scholarly journals HIERARCHICAL AND MIXING PROPERTIES OF STATIC COMPLEX NETWORKS EMERGING FROM FLUCTUATING CLASSICAL RANDOM GRAPHS

2006 ◽  
Vol 17 (09) ◽  
pp. 1303-1311 ◽  
Author(s):  
SUMIYOSHI ABE ◽  
STEFAN THURNER
Keyword(s):  
Complex Network ◽  
Preferential Attachment ◽  
Hierarchical Organization ◽  
Scale Free Network ◽  
Mixing Properties ◽  
Scale Free ◽  
Free Network ◽  
Growing Network ◽  
Arbitrary Connectivity

The Erdös–Rényi classical random graph is characterized by a fixed linking probability for all pairs of vertices. Here, this concept is generalized by drawing the linking probability from a certain distribution. Such a procedure is found to lead to a static complex network with an arbitrary connectivity distribution. In particular, a scale-free network with the hierarchical organization is constructed without assuming any knowledge about the global linking structure, in contrast to the preferential attachment rule for a growing network. The hierarchical and mixing properties of the static scale-free network thus constructed are studied. The present approach establishes a bridge between a scalar characterization of individual vertices and topology of an emerging complex network. The result may offer a clue for understanding the origin of a few abundance of connectivity distributions in a wide variety of static real-world networks.

scholarly journals A Novel BA Complex Network Model on Color Template Matching

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Risheng Han ◽  
Shigen Shen ◽  
Guangxue Yue ◽  
Hui Ding
Keyword(s):  
Complex Network ◽  
Network Model ◽  
Template Matching ◽  
Preferential Attachment ◽  
Color Space ◽  
Scale Free Network ◽  
Color Distribution ◽  
Scale Free ◽  
Matching Process ◽  
Free Network

A novel BA complex network model of color space is proposed based on two fundamental rules of BA scale-free network model: growth and preferential attachment. The scale-free characteristic of color space is discovered by analyzing evolving process of template’s color distribution. And then the template’s BA complex network model can be used to select important color pixels which have much larger effects than other color pixels in matching process. The proposed BA complex network model of color space can be easily integrated into many traditional template matching algorithms, such as SSD based matching and SAD based matching. Experiments show the performance of color template matching results can be improved based on the proposed algorithm. To the best of our knowledge, this is the first study about how to model the color space of images using a proper complex network model and apply the complex network model to template matching.

scholarly journals The Formation of Social Network Assortativity: A Cultural Trait-Matching Mechanism

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Wei Wang ◽  
Xiaoming Sun ◽  
Yalan Wang ◽  
Wentian Cui
Keyword(s):  
Preferential Attachment ◽  
Scale Free Network ◽  
Selection Probability ◽  
Network Nodes ◽  
Scale Free ◽  
Cultural Trait ◽  
Free Network ◽  
Matching Mechanism ◽  
Simulation Results ◽  
Attachment Mechanism

The preferential attachment mechanism that forms scale-free network cannot display assortativity, i.e., the degree of one node is positively correlated with that of their neighbors in the network. Given the attributes of network nodes, a cultural trait-matching mechanism is further introduced in this paper. Both theoretical analysis and simulation results indicate that the higher selection probability of such mechanism, the more obvious the assortativity is shown in networks. Further, the degree of nodes presents a positive logarithm correlation with that of adjacent ones. Finally, this study discusses the theoretical and practical significances of the introduction of such a cultural trait-matching mechanism.

scholarly journals A Multilevel Simplification Algorithm for Computing the Average Shortest-Path Length of Scale-Free Complex Network

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Guoyong Mao ◽  
Ning Zhang
Keyword(s):  
Complex Network ◽  
Shortest Path ◽  
Path Length ◽  
Large Scale ◽  
Computation Time ◽  
Scale Free Network ◽  
Original Network ◽  
Memory Space ◽  
Scale Free ◽  
Free Network

Computing the average shortest-path length (ASPL) of a large scale-free network needs much memory space and computation time. Based on the feature of scale-free network, we present a simplification algorithm by cutting the suspension points and the connected edges; the ASPL of the original network can be computed through that of the simplified network. We also present a multilevel simplification algorithm to get ASPL of the original network directly from that of the multisimplified network. Our experiment shows that these algorithms require less memory space and time in computing the ASPL of scale-free network, which makes it possible to analyze large networks that were previously impossible due to memory limitations.

Random Immunization Algorithm to Energy Consumption in Optical Network

2014 ◽  
Vol 926-930 ◽  
pp. 1993-1996
Author(s):  
Dong Yan Zhao ◽  
Xiang Lou Liu ◽  
Dong Xue Wang ◽  
Hai Wei Mu ◽  
Hong Mei Song ◽  
...  
Keyword(s):  
Energy Consumption ◽  
Energy Saving ◽  
Complex Network ◽  
Optical Network ◽  
Scale Free Network ◽  
Scale Free ◽  
Free Network ◽  
Simulation Results ◽  
Save Energy ◽  
Node Immunization

The immunization algorithm is from the theory of complex network. The algorithm is simple, highly feasible based on scale-free network model. This paper uses random immunization algorithm to solve optical network energy issues. This paper selects the service to be the operator and to save energy through node immunization. The simulation results show the algorithm can be implemented. This paper provides another possibility to energy saving on optical network.

scholarly journals Influence Cascades: Entropy-Based Characterization of Behavioral Influence Patterns in Social Media

Entropy ◽  
2021 ◽  
Vol 23 (2) ◽  
pp. 160
Author(s):  
Chathurani Senevirathna ◽  
Chathika Gunaratne ◽  
William Rand ◽  
Chathura Jayalath ◽  
Ivan Garibay
Keyword(s):  
Social Media ◽  
Null Model ◽  
Scale Free Network ◽  
Visualization Technique ◽  
Scale Free ◽  
Online Social Media ◽  
Social Media Platforms ◽  
Free Network ◽  
Novel Method

Influence cascades are typically analyzed using a single metric approach, i.e., all influence is measured using one number. However, social influence is not monolithic; different users exercise different influences in different ways, and influence is correlated with the user and content-specific attributes. One such attribute could be whether the action is an initiation of a new post, a contribution to a post, or a sharing of an existing post. In this paper, we present a novel method for tracking these influence relationships over time, which we call influence cascades, and present a visualization technique to better understand these cascades. We investigate these influence patterns within and across online social media platforms using empirical data and comparing to a scale-free network as a null model. Our results show that characteristics of influence cascades and patterns of influence are, in fact, affected by the platform and the community of the users.

Design of the Small World Model by NS2

2014 ◽  
Vol 496-500 ◽  
pp. 2338-2341
Author(s):  
Jun Shang ◽  
Hao Qiang Liu ◽  
Qiang Liu ◽  
Zi Qi Liu
Keyword(s):  
Complex Network ◽  
Network Theory ◽  
Applied Research ◽  
Lower Cost ◽  
Small World ◽  
Scale Free Network ◽  
World Model ◽  
Complex Network Theory ◽  
Scale Free ◽  
Free Network

WSN is the network which is used mostly in the world nowadays, and it has the characteristics that lower cost and better functions than other kinds of the network, and the WSN network is built by the ordinary nodes and the super nodes.Theoretical study of the complex network is widely involved in the fields of computer networks, and the applied research becomes more and more important in the future. It has caused many academic attention about how to apply the complex network theory among the specific application in recent years. In the complex network theory, there has been a number of important research results about the use of the small-world network, scale-free network in the field of transportation.

scholarly journals Eigenvalue-based entropy in directed complex networks

PLoS ONE ◽  
2021 ◽  
Vol 16 (6) ◽  
pp. e0251993
Author(s):  
Yan Sun ◽  
Haixing Zhao ◽  
Jing Liang ◽  
Xiujuan Ma
Keyword(s):  
Complex Networks ◽  
Complex Network ◽  
Network Models ◽  
Small World ◽  
Laplacian Matrix ◽  
Directed Network ◽  
Small World Network ◽  
Scale Free Network ◽  
Scale Free ◽  
Free Network

Entropy is an important index for describing the structure, function, and evolution of network. The existing research on entropy is primarily applied to undirected networks. Compared with an undirected network, a directed network involves a special asymmetric transfer. The research on the entropy of directed networks is very significant to effectively quantify the structural information of the whole network. Typical complex network models include nearest-neighbour coupling network, small-world network, scale-free network, and random network. These network models are abstracted as undirected graphs without considering the direction of node connection. For complex networks, modeling through the direction of network nodes is extremely challenging. In this paper, based on these typical models of complex network, a directed network model considering node connection in-direction is proposed, and the eigenvalue entropies of three matrices in the directed network is defined and studied, where the three matrices are adjacency matrix, in-degree Laplacian matrix and in-degree signless Laplacian matrix. The eigenvalue-based entropies of three matrices are calculated in directed nearest-neighbor coupling, directed small world, directed scale-free and directed random networks. Through the simulation experiment on the real directed network, the result shows that the eigenvalue entropy of the real directed network is between the eigenvalue entropy of directed scale-free network and directed small-world network.

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.

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.

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.

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