scholarly journals A new structure entropy of complex networks based on nonextensive statistical mechanics and similarity of nodes

2021 ◽  
Vol 18 (4) ◽  
pp. 3718-3732
Author(s):  
Bing Wang ◽  
◽  
Fu Tan ◽  
Jia Zhu ◽  
Daijun Wei
Keyword(s):  
Statistical Mechanics ◽  
Complex Networks ◽  
Nonextensive Statistical Mechanics

A new structure entropy of complex networks based on nonextensive statistical mechanics

2016 ◽  
Vol 27 (10) ◽  
pp. 1650118 ◽  
Author(s):  
Qi Zhang ◽  
Meizhu Li ◽  
Yong Deng
Keyword(s):  
Statistical Mechanics ◽  
Complex Networks ◽  
Fundamental Problem ◽  
New Method ◽  
Nonextensive Statistical Mechanics ◽  
Index Set ◽  
Single Structure ◽  
Degree Structure ◽  
Structure Complexity ◽  
Entropic Index

The quantification of the complexity of network is a fundamental problem in the research of complex networks. There are many methods that have been proposed to solve this problem. Most of the existing methods are based on the Shannon entropy. In this paper, a new method which is based on the nonextensive statistical mechanics is proposed to quantify the complexity of complex network. On the other hand, most of the existing methods are based on a single structure factor, such as the degree of each node or the betweenness of each node. In the proposed method, both of the influence of the degree and betweenness are quantified. In the new method, the degree of each node is used as the constitution of the discrete probability distribution. The betweenness centrality is used as the entropic index q. The nodes which have big value of degree and betweenness will be have big influence on the quantification of network’s structure complexity. In order to describe the relationship between the nodes and the whole network more reasonable, a entropy index set is defined in this new method. Therefore, every node’s influence on the network structure will be quantified. When the value of all the elements in the entropic index set is equal to 1, the new structure entropy is degenerated to the degree entropy. It means that the betweenness of each node in the network is equal to each other. And the structure complexity of the network is determined by the node’s degree distribution. In other words, the new structure entropy is a generalization of the existing degree structure entropy of complex networks. The new structure entropy can be used to quantify the complexity of complex networks, especially for the networks which have a special structure.

scholarly journals A new structural entropy measurement of networks based on the nonextensive statistical mechanics and hub repulsion

2021 ◽  
Vol 18 (6) ◽  
pp. 9253-9263
Author(s):  
Fu Tan ◽  
◽  
Bing Wang ◽  
Daijun Wei
Keyword(s):  
Statistical Mechanics ◽  
Complex Networks ◽  
Structural Properties ◽  
Complex Network ◽  
Repulsive Force ◽  
Nonextensive Statistical Mechanics ◽  
Entropy Measurement ◽  
Structural Entropy ◽  
Degree Structure ◽  
The Difference

<abstract><p>The structure properties of complex networks are an open issue. As the most important parameter to describe the structural properties of the complex network, the structure entropy has attracted much attention. Recently, the researchers note that hub repulsion plays an role in structural entropy. In this paper, the repulsion between nodes in complex networks is simulated when calculating the structure entropy of the complex network. Coulomb's law is used to quantitatively express the repulsive force between two nodes of the complex network, and a new structural entropy based on the Tsallis nonextensive statistical mechanics is proposed. The new structure entropy synthesizes the influence of repulsive force and betweenness. We study several construction networks and some real complex networks, the results show that the proposed structure entropy can describe the structural properties of complex networks more reasonably. In particular, the new structural entropy has better discrimination in describing the complexity of the irregular network. Because in the irregular network, the difference of the new structure entropy is larger than that of degree structure entropy, betweenness structure entropy and Zhang's structure entropy. It shows that the new method has better discrimination for irregular networks, and experiments on Graph, Centrality literature, US Aire lines and Yeast networks confirm this conclusion.</p></abstract>

scholarly journals Connecting complex networks to nonadditive entropies

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
R. M. de Oliveira ◽  
Samuraí Brito ◽  
L. R. da Silva ◽  
Constantino Tsallis
Keyword(s):  
Statistical Mechanics ◽  
Energy Distribution ◽  
Complex Networks ◽  
Wide Class ◽  
Scale Invariant ◽  
Nonlocal Effects ◽  
Geometric Problem ◽  
Exponential Factor ◽  
Research Areas ◽  
Quasi Stationary State

AbstractBoltzmann–Gibbs statistical mechanics applies satisfactorily to a plethora of systems. It fails however for complex systems generically involving nonlocal space–time entanglement. Its generalization based on nonadditive q-entropies adequately handles a wide class of such systems. We show here that scale-invariant networks belong to this class. We numerically study a d-dimensional geographically located network with weighted links and exhibit its ‘energy’ distribution per site at its quasi-stationary state. Our results strongly suggest a correspondence between the random geometric problem and a class of thermal problems within the generalised thermostatistics. The Boltzmann–Gibbs exponential factor is generically substituted by its q-generalisation, and is recovered in the $$q=1$$ q = 1 limit when the nonlocal effects fade away. The present connection should cross-fertilise experiments in both research areas.

Laws of large numbers for q-dependent random variables and nonextensive statistical mechanics

2017 ◽  
Vol 31 (15) ◽  
pp. 1750117
Author(s):  
Marco A. S. Trindade
Keyword(s):  
Statistical Mechanics ◽  
Stochastic Processes ◽  
Law Of Large Numbers ◽  
Random Variables ◽  
Nonextensive Statistical Mechanics ◽  
Dependent Random Variables ◽  
Strong Law ◽  
Laws Of Large Numbers ◽  
Large Numbers

In this work, we prove a weak law and a strong law of large numbers through the concept of [Formula: see text]-product for dependent random variables, in the context of nonextensive statistical mechanics. Applications for the consistency of estimators are presented and connections with stochastic processes are discussed.

scholarly journals Nondistributive algebraic structures derived from nonextensive statistical mechanics

2008 ◽  
Vol 49 (9) ◽  
pp. 093509 ◽  
Author(s):  
Pedro G. S. Cardoso ◽  
Ernesto P. Borges ◽  
Thierry C. P. Lobão ◽  
Suani T. R. Pinho
Keyword(s):  
Statistical Mechanics ◽  
Algebraic Structures ◽  
Nonextensive Statistical Mechanics
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