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>

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.

On the Proper Description of Complex Network Dynamics

2018 ◽  
Author(s):  
Chun-Lin Yang ◽  
C. Steve Suh
Keyword(s):  
Complex Networks ◽  
Complex Network ◽  
Collective Behavior ◽  
Local Level ◽  
Network Dynamics ◽  
Global Dynamics ◽  
Statistical Entropy ◽  
Network Systems ◽  
Local Dynamics ◽  
The Difference

Real-world networks are dynamical complex network systems. The dynamics of a network system is a coupling of the local dynamics with the global dynamics. The local dynamics is the time-varying behaviors of ensembles at the local level. The global dynamics is the collective behavior of the ensembles following specific laws at the global level. These laws include basic physical principles and constraints. Complex networks have inherent resilience that offsets disturbance and maintains the state of the system. However, when disturbance is potent enough, network dynamics can be perturbed to a level that ensembles no longer follow the constraint conditions. As a result, the collective behavior of a complex network diminishes and the network collapses. The characteristic of a complex network is the response of the system which is time-dependent. Therefore, complex networks need to account for time-dependency and obey physical laws and constraints. Statistical mechanics is viable for the study of multi-body dynamic systems having uncertain states such as complex network systems. Statistical entropy can be used to define the distribution of the states of ensembles. The difference between the states of ensembles define the interaction between them. This interaction is known as the collective behavior. In other words statistical entropy defines the dynamics of a complex network. Variation of entropy corresponds to the variation of network dynamics and vice versa. Therefore, entropy can serve as an indicator of network dynamics. A stable network is characterized by a specific entropy while a network on the verge of collapse is characterized by another. As the collective behavior of a complex network can be described by entropy, the correlation between the statistical entropy and network dynamics is investigated.

scholarly journals Exponential Synchronization Analysis and Control for Discrete-Time Uncertain Delay Complex Networks with Stochastic Effects

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Tianbo Wang ◽  
Wuneng Zhou ◽  
Dejun Zhao ◽  
Shouwei Zhao
Keyword(s):  
Complex Networks ◽  
Complex Network ◽  
Discrete Time ◽  
Lyapunov Stability Theory ◽  
Exponential Synchronization ◽  
Control Methods ◽  
Stochastic Effects ◽  
Inequality Technique ◽  
The Difference ◽  
And Control

The exponential synchronization for a class of discrete-time uncertain complex networks with stochastic effects and time delay is investigated by using the Lyapunov stability theory and discrete Halanay inequality. The uncertainty arises from the difference of the nodes’ reliability in the complex network. Through constructing an appropriate Lyapunov function and applying inequality technique, some synchronization criteria and two control methods are obtained to ensure the considered complex network being exponential synchronization. Finally, a numerical example is provided to show the effectiveness of our proposed methods.

GRAPH ZETA FUNCTION AND DIMENSION OF COMPLEX NETWORK

2007 ◽  
Vol 21 (11) ◽  
pp. 639-644 ◽  
Author(s):  
O. SHANKER
Keyword(s):  
Statistical Mechanics ◽  
Complex Networks ◽  
Zeta Function ◽  
Complex Network ◽  
System Behavior ◽  
Mathematical Properties ◽  
Scaling Property ◽  
Definition Of

In a recent paper we had defined the dimension of a complex network in terms of the scaling property of the volume. The question assumes significance because the dependence of system behavior on dimension is an important topic in statistical mechanics. Hence we consider the definition in more detail, and we propose a more widely applicable definition in this work. This definition has good mathematical properties, and it is based on the definition of a zeta function for complex networks.

DEFINING DIMENSION OF A COMPLEX NETWORK

2007 ◽  
Vol 21 (06) ◽  
pp. 321-326 ◽  
Author(s):  
O. SHANKER
Keyword(s):  
Statistical Mechanics ◽  
Complex Networks ◽  
Complex Network ◽  
Power Law ◽  
Regular Lattices ◽  
Extensive Property ◽  
Definition Of

An important question in statistical mechanics is the dependence of model behavior on the dimension of the system. In this paper, we discuss extending the definition of dimension from regular lattices to complex networks. We use the definition to study how the extensive property of the power law potential exponent depends on dimension.

scholarly journals STRENGTH DISTRIBUTION IN DERIVATIVE NETWORKS

2005 ◽  
Vol 16 (07) ◽  
pp. 1097-1105 ◽  
Author(s):  
LUCIANO DA FONTOURA COSTA ◽  
GONZALO TRAVIESO
Keyword(s):  
Complex Networks ◽  
Complex Network ◽  
Lower Limit ◽  
Network Model ◽  
Power Law ◽  
Neuronal Networks ◽  
Strength Distribution ◽  
Node Degree ◽  
Upper Limit ◽  
The Difference

This article describes a complex network model whose weights are proportional to the difference between uniformly distributed "fitness" values assigned to the nodes. It is shown both analytically and experimentally that the strength density (i.e., the weighted node degree) for this model, called derivative complex networks, follows a power law with exponent γ<1 if the fitness has an upper limit and γ>1 if the fitness has no upper limit but a positive lower limit. Possible implications for neuronal networks topology and dynamics are also discussed.

scholarly journals A Structural Entropy Measurement Principle of Propositional Formulas in Conjunctive Normal Form

Entropy ◽  
2021 ◽  
Vol 23 (3) ◽  
pp. 303
Author(s):  
Zaijun Zhang ◽  
Daoyun Xu ◽  
Jincheng Zhou
Keyword(s):  
Normal Form ◽  
Local Search ◽  
Structural Properties ◽  
Structural Characteristics ◽  
Complex Structure ◽  
Solution Process ◽  
Conjunctive Normal Form ◽  
Experimental Results ◽  
Entropy Measurement ◽  
Structural Entropy

The satisfiability (SAT) problem is a core problem in computer science. Existing studies have shown that most industrial SAT instances can be effectively solved by modern SAT solvers while random SAT instances cannot. It is believed that the structural characteristics of different SAT formula classes are the reasons behind this difference. In this paper, we study the structural properties of propositional formulas in conjunctive normal form (CNF) by the principle of structural entropy of formulas. First, we used structural entropy to measure the complex structure of a formula and found that the difficulty solving the formula is related to the structural entropy of the formula. The smaller the compressing information of a formula, the more difficult it is to solve the formula. Secondly, we proposed a λ-approximation strategy to approximate the structural entropy of large formulas. The experimental results showed that the proposed strategy can effectively approximate the structural entropy of the original formula and that the approximation ratio is more than 92%. Finally, we analyzed the structural properties of a formula in the solution process and found that a local search solver tends to select variables in different communities to perform the next round of searches during a search and that the structural entropy of a variable affects the probability of the variable being flipped. By using these conclusions, we also proposed an initial candidate solution generation strategy for a local search for SAT, and the experimental results showed that this strategy effectively improves the performance of the solvers CCAsat and Sparrow2011 when incorporated into these two solvers.

Information on evolutionary age in redundancy of complex network

2019 ◽  
Vol 33 (27) ◽  
pp. 1950331
Author(s):  
Shiguo Deng ◽  
Henggang Ren ◽  
Tongfeng Weng ◽  
Changgui Gu ◽  
Huijie Yang
Keyword(s):  
Principal Component Analysis ◽  
Complex Networks ◽  
Metabolic Network ◽  
Complex Network ◽  
Cellular Networks ◽  
Topological Structure ◽  
Quantitative Measure ◽  
Principal Component ◽  
Evolutionary Information ◽  
Local Patterns

Evolutionary processes of many complex networks in reality are dominated by duplication and divergence. This mechanism leads to redundant structures, i.e. some nodes share most of their neighbors and some local patterns are similar, called redundancy of network. An interesting reverse problem is to discover evolutionary information from the present topological structure. We propose a quantitative measure of redundancy of network from the perspective of principal component analysis. The redundancy of a community in the empirical human metabolic network is negatively and closely related with its evolutionary age, which is consistent with that for the communities in the modeling protein–protein network. This behavior can be used to find the evolutionary difference stored in cellular networks.

scholarly journals CNFE-SE: a novel approach combining complex network-based feature engineering and stacked ensemble to predict the success of intrauterine insemination and ranking the features

2021 ◽  
Vol 21 (1) ◽  
Author(s):  
Sima Ranjbari ◽  
Toktam Khatibi ◽  
Ahmad Vosough Dizaji ◽  
Hesamoddin Sajadi ◽  
Mehdi Totonchi ◽  
...  
Keyword(s):  
Complex Networks ◽  
Complex Network ◽  
Semen Quality ◽  
Intrauterine Insemination ◽  
Machine Learning Algorithms ◽  
Semen Parameters ◽  
Feature Engineering ◽  
Operating Characteristics ◽  
Scoring Method ◽  
Novel Approach

Abstract Background Intrauterine Insemination (IUI) outcome prediction is a challenging issue which the assisted reproductive technology (ART) practitioners are dealing with. Predicting the success or failure of IUI based on the couples' features can assist the physicians to make the appropriate decision for suggesting IUI to the couples or not and/or continuing the treatment or not for them. Many previous studies have been focused on predicting the in vitro fertilization (IVF) and intracytoplasmic sperm injection (ICSI) outcome using machine learning algorithms. But, to the best of our knowledge, a few studies have been focused on predicting the outcome of IUI. The main aim of this study is to propose an automatic classification and feature scoring method to predict intrauterine insemination (IUI) outcome and ranking the most significant features. Methods For this purpose, a novel approach combining complex network-based feature engineering and stacked ensemble (CNFE-SE) is proposed. Three complex networks are extracted considering the patients' data similarities. The feature engineering step is performed on the complex networks. The original feature set and/or the features engineered are fed to the proposed stacked ensemble to classify and predict IUI outcome for couples per IUI treatment cycle. Our study is a retrospective study of a 5-year couples' data undergoing IUI. Data is collected from Reproductive Biomedicine Research Center, Royan Institute describing 11,255 IUI treatment cycles for 8,360 couples. Our dataset includes the couples' demographic characteristics, historical data about the patients' diseases, the clinical diagnosis, the treatment plans and the prescribed drugs during the cycles, semen quality, laboratory tests and the clinical pregnancy outcome. Results Experimental results show that the proposed method outperforms the compared methods with Area under receiver operating characteristics curve (AUC) of 0.84 ± 0.01, sensitivity of 0.79 ± 0.01, specificity of 0.91 ± 0.01, and accuracy of 0.85 ± 0.01 for the prediction of IUI outcome. Conclusions The most important predictors for predicting IUI outcome are semen parameters (sperm motility and concentration) as well as female body mass index (BMI).

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