non-random DD strategies. These results are independent of the weight parameter of the nodes. Due to the strongly improved robustness and easy realization with low cost on networks, the method for enforcing proper links to the unidirectional ones may be useful for leading to insights into the control of cascading failures in real-world networks, like communication and transportation networks.

scholarly journals On ISRC Rumor Spreading Model for Scale-Free Networks with Self-Purification Mechanism

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Zijun Wang ◽  
An Chen
Keyword(s):  
Numerical Simulations ◽  
Model Parameters ◽  
Rumor Spreading ◽  
Scale Free ◽  
Spreading Model ◽  
Scale Free Networks ◽  
Simulation Results ◽  
Key Indicators ◽  
The Impact

At present, the feasibility of using self-purification mechanism to inhibit rumor spreading has been confirmed by studies from different perspectives. This paper improves the classical rumor spreading models with self-purification mechanism, analyzes the correlation between spreading threshold in the model and its self-purification level theoretically, and conducts numerical simulations to study the impact of the changes of model parameters on key indicators in the process of rumor spreading. The simulation results show that changes of model parameters, including self-purification level and forgetting rate, exert significant influences on rumor spreading exactly.

EFFECT OF ATTACK ON SCALE-FREE NETWORKS DUE TO CASCADING FAILURE

2009 ◽  
Vol 23 (12) ◽  
pp. 1577-1587 ◽  
Author(s):  
JIAN-WEI WANG ◽  
LI-LI RONG ◽  
LIANG ZHANG
Keyword(s):  
Real Life ◽  
Critical Threshold ◽  
Cascading Failure ◽  
Cascading Failures ◽  
Scale Free ◽  
Scale Free Networks ◽  
The One ◽  
Random Removal ◽  
Random Failures ◽  
Failed Node

In this paper, based on the local preferential redistribution rule of the load after removing a node, we propose a cascading model and explore cascading failures on scale-free networks. Assuming that a failed node leads only to a redistribution of the load passing through it to its neighboring nodes, we study the response of scale-free networks subject to attacks on nodes. The network robustness against cascading failures is quantitatively measured by the critical threshold Tc, at which a phase transition occurs from normal state to collapse. For each case of attacks on nodes, four different attack strategies are used: removal by the descending order of the degree, attack by the ascending order of the degree, random removal of breakdown, and removal by the ascending order of the average degree of neighboring nodes of a broken node. Compared with the previous result, i.e. the robust-yet-fragile property of scale-free networks on random failures of nodes and intentional attacks, our cascading model has totally different and interesting results. On the one hand, as unexpected, choosing the node with the lowest degree is more efficient than the one with the highest degree when α < 1, which is a tunable parameter in our model. On the other hand, the robustness against cascading failures and the harm order of four attack strategies strongly depends on the parameter α. These results may be very helpful for real-life networks to protect the key nodes and avoid cascading-failure-induced disasters.

Impact of core-periphery structure on cascading failures in interdependent scale-free networks

2019 ◽  
Vol 383 (7) ◽  
pp. 607-616 ◽  
Author(s):  
Zhengcheng Dong ◽  
Meng Tian ◽  
Yuxin Lu ◽  
Jingang Lai ◽  
Ruoli Tang ◽  
...  
Keyword(s):  
Cascading Failures ◽  
Scale Free ◽  
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.

scholarly journals Controllability and Optimization of Complex Networks Based on Bridges

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Lifu Wang ◽  
Guotao Zhao ◽  
Zhi Kong ◽  
Yunkang Zhao
Keyword(s):  
Complex Networks ◽  
Complex Network ◽  
Betweenness Centrality ◽  
The Other ◽  
Connected Components ◽  
Scale Free ◽  
Scale Free Networks ◽  
Model Networks ◽  
Simulation Results ◽  
And Control

In a complex network, each edge has different functions on controllability of the whole network. A network may be out of control due to failure or attack of some specific edges. Bridges are a kind of key edges whose removal will disconnect a network and increase connected components. Here, we investigate the effects of removing bridges on controllability of network. Various strategies, including random deletion of edges, deletion based on betweenness centrality, and deletion based on degree of source or target nodes, are used to compare with the effect of removing bridges. It is found that the removing bridges strategy is more efficient on reducing controllability than the other strategies of removing edges for ER networks and scale-free networks. In addition, we also found the controllability robustness under edge attack is related to the average degree of complex networks. Therefore, we propose two optimization strategies based on bridges to improve the controllability robustness of complex networks against attacks. The effectiveness of the proposed strategies is demonstrated by simulation results of some model networks. These results are helpful for people to understand and control spreading processes of epidemic across different paths.

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