scholarly journals Characterization of Symmetry of Complex Networks

Symmetry ◽  
2019 ◽  
Vol 11 (5) ◽  
pp. 692
Author(s):  
Yangyang Chen ◽  
Yi Zhao ◽  
Xinyu Han
Keyword(s):  
Automorphism Group ◽  
Complex Networks ◽  
Complex Network ◽  
Real World ◽  
Symmetry Property ◽  
Global Symmetry ◽  
Quantitative Characterization ◽  
Natural Action ◽  
Vertex Set

Recently, symmetry in complex network structures has attracted some research interest. One of the fascinating problems is to give measures of the extent to which the network is symmetric. In this paper, based on the natural action of the automorphism group Aut ( Γ ) of Γ on the vertex set V of a given network Γ = Γ ( V , E ) , we propose three indexes for the characterization of the global symmetry of complex networks. Using these indexes, one can get a quantitative characterization of how symmetric a network is and can compare the symmetry property of different networks. Moreover, we compare these indexes to some existing ones in the literature and apply these indexes to real-world networks, concluding that real-world networks are far from vertex symmetric ones.

scholarly journals Power-law distribution of degree–degree distance: A better representation of the scale-free property of complex networks

2020 ◽  
Vol 117 (26) ◽  
pp. 14812-14818 ◽  
Author(s):  
Bin Zhou ◽  
Xiangyi Meng ◽  
H. Eugene Stanley
Keyword(s):  
Complex Networks ◽  
Complex Network ◽  
Power Law ◽  
Real World ◽  
Preferential Attachment ◽  
Statistical Tests ◽  
Finite Size ◽  
Distance Distribution ◽  
Scale Free ◽  
Degree Distance

Whether real-world complex networks are scale free or not has long been controversial. Recently, in Broido and Clauset [A. D. Broido, A. Clauset,Nat. Commun.10, 1017 (2019)], it was claimed that the degree distributions of real-world networks are rarely power law under statistical tests. Here, we attempt to address this issue by defining a fundamental property possessed by each link, the degree–degree distance, the distribution of which also shows signs of being power law by our empirical study. Surprisingly, although full-range statistical tests show that degree distributions are not often power law in real-world networks, we find that in more than half of the cases the degree–degree distance distributions can still be described by power laws. To explain these findings, we introduce a bidirectional preferential selection model where the link configuration is a randomly weighted, two-way selection process. The model does not always produce solid power-law distributions but predicts that the degree–degree distance distribution exhibits stronger power-law behavior than the degree distribution of a finite-size network, especially when the network is dense. We test the strength of our model and its predictive power by examining how real-world networks evolve into an overly dense stage and how the corresponding distributions change. We propose that being scale free is a property of a complex network that should be determined by its underlying mechanism (e.g., preferential attachment) rather than by apparent distribution statistics of finite size. We thus conclude that the degree–degree distance distribution better represents the scale-free property of a complex network.

scholarly journals On Ve-Degree-Based Irregularity Properties of the Crystallographic Structure of Molecules

2021 ◽  
Vol 2021 ◽  
pp. 1-22
Author(s):  
Akbar Jahanbani ◽  
Rana Khoeilar ◽  
Hajar Shooshtari
Keyword(s):  
Molecular Structure ◽  
Complex Network ◽  
Topological Structure ◽  
Organic Molecules ◽  
Crystallographic Structure ◽  
Quantitative Characterization ◽  
Material Engineering ◽  
Structure Of Molecules ◽  
Crystallographic Structures

Irregularity indices are usually used for quantitative characterization of the topological structure of nonregular graphs. In numerous applications and problems in material engineering and chemistry, it is useful to be aware that how irregular a molecular structure is? In this paper, we are interested in formulating closed forms of irregularity measures of some of the crystallographic structures of Cu 2 O p , q , r and crystallographic structure of titanium difluoride of T i F 2 p , q , r . These theoretical conclusions provide practical guiding significance for pharmaceutical engineering and complex network and quantify the degree of folding of long organic molecules.

scholarly journals Identifying Influential Nodes of Complex Networks Based on Trust-Value

Algorithms ◽  
2020 ◽  
Vol 13 (11) ◽  
pp. 280
Author(s):  
Jinfang Sheng ◽  
Jiafu Zhu ◽  
Yayun Wang ◽  
Bin Wang ◽  
Zheng’ang Hou
Keyword(s):  
Complex Networks ◽  
Complex Network ◽  
Real World ◽  
Trust Value ◽  
The Real ◽  
The World ◽  
Attribute Information ◽  
Similarity Ratio ◽  
Influential Nodes ◽  
Influential Node

The real world contains many kinds of complex network. Using influence nodes in complex networks can promote or inhibit the spread of information. Identifying influential nodes has become a hot topic around the world. Most of the existing algorithms used for influential node identification are based on the structure of the network such as the degree of the nodes. However, the attribute information of nodes also affects the ranking of nodes’ influence. In this paper, we consider both the attribute information between nodes and the structure of networks. Therefore, the similarity ratio, based on attribute information, and the degree ratio, based on structure derived from trust-value, are proposed. The trust–PageRank (TPR) algorithm is proposed to identify influential nodes in complex networks. Finally, several real networks from different fields are selected for experiments. Compared with some existing algorithms, the results suggest that TPR more rationally and effectively identifies the influential nodes in networks.

scholarly journals Induzierbare Promotoren für Cyanobakterien

BIOspektrum ◽  
2021 ◽  
Vol 27 (5) ◽  
pp. 557-559
Author(s):  
Anna Behle ◽  
Ilka M. Axmann
Keyword(s):  
Complex Networks ◽  
Phylogenetic Diversity ◽  
Model Organism ◽  
Model Organisms ◽  
Quantitative Characterization ◽  
Inducible Promoters ◽  
Sustainable Solutions ◽  
Biotechnology Sector ◽  
Pcc 6803

AbstractCyanobacteria are versatile organisms with extreme phylogenetic diversity. With increasing need for alternative sustainable solutions, they are becoming increasingly attractive as production hosts in the biotechnology sector. Opposed to established heterotrophic model organisms, newer production hosts still require extensive characterization of standard biological parts in order to build complex networks and circuits. Here, we present examples of quantitative characterization of inducible promoters in the model organism Synechocystis sp. PCC 6803.

scholarly journals Node diversification in complex networks by decentralized colouring

2018 ◽  
Vol 7 (4) ◽  
pp. 554-563 ◽  
Author(s):  
Richard Garcia-Lebron ◽  
David J Myers ◽  
Shouhuai Xu ◽  
Jie Sun
Keyword(s):  
Complex Networks ◽  
Complex Network ◽  
Real World ◽  
Local Information ◽  
Connected Component ◽  
Scale Free ◽  
Scale Free Networks

Abstract We develop a decentralized colouring approach to diversify the nodes in a complex network. The key is the introduction of a local conflict index (LCI) that measures the colour conflicts arising at each node which can be efficiently computed using only local information. We demonstrate via both synthetic and real-world networks that the proposed approach significantly outperforms random colouring as measured by the size of the largest colour-induced connected component. Interestingly, for scale-free networks further improvement of diversity can be achieved by tuning a degree-biasing weighting parameter in the LCI.

Uncovering the fuzzy community structure accurately based on steepest descent projection

2017 ◽  
Vol 31 (27) ◽  
pp. 1750249 ◽  
Author(s):  
Changjian Fang ◽  
Dejun Mu ◽  
Zhenghong Deng ◽  
Jiaqi Yan
Keyword(s):  
Community Structure ◽  
Complex Networks ◽  
Complex Network ◽  
Real World ◽  
Large Scale ◽  
Steepest Descent ◽  
Topological Information ◽  
Generalized Framework ◽  
Open Question ◽  
Fuzzy C Means Algorithm

Uncovering the community structure in complex network is a hot research point in recent years. How to identify the community structure accurately in complex network is still an open question under research. There are lots of methods based on topological information, which have some good performances at the expense of longer runtimes. In this paper, we propose a new fuzzy algorithm which follows the line of fuzzy c-means algorithm. A steepest descent framework with projection by optimizing the quality function is presented under the generalized framework. The results of experiments on both real-world networks and synthetic networks show that the proposed method achieves the highest efficiency and is easy for detecting fuzzy community structure in large-scale complex networks.

scholarly journals A detailed characterization of complex networks using Information Theory

2021 ◽  
Author(s):  
CGS Freitas ◽  
ALL Aquino ◽  
HS Ramos ◽  
Alejandro Frery ◽  
OA Rosso
Keyword(s):  
Information Theory ◽  
Complex Networks ◽  
Complex Network ◽  
Preferential Attachment ◽  
Configuration Model ◽  
Complex Network Theory ◽  
Scale Free ◽  
Network Entropy ◽  
Law Degree

Understanding the structure and the dynamics of networks is of paramount importance for many scientific fields that rely on network science. Complex network theory provides a variety of features that help in the evaluation of network behavior. However, such analysis can be confusing and misleading as there are many intrinsic properties for each network metric. Alternatively, Information Theory methods have gained the spotlight because of their ability to create a quantitative and robust characterization of such networks. In this work, we use two Information Theory quantifiers, namely Network Entropy and Network Fisher Information Measure, to analyzing those networks. Our approach detects non-trivial characteristics of complex networks such as the transition present in the Watts-Strogatz model from k-ring to random graphs; the phase transition from a disconnected to an almost surely connected network when we increase the linking probability of Erdős-Rényi model; distinct phases of scale-free networks when considering a non-linear preferential attachment, fitness, and aging features alongside the configuration model with a pure power-law degree distribution. Finally, we analyze the numerical results for real networks, contrasting our findings with traditional complex network methods. In conclusion, we present an efficient method that ignites the debate on network characterization.

A New Evaluation Method of Node Importance in Directed Weighted Complex Networks

2017 ◽  
Vol 5 (4) ◽  
pp. 367-375 ◽  
Author(s):  
Yu Wang ◽  
Jinli Guo ◽  
Han Liu
Keyword(s):  
Complex Networks ◽  
Complex Network ◽  
Real World ◽  
Evaluation Method ◽  
Network Models ◽  
Node Importance ◽  
Weighted Complex Network ◽  
Complex Network Models ◽  
Evaluation Matrix ◽  
Key Nodes

AbstractCurrent researches on node importance evaluation mainly focus on undirected and unweighted networks, which fail to reflect the real world in a comprehensive and objective way. Based on directed weighted complex network models, the paper introduces the concept of in-weight intensity of nodes and thereby presents a new method to identify key nodes by using an importance evaluation matrix. The method not only considers the direction and weight of edges, but also takes into account the position importance of nodes and the importance contributions of adjacent nodes. Finally, the paper applies the algorithm to a microblog-forwarding network composed of 34 users, then compares the evaluation results with traditional methods. The experiment shows that the method proposed can effectively evaluate the node importance in directed weighted networks.

scholarly journals A detailed characterization of complex networks using Information Theory

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Cristopher G. S. Freitas ◽  
Andre L. L. Aquino ◽  
Heitor S. Ramos ◽  
Alejandro C. Frery ◽  
Osvaldo A. Rosso
Keyword(s):  
Information Theory ◽  
Complex Networks ◽  
Complex Network ◽  
Preferential Attachment ◽  
Configuration Model ◽  
Complex Network Theory ◽  
Scale Free ◽  
Network Entropy ◽  
Law Degree

Abstract Understanding the structure and the dynamics of networks is of paramount importance for many scientific fields that rely on network science. Complex network theory provides a variety of features that help in the evaluation of network behavior. However, such analysis can be confusing and misleading as there are many intrinsic properties for each network metric. Alternatively, Information Theory methods have gained the spotlight because of their ability to create a quantitative and robust characterization of such networks. In this work, we use two Information Theory quantifiers, namely Network Entropy and Network Fisher Information Measure, to analyzing those networks. Our approach detects non-trivial characteristics of complex networks such as the transition present in the Watts-Strogatz model from k-ring to random graphs; the phase transition from a disconnected to an almost surely connected network when we increase the linking probability of Erdős-Rényi model; distinct phases of scale-free networks when considering a non-linear preferential attachment, fitness, and aging features alongside the configuration model with a pure power-law degree distribution. Finally, we analyze the numerical results for real networks, contrasting our findings with traditional complex network methods. In conclusion, we present an efficient method that ignites the debate on network characterization.

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