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.

STABILITY OF TWO TYPICAL COMPLEX DYNAMICAL NETWORKS

2008 ◽  
Vol 22 (05) ◽  
pp. 553-560 ◽  
Author(s):  
WU-JIE YUAN ◽  
XIAO-SHU LUO ◽  
PIN-QUN JIANG ◽  
BING-HONG WANG ◽  
JIN-QING FANG
Keyword(s):  
Numerical Simulation ◽  
Dissipative System ◽  
Small World ◽  
Complex Dynamical Networks ◽  
Dynamical Networks ◽  
Scale Free ◽  
Scale Free Networks ◽  
General Complex ◽  
The Stability ◽  
Theoretical Results

When being constructed, complex dynamical networks can lose stability in the sense of Lyapunov (i. s. L.) due to positive feedback. Thus, there is much important worthiness in the theory and applications of complex dynamical networks to study the stability. In this paper, according to dissipative system criteria, we give the stability condition in general complex dynamical networks, especially, in NW small-world and BA scale-free networks. The results of theoretical analysis and numerical simulation show that the stability i. s. L. depends on the maximal connectivity of the network. Finally, we show a numerical example to verify our theoretical results.

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 Financialization and Income Inequality in Selected European Countries, 2004–2013

e-Finanse ◽  
2017 ◽  
Vol 12 (4) ◽  
pp. 20-32
Author(s):  
Grzegorz Golebiowski ◽  
Piotr Szczepankowski ◽  
Dorota Wisniewska
Keyword(s):  
Income Inequality ◽  
Eastern Europe ◽  
Gini Coefficient ◽  
Central And Eastern Europe ◽  
Value Added ◽  
European Countries ◽  
Total Employment ◽  
The Gini Coefficient ◽  
Synthetic Indicator ◽  
The Impact

Abstract The article examines the impact of financialization on income inequality between 2004 and 2013, through a panel analysis of seven European countries. Moreover, it attempts to examine differences in the perception of the phenomenon between the selected European countries belonging to the G-7 and countries from Central and Eastern Europe. The results demonstrate the existence of individual effects, which means that the level of inequality under examination is influenced predominantly by country-specific factors. The most significant correlation is noticeable between the level of unemployment and the degree of income inequality. An increase in unemployment is accompanied by a rise in the disproportions in the level of income that individual citizens have at their disposal whereas a decrease in the unemployment level contributes to an improvement of the GINI coefficient. Simultaneously, the results confirm the existence of significant correlations between the level of the GINI coefficient and such financialization indicators as the share of employment in finance in total employment and the contribution of the financial sector to total value added creation. The most prominent dependency was discovered when a constructed synthetic indicator was adopted as an indicator of financialization. At the same time, analysis of the synthetic country financialization indicator points to a conclusion that the level of financialization is higher in European countries belonging to the G-7 (especially Great Britain) than in countries from Central and Eastern Europe.

The Problem of Income Inequality

2019 ◽  
pp. 42-44
Author(s):  
Andrew Smithers
Keyword(s):  
Income Inequality ◽  
Gini Coefficient ◽  
Living Standards ◽  
Living Standard ◽  
The Gini Coefficient ◽  
The Us ◽  
The Uk ◽  
Distribution Of Income

Living standards change in line with GDP per head only if the distribution of incomes is unchanged. If incomes become less equally distributed the living standards of most people will fall even if GDP per head is stable. The Gini Coefficient is the most widely used indicator designed to measure the distribution of income. UK inequality, on this measure, has risen since 1977, stabilized since 1987, and fallen in recent years. In the US there has been a long-term increase in income inequality. Unless this US trend for increased income inequality halts, it is quite likely that even if GDP per head rises in the US, the living standard of the average voter will fall. The recent data suggest that changes in income inequality pose less of a threat to living standards in the UK then they do to those in the US.

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.

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.

EFFECTS OF CONFIDENCE SCALE AND NETWORK STRUCTURE ON MINORITY OPINION SPREADING

2010 ◽  
Vol 21 (08) ◽  
pp. 1001-1010 ◽  
Author(s):  
BO SHEN ◽  
YUN LIU
Keyword(s):  
Simple Model ◽  
Network Structure ◽  
Random Network ◽  
Random Networks ◽  
Scale Free Network ◽  
Opinion Formation ◽  
Scale Free ◽  
Scale Free Networks ◽  
Free Network ◽  
Confidence Scale

We study the dynamics of minority opinion spreading using a proposed simple model, in which the exchange of views between agents is determined by a quantity named confidence scale. To understand what will promote the success of minority, two types of networks, random network and scale-free network are considered in opinion formation. We demonstrate that the heterogeneity of networks is advantageous to the minority and exchanging views between more agents will reduce the opportunity of minority's success. Further, enlarging the degree that agents trust each other, i.e. confidence scale, can increase the probability that opinions of the minority could be accepted by the majority. We also show that the minority in scale-free networks are more sensitive to the change of confidence scale than that in random networks.

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.

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