scholarly journals Network robustness improvement via long-range links

2019 ◽  
Vol 6 (1) ◽  
Author(s):  
Vincenza Carchiolo ◽  
Marco Grassia ◽  
Alessandro Longheu ◽  
Michele Malgeri ◽  
Giuseppe Mangioni
Keyword(s):  
Complex Networks ◽  
Long Range ◽  
Real World ◽  
Network Robustness ◽  
Scale Free ◽  
Area Of Interest ◽  
Before And After ◽  
Significant Area ◽  
Better Than

AbstractMany systems are today modelled as complex networks, since this representation has been proven being an effective approach for understanding and controlling many real-world phenomena. A significant area of interest and research is that of networks robustness, which aims to explore to what extent a network keeps working when failures occur in its structure and how disruptions can be avoided. In this paper, we introduce the idea of exploiting long-range links to improve the robustness of Scale-Free (SF) networks. Several experiments are carried out by attacking the networks before and after the addition of links between the farthest nodes, and the results show that this approach effectively improves the SF network correct functionalities better than other commonly used strategies.

scholarly journals A Novel Edge Rewire Mechanism Based on Multiobjective Optimization for Network Robustness Enhancement

2021 ◽  
Vol 9 ◽  
Author(s):  
Zhaoxing Li ◽  
Qionghai Liu ◽  
Li Chen
Keyword(s):  
Multiobjective Optimization ◽  
Complex Networks ◽  
Optimization Algorithm ◽  
Real World ◽  
Network Robustness ◽  
Objective Functions ◽  
Swarm Optimization ◽  
Scale Free ◽  
Scale Free Networks ◽  
The Given

A complex network can crash down due to disturbances which significantly reduce the network’s robustness. It is of great significance to study on how to improve the robustness of complex networks. In the literature, the network rewire mechanism is one of the most widely adopted methods to improve the robustness of a given network. Existing network rewire mechanism improves the robustness of a given network by re-connecting its nodes but keeping the total number of edges or by adding more edges to the given network. In this work we propose a novel yet efficient network rewire mechanism which is based on multiobjective optimization. The proposed rewire mechanism simultaneously optimizes two objective functions, i.e., maximizing network robustness and minimizing edge rewire operations. We further develop a multiobjective discrete partite swarm optimization algorithm to solve the proposed mechanism. Compared to existing network rewire mechanisms, the developed mechanism has two advantages. First, the proposed mechanism does not require specific constraints on the rewire mechanism to the studied network, which makes it more feasible for applications. Second, the proposed mechanism can suggest a set of network rewire choices each of which can improve the robustness of a given network, which makes it be more helpful for decision makings. To validate the effectiveness of the proposed mechanism, we carry out experiments on computer-generated Erdős–Rényi and scale-free networks, as well as real-world complex networks. The results demonstrate that for each tested network, the proposed multiobjective optimization based edge rewire mechanism can recommend a set of edge rewire solutions to improve its robustness.

scholarly journals Power-law distribution of degree–degree distance: A better representation of the scale-free property of complex networks

2020 ◽  
Vol 117 (26) ◽  
pp. 14812-14818 ◽  
Author(s):  
Bin Zhou ◽  
Xiangyi Meng ◽  
H. Eugene Stanley
Keyword(s):  
Complex Networks ◽  
Complex Network ◽  
Power Law ◽  
Real World ◽  
Preferential Attachment ◽  
Statistical Tests ◽  
Finite Size ◽  
Distance Distribution ◽  
Scale Free ◽  
Degree Distance

Whether real-world complex networks are scale free or not has long been controversial. Recently, in Broido and Clauset [A. D. Broido, A. Clauset,Nat. Commun.10, 1017 (2019)], it was claimed that the degree distributions of real-world networks are rarely power law under statistical tests. Here, we attempt to address this issue by defining a fundamental property possessed by each link, the degree–degree distance, the distribution of which also shows signs of being power law by our empirical study. Surprisingly, although full-range statistical tests show that degree distributions are not often power law in real-world networks, we find that in more than half of the cases the degree–degree distance distributions can still be described by power laws. To explain these findings, we introduce a bidirectional preferential selection model where the link configuration is a randomly weighted, two-way selection process. The model does not always produce solid power-law distributions but predicts that the degree–degree distance distribution exhibits stronger power-law behavior than the degree distribution of a finite-size network, especially when the network is dense. We test the strength of our model and its predictive power by examining how real-world networks evolve into an overly dense stage and how the corresponding distributions change. We propose that being scale free is a property of a complex network that should be determined by its underlying mechanism (e.g., preferential attachment) rather than by apparent distribution statistics of finite size. We thus conclude that the degree–degree distance distribution better represents the scale-free property of a complex network.

Efficient weighting strategy for enhancing synchronizability of complex networks

2018 ◽  
Vol 32 (11) ◽  
pp. 1850128 ◽  
Author(s):  
Youquan Wang ◽  
Feng Yu ◽  
Shucheng Huang ◽  
Juanjuan Tu ◽  
Yan Chen
Keyword(s):  
Complex Networks ◽  
Structural Properties ◽  
Real World ◽  
Centrality Measures ◽  
Node Degree ◽  
Scale Free ◽  
High Propensity ◽  
Network Link ◽  
Weighting Strategy ◽  
Weighting Methods

Networks with high propensity to synchronization are desired in many applications ranging from biology to engineering. In general, there are two ways to enhance the synchronizability of a network: link rewiring and/or link weighting. In this paper, we propose a new link weighting strategy based on the concept of the neighborhood subgroup. The neighborhood subgroup of a node i through node j in a network, i.e. [Formula: see text], means that node u belongs to [Formula: see text] if node u belongs to the first-order neighbors of j (not include i). Our proposed weighting schema used the local and global structural properties of the networks such as the node degree, betweenness centrality and closeness centrality measures. We applied the method on scale-free and Watts–Strogatz networks of different structural properties and show the good performance of the proposed weighting scheme. Furthermore, as model networks cannot capture all essential features of real-world complex networks, we considered a number of undirected and unweighted real-world networks. To the best of our knowledge, the proposed weighting strategy outperformed the previously published weighting methods by enhancing the synchronizability of these real-world 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.

EFFECT OF CLIENT DEMANDS ON DESTRUCTIVENESS OF TARGETED ATTACKS IN DIRECTED WEIGHTED SCALE-FREE NETWORKS

2011 ◽  
Vol 25 (19) ◽  
pp. 1603-1617 ◽  
Author(s):  
LI-LI MA ◽  
XIN JIANG ◽  
ZHAN-LI ZHANG ◽  
ZHI-MING ZHENG
Keyword(s):  
Real World ◽  
Weight Distribution ◽  
Network Robustness ◽  
Network Nodes ◽  
Scale Free ◽  
Node Importance ◽  
Targeted Attacks ◽  
Link Weight ◽  
Scale Free Networks ◽  
Unique Mechanism

Network resilience is vital for the survival of networks, and scale-free networks are fragile when confronted with targeted attacks. We survey network robustness to targeted attacks from the viewpoint of network clients by designing a unique mechanism based on the undeniable roles of network clients in real-world networks. Especially, the mechanism here is designed on the actual phenomenon that the vital nodes in a network may be totally different for clients with different demands. Concretely, node client-demand centrality is proposed to quantify the contributions of nodes to network clients and we show that it is a proper index to assign an order to network nodes according to node importance for network clients. Great discrepancy of node importance order for clients with different demands is found in scale-free networks with four different kinds of link weight distribution, which suggests that the destructiveness of fatal attacks on networks can be greatly reduced by adjusting the demands of network clients.

scholarly journals Modularity affects the robustness of scale-free model and real-world social networks under betweenness and degree-based node attack

2021 ◽  
Vol 6 (1) ◽  
Author(s):  
Quang Nguyen ◽  
Tuan V. Vu ◽  
Hanh-Duyen Dinh ◽  
Davide Cassi ◽  
Francesco Scotognella ◽  
...  
Keyword(s):  
Social Networks ◽  
Community Structure ◽  
Real World ◽  
Ad Hoc ◽  
Modular Structure ◽  
Network Robustness ◽  
Node Degree ◽  
Percolation Transition ◽  
Scale Free ◽  
Model Networks

AbstractIn this paper we investigate how the modularity of model and real-world social networks affect their robustness and the efficacy of node attack (removal) strategies based on node degree (ID) and node betweenness (IB). We build Barabasi–Albert model networks with different modularity by a new ad hoc algorithm that rewire links forming networks with community structure. We traced the network robustness using the largest connected component (LCC). We find that when model networks present absent or low modular structure ID strategy is more effective than IB to decrease the LCC. Conversely, in the case the model network present higher modularity, the IB strategy becomes the most effective to fragment the LCC. In addition, networks with higher modularity present a signature of a 1st order percolation transition and a decrease of the LCC with one or several abrupt changes when nodes are removed, for both strategies; differently, networks with non-modular structure or low modularity show a 2nd order percolation transition networks when nodes are removed. Last, we investigated how the modularity of the network structure evaluated by the modularity indicator (Q) affect the network robustness and the efficacy of the attack strategies in 12 real-world social networks. We found that the modularity Q is negatively correlated with the robustness of the real-world social networks for both the node attack strategies, especially for the IB strategy (p-value < 0.001). This result indicates how real-world networks with higher modularity (i.e. with higher community structure) may be more fragile to node attack. The results presented in this paper unveil the role of modularity and community structure for the robustness of networks and may be useful to select the best node attack strategies in network.

scholarly journals Node diversification in complex networks by decentralized colouring

2018 ◽  
Vol 7 (4) ◽  
pp. 554-563 ◽  
Author(s):  
Richard Garcia-Lebron ◽  
David J Myers ◽  
Shouhuai Xu ◽  
Jie Sun
Keyword(s):  
Complex Networks ◽  
Complex Network ◽  
Real World ◽  
Local Information ◽  
Connected Component ◽  
Scale Free ◽  
Scale Free Networks

Abstract We develop a decentralized colouring approach to diversify the nodes in a complex network. The key is the introduction of a local conflict index (LCI) that measures the colour conflicts arising at each node which can be efficiently computed using only local information. We demonstrate via both synthetic and real-world networks that the proposed approach significantly outperforms random colouring as measured by the size of the largest colour-induced connected component. Interestingly, for scale-free networks further improvement of diversity can be achieved by tuning a degree-biasing weighting parameter in the LCI.

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 Identifying Vulnerable Nodes of Complex Networks in Cascading Failures Induced by Node-Based Attacks

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Shudong Li ◽  
Lixiang Li ◽  
Yan Jia ◽  
Xinran Liu ◽  
Yixian Yang
Keyword(s):  
Complex Networks ◽  
Real World ◽  
Small World ◽  
Cascading Failures ◽  
Small World Networks ◽  
Power Law Distribution ◽  
Scale Free ◽  
Potential Safety ◽  
High Degree ◽  
Fourth Kind

In the research on network security, distinguishing the vulnerable components of networks is very important for protecting infrastructures systems. Here, we probe how to identify the vulnerable nodes of complex networks in cascading failures, which was ignored before. Concerned with random attack (RA) and highest load attack (HL) on nodes, we model cascading dynamics of complex networks. Then, we introduce four kinds of weighting methods to characterize the nodes of networks including Barabási-Albert scale-free networks (SF), Watts-Strogatz small-world networks (WS), Erdos-Renyi random networks (ER), and two real-world networks. The simulations show that, for SF networks under HL attack, the nodes with small value of the fourth kind of weight are the most vulnerable and the ones with small value of the third weight are also vulnerable. Also, the real-world autonomous system with power-law distribution verifies these findings. Moreover, for WS and ER networks under both RA and HL attack, when the nodes have low tolerant ability, the ones with small value of the fourth kind of weight are more vulnerable and also the ones with high degree are easier to break down. The results give us important theoretical basis for digging the potential safety loophole and making protection strategy.

scholarly journals Measure for degree heterogeneity in complex networks and its application to recurrence network analysis

2017 ◽  
Vol 4 (1) ◽  
pp. 160757 ◽  
Author(s):  
Rinku Jacob ◽  
K. P. Harikrishnan ◽  
R. Misra ◽  
G. Ambika
Keyword(s):  
Time Series ◽  
Network Analysis ◽  
Complex Networks ◽  
Network Topology ◽  
Real World ◽  
Degree Distribution ◽  
Structural Complexity ◽  
Chaotic Attractors ◽  
Scale Free ◽  
Low Dimensional

We propose a novel measure of degree heterogeneity, for unweighted and undirected complex networks, which requires only the degree distribution of the network for its computation. We show that the proposed measure can be applied to all types of network topology with ease and increases with the diversity of node degrees in the network. The measure is applied to compute the heterogeneity of synthetic (both random and scale free (SF)) and real-world networks with its value normalized in the interval [ 0 , 1 ] . To define the measure, we introduce a limiting network whose heterogeneity can be expressed analytically with the value tending to 1 as the size of the network N tends to infinity. We numerically study the variation of heterogeneity for random graphs (as a function of p and N ) and for SF networks with γ and N as variables. Finally, as a specific application, we show that the proposed measure can be used to compare the heterogeneity of recurrence networks constructed from the time series of several low-dimensional chaotic attractors, thereby providing a single index to compare the structural complexity of chaotic attractors.

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