scholarly journals Optimal shattering of complex networks

2019 ◽  
Vol 4 (1) ◽  
Author(s):  
Nicole Balashov ◽  
Reuven Cohen ◽  
Avieli Haber ◽  
Michael Krivelevich ◽  
Simi Haber
Keyword(s):  
Complex Networks ◽  
Random Graphs ◽  
Polynomial Time ◽  
Optimal Performance ◽  
Regular Graphs ◽  
Scale Free ◽  
Scale Free Networks ◽  
Minimum Number

Abstract We consider optimal attacks or immunization schemes on different models of random graphs. We derive bounds for the minimum number of nodes needed to be removed from a network such that all remaining components are fragments of negligible size.We obtain bounds for different regimes of random regular graphs, Erdős-Rényi random graphs, and scale free networks, some of which are tight. We show that the performance of attacks by degree is bounded away from optimality.Finally we present a polynomial time attack algorithm and prove its optimal performance in certain cases.

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.

The Scale-Free Characteristics of the Micro-Blog Community

2013 ◽  
Vol 278-280 ◽  
pp. 2118-2122
Author(s):  
Bo Wang ◽  
Meng Jia Zhao ◽  
Sheng Li
Keyword(s):  
Complex Networks ◽  
Complex Network ◽  
Government Policies ◽  
Scale Free ◽  
Scale Free Networks

The micro-blog community is the complex composed of many nodes. Based on interrelated theory of complex networks, this paper constructs the micro-blog community complex network by taking users as nodes, relationship between users as edges, then analyzes the scale-free features and shows that micro-blog community fits the two main characteristics of scale-free networks. Finally from the aspects of government policies、operators and users, putting forward some suggestions about micro-blog community according to its scale-free characteristics in order to let micro-blog play a better role in society.

Propagation and stability in software: A complex network perspective

2015 ◽  
Vol 26 (05) ◽  
pp. 1550052 ◽  
Author(s):  
Lei Wang ◽  
Ping Wang
Keyword(s):  
Software Engineering ◽  
Complex Networks ◽  
Large Scale ◽  
Structural Difference ◽  
Small World ◽  
Change Propagation ◽  
Small World Networks ◽  
Typical Structure ◽  
Scale Free ◽  
Scale Free Networks

In this paper, we attempt to understand the propagation and stability feature of large-scale complex software from the perspective of complex networks. Specifically, we introduced the concept of "propagation scope" to investigate the problem of change propagation in complex software. Although many complex software networks exhibit clear "small-world" and "scale-free" features, we found that the propagation scope of complex software networks is much lower than that of small-world networks and scale-free networks. Furthermore, because the design of complex software always obeys the principles of software engineering, we introduced the concept of "edge instability" to quantify the structural difference among complex software networks, small-world networks and scale-free networks. We discovered that the edge instability distribution of complex software networks is different from that of small-world networks and scale-free networks. We also found a typical structure that contributes to the edge instability distribution of complex software networks. Finally, we uncovered the correlation between propagation scope and edge instability in complex networks by eliminating the edges with different instability ranges.

THE GINI COEFFICIENT'S APPLICATION TO GENERAL COMPLEX NETWORKS

2005 ◽  
Vol 08 (01) ◽  
pp. 159-167 ◽  
Author(s):  
HAI-BO HU ◽  
LIN WANG
Keyword(s):  
Income Inequality ◽  
Complex Networks ◽  
Network Structure ◽  
Gini Coefficient ◽  
Scale Free ◽  
The Gini Coefficient ◽  
Scale Free Networks ◽  
General Complex

The Gini coefficient, which was originally used in microeconomics to describe income inequality, is introduced into the research of general complex networks as a metric on the heterogeneity of network structure. Some parameters such as degree exponent and degree-rank exponent were already defined in the case of scale-free networks also as a metric on the heterogeneity. In scale-free networks, the Gini coefficient is proved to be equivalent to the parameters mentioned above, and moreover, a classification of infinite scale-free networks is given according to the value of the Gini coefficient.

scholarly journals A process of rumour scotching on finite populations

2015 ◽  
Vol 2 (9) ◽  
pp. 150240 ◽  
Author(s):  
Guilherme Ferraz de Arruda ◽  
Elcio Lebensztayn ◽  
Francisco A. Rodrigues ◽  
Pablo Martín Rodríguez
Keyword(s):  
Monte Carlo ◽  
Random Graphs ◽  
Information Dissemination ◽  
Initial Conditions ◽  
Qualitative Behaviour ◽  
Analytical Treatment ◽  
Scale Free ◽  
Pairwise Interactions ◽  
Scale Free Networks ◽  
Optimal Information

Rumour spreading is a ubiquitous phenomenon in social and technological networks. Traditional models consider that the rumour is propagated by pairwise interactions between spreaders and ignorants. Only spreaders are active and may become stiflers after contacting spreaders or stiflers. Here we propose a competition-like model in which spreaders try to transmit an information, while stiflers are also active and try to scotch it. We study the influence of transmission/scotching rates and initial conditions on the qualitative behaviour of the process. An analytical treatment based on the theory of convergence of density-dependent Markov chains is developed to analyse how the final proportion of ignorants behaves asymptotically in a finite homogeneously mixing population. We perform Monte Carlo simulations in random graphs and scale-free networks and verify that the results obtained for homogeneously mixing populations can be approximated for random graphs, but are not suitable for scale-free networks. Furthermore, regarding the process on a heterogeneous mixing population, we obtain a set of differential equations that describes the time evolution of the probability that an individual is in each state. Our model can also be applied for studying systems in which informed agents try to stop the rumour propagation, or for describing related susceptible–infected–recovered systems. In addition, our results can be considered to develop optimal information dissemination strategies and approaches to control rumour propagation.

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 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.

Documenting Artistic Networks: Anna Oppermann's Ensembles Are Complex Networks!

Leonardo ◽  
2011 ◽  
Vol 44 (3) ◽  
pp. 258-259
Author(s):  
Martin Warnke ◽  
Carmen Wedemeyer
Keyword(s):  
Complex Networks ◽  
Scale Free ◽  
Scale Free Networks

Anna Oppermann's Ensembles are scale-free networks. This explains their robustness and legitimates the art critic's metaphors.

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