scholarly journals Correlation Analysis between Maximal Clique Size and Centrality Metrics for Random Networks and Scale-Free Networks

2016 ◽  
Vol 9 (2) ◽  
pp. 41 ◽  
Author(s):  
Natarajan Meghanathan
Keyword(s):  
Correlation Coefficient ◽  
Random Network ◽  
Maximal Clique ◽  
Random Networks ◽  
Font Size ◽  
Scale Free ◽  
Node Centrality ◽  
Centrality Metrics ◽  
Scale Free Networks ◽  
The Impact

<p><span style="font-size: 10.5pt; font-family: 'Times New Roman','serif'; mso-bidi-font-size: 12.0pt; mso-fareast-font-family: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA;" lang="EN-US">The high-level contribution of this paper is a comprehensive analysis of the correlation levels between node centrality (a computationally light-weight metric) and maximal clique size (a computationally hard metric) in random network and scale-free network graphs generated respectively from the well-known Erdos-Renyi (ER) and Barabasi-Albert (BA) models. We use three well-known measures for evaluating the level of correlation: Product-moment based Pearson's correlation coefficient, Rank-based Spearman's correlation coefficient and Concordance-based Kendall's correlation coefficient. For each of the several variants of the theoretical graphs generated from the ER and BA models, we compute the above three correlation coefficient values between the maximal clique size for a node (maximum size of the clique the node is part of) and each of the four prominent node centrality metrics (degree, eigenvector, betweenness and closeness). We also explore the impact of the operating parameters of the theoretical models for generating random networks and scale-free networks on the correlation between maximal clique size and the centrality metrics.</span></p>

Clique Size and Centrality Metrics for Analysis of Real-World Network Graphs

2019 ◽  
pp. 1183-1198
Author(s):  
Natarajan Meghanathan
Keyword(s):  
Real World ◽  
Random Network ◽  
Maximal Clique ◽  
Closeness Centrality ◽  
Node Degree ◽  
Degree Centrality ◽  
Eigenvector Centrality ◽  
Scale Free ◽  
Centrality Metrics ◽  
Free Network

The authors present correlation analysis between the centrality values observed for nodes (a computationally lightweight metric) and the maximal clique size (a computationally hard metric) that each node is part of in complex real-world network graphs. They consider the four common centrality metrics: degree centrality (DegC), eigenvector centrality (EVC), closeness centrality (ClC), and betweenness centrality (BWC). They define the maximal clique size for a node as the size of the largest clique (in terms of the number of constituent nodes) the node is part of. The real-world network graphs studied range from regular random network graphs to scale-free network graphs. The authors observe that the correlation between the centrality value and the maximal clique size for a node increases with increase in the spectral radius ratio for node degree, which is a measure of the variation of the node degree in the network. They observe the degree-based centrality metrics (DegC and EVC) to be relatively better correlated with the maximal clique size compared to the shortest path-based centrality metrics (ClC and BWC).

Clique Size and Centrality Metrics for Analysis of Real-World Network Graphs

2018 ◽  
pp. 6507-6521
Author(s):  
Natarajan Meghanathan
Keyword(s):  
Real World ◽  
Random Network ◽  
Maximal Clique ◽  
Closeness Centrality ◽  
Node Degree ◽  
Degree Centrality ◽  
Eigenvector Centrality ◽  
Scale Free ◽  
Centrality Metrics ◽  
Free Network

We present correlation analysis between the centrality values observed for nodes (a computationally lightweight metric) and the maximal clique size (a computationally hard metric) that each node is part of in complex real-world network graphs. We consider the four common centrality metrics: degree centrality (DegC), eigenvector centrality (EVC), closeness centrality (ClC) and betweenness centrality (BWC). We define the maximal clique size for a node as the size of the largest clique (in terms of the number of constituent nodes) the node is part of. The real-world network graphs studied range from regular random network graphs to scale-free network graphs. We observe that the correlation between the centrality value and the maximal clique size for a node increases with increase in the spectral radius ratio for node degree, which is a measure of the variation of the node degree in the network. We observe the degree-based centrality metrics (DegC and EVC) to be relatively better correlated with the maximal clique size compared to the shortest path-based centrality metrics (ClC and BWC).

scholarly journals EPIDEMIC DYNAMICS ON RANDOM AND SCALE-FREE NETWORKS

2012 ◽  
Vol 54 (1-2) ◽  
pp. 3-22 ◽  
Author(s):  
J. BARTLETT ◽  
M. J. PLANK
Keyword(s):  
Random Network ◽  
Infectious Agent ◽  
Mixed Population ◽  
Random Networks ◽  
Scale Free Network ◽  
Final Size ◽  
Scale Free ◽  
Epidemic Dynamics ◽  
Scale Free Networks ◽  
Free Network

AbstractRandom networks were first used to model epidemic dynamics in the 1950s, but in the last decade it has been realized that scale-free networks more accurately represent the network structure of many real-world situations. Here we give an analytical and a Monte Carlo method for approximating the basic reproduction number ${R}_{0} $ of an infectious agent on a network. We investigate how final epidemic size depends on ${R}_{0} $ and on network density in random networks and in scale-free networks with a Pareto exponent of 3. Our results show that: (i) an epidemic on a random network has the same average final size as an epidemic in a well-mixed population with the same value of ${R}_{0} $; (ii) an epidemic on a scale-free network has a larger average final size than in an equivalent well-mixed population if ${R}_{0} \lt 1$, and a smaller average final size than in a well-mixed population if ${R}_{0} \gt 1$; (iii) an epidemic on a scale-free network spreads more rapidly than an epidemic on a random network or in a well-mixed population.

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.

scholarly journals Network topology optimization by turning non-scale-free networks into scale-free networks using nonlinear preferential rewiring method

2018 ◽  
Vol 14 (11) ◽  
pp. 155014771878447 ◽  
Author(s):  
Feng Su ◽  
Peijiang Yuan ◽  
Yuanwei Liu ◽  
Shuangqian Cao
Keyword(s):  
Topology Optimization ◽  
Network Topology ◽  
Random Networks ◽  
Practical Application ◽  
Performance Simulation ◽  
Scale Free ◽  
Scale Free Networks ◽  
Network Topologies ◽  
Network Topology Optimization ◽  
Rigorous Mathematical Model

In practical application, the generation and evolution of many real networks always do not follow rigorous mathematical model, making network topology optimization a great challenge in the field of complex networks. In this research, we optimize the topology of non-scale-free networks by turning it into scale-free networks using a nonlinear preferential rewiring method. For different kinds of original networks generated by Watts and Strogatz model, we systematically demonstrate the optimization process and the modified networks to verify the performance of nonlinear preferential rewiring. We conduct further researches to explore the effect of nonlinear preferential rewiring’s parameters on performance. Simulation results show that various non-scale-free networks with different network topologies generated by WS model, including random networks and various networks between regular and random, are turned into scale-free networks perfectly by nonlinear preferential rewiring method.

scholarly journals Rank correlation between centrality metrics in complex networks: an empirical study

Open Physics ◽  
2018 ◽  
Vol 16 (1) ◽  
pp. 1009-1023 ◽  
Author(s):  
Chengcheng Shao ◽  
Pengshuai Cui ◽  
Peng Xun ◽  
Yuxing Peng ◽  
Xinwen Jiang
Keyword(s):  
Pearson Correlation ◽  
Rank Correlation ◽  
Low Complexity ◽  
Middle Level ◽  
High Complexity ◽  
Computation Complexity ◽  
Scale Free ◽  
Centrality Metrics ◽  
Scale Free Networks ◽  
Better Than

Abstract Centrality is widely used to measure which nodes are important in a network. In recent decades, numerous metrics have been proposed with varying computation complexity. To test the idea that approximating a high-complexity metric by a low-complexity metric, researchers have studied the correlation between them. However, these works are based on Pearson correlation which is sensitive to the data distribution. Intuitively, a centrality metric is a ranking of nodes (or edges). It would be more reasonable to use rank correlation to do the measurement. In this paper, we use degree, a low-complexity metric, as the base to approximate three other metrics: closeness, betweenness, and eigenvector. We first demonstrate that rank correlation performs better than the Pearson one in scale-free networks. Then we study the correlation between centrality metrics in real networks, and find that the betweenness occupies the highest coefficient, closeness is at the middle level, and eigenvector fluctuates dramatically. At last, we evaluate the performance of using top degree nodes to approximate three other metrics in the real networks. We find that the intersection ratio of betweenness is the highest, and closeness and eigenvector follows; most often, the largest degree nodes could approximate largest betweenness and closeness nodes, but not the largest eigenvector nodes.

scholarly journals The use of the power law for designing wireless networks

2018 ◽  
Vol 21 ◽  
pp. 00012
Author(s):  
Andrzej Paszkiewicz
Keyword(s):  
Wireless Networks ◽  
Power Law ◽  
Degree Distribution ◽  
Limited Resources ◽  
Random Networks ◽  
New Approach ◽  
Available Bandwidth ◽  
Scale Free ◽  
Scale Free Networks ◽  
Node Removal

The paper concerns the use of the scale-free networks theory and the power law in designing wireless networks. An approach based on generating random networks as well as on the classic Barabási-Albert algorithm were presented. The paper presents a new approach taking the limited resources for wireless networks into account, such as available bandwidth. In addition, thanks to the introduction of opportunities for dynamic node removal it was possible to realign processes occurring in wireless networks. After introduction of these modifications, the obtained results were analyzed in terms of a power law and the degree distribution of each node.

Asymptotic Behavior and Synchronizability Characteristics of a Class of Recurrent Neural Networks

2007 ◽  
Vol 19 (9) ◽  
pp. 2492-2514 ◽  
Author(s):  
Christof Cebulla
Keyword(s):  
Neural Network ◽  
Asymptotic Behavior ◽  
Recurrent Neural Networks ◽  
Random Networks ◽  
Scale Free ◽  
Scale Free Networks ◽  
Zhang Model ◽  
Random Scale ◽  
Connectivity Distribution ◽  
Time Asymptotic Behavior

We propose an approach to the analysis of the influence of the topology of a neural network on its synchronizability in the sense of equal output activity rates given by a particular neural network model. The model we introduce is a variation of the Zhang model. We investigate the time-asymptotic behavior of the corresponding dynamical system (in particular, the conditions for the existence of an invariant compact asymptotic set) and apply the results of the synchronizability analysis on a class of random scale free networks and to the classical random networks with Poisson connectivity distribution.

scholarly journals Network rewiring dynamics with convergence towards a star network

2016 ◽  
Vol 472 (2194) ◽  
pp. 20160236 ◽  
Author(s):  
P. A. Whigham ◽  
G. Dick ◽  
M. Parry
Keyword(s):  
Infectious Disease ◽  
Random Network ◽  
Small World ◽  
Fixation Time ◽  
Fixed Size ◽  
Star Network ◽  
Scale Free ◽  
Link Type ◽  
Scale Free Networks ◽  
Network Rewiring

Network rewiring as a method for producing a range of structures was first introduced in 1998 by Watts & Strogatz ( Nature 393 , 440–442. ( doi:10.1038/30918 )). This approach allowed a transition from regular through small-world to a random network. The subsequent interest in scale-free networks motivated a number of methods for developing rewiring approaches that converged to scale-free networks. This paper presents a rewiring algorithm (RtoS) for undirected, non-degenerate, fixed size networks that transitions from regular, through small-world and scale-free to star-like networks. Applications of the approach to models for the spread of infectious disease and fixation time for a simple genetics model are used to demonstrate the efficacy and application of the approach.

Temporal Variation of the Node Centrality Metrics for Scale-Free Networks

2018 ◽  
pp. 78-97
Keyword(s):  
Temporal Variation ◽  
Closeness Centrality ◽  
The Other ◽  
Centrality Measures ◽  
Degree Centrality ◽  
Eigenvector Centrality ◽  
Scale Free ◽  
Centrality Metrics ◽  
Scale Free Networks ◽  
Free Network

Scale-free networks are a type of complex networks in which the degree distribution of the nodes is according to the power law. In this chapter, the author uses the widely studied Barabasi-Albert (BA) model to simulate the evolution of scale-free networks and study the temporal variation of degree centrality, eigenvector centrality, closeness centrality, and betweenness centrality of the nodes during the evolution of a scale-free network according to the BA model. The model works by adding new nodes to the network, one at a time, with the new node connected to m of the currently existing nodes. Accordingly, nodes that have been in the network for a longer time have greater chances of acquiring more links and hence a larger degree centrality. While the degree centrality of the nodes has been observed to show a concave down pattern of increase with time, the temporal (time) variation of the other centrality measures has not been analyzed until now.

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