EVOLVING SCALE-FREE NETWORK MODEL

The Barabási–Albert (BA) model is extended here to include the concept of modifying the preferential attachment and combining the global preferential attachment with local preferential attachment. Our preferential attachment makes the nodes with higher degree increase less rapidly than the BA model after a long time. The maximum degree is introduced. We compare the time-evolution of the degree of the BA model and our model to illustrate that our model can control the degree of some nodes increasing dramatically with increasing time. Using the continuum theory and the rate equation method, we obtain the analytical expressions of the time-evolution of the degree and the power-law degree distribution.

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EVOLVING SCALE-FREE NETWORK MODEL WITH TUNABLE CLUSTERING

International Journal of Modern Physics B ◽

10.1142/s0217979205032437 ◽

2005 ◽

Vol 19 (26) ◽

pp. 3951-3959 ◽

Cited By ~ 13

Author(s):

BING WANG ◽

HUANWEN TANG ◽

ZHONGZHI ZHANG ◽

ZHILONG XIU

Keyword(s):

Rate Equation ◽

Continuum Theory ◽

Clustering Coefficient ◽

Scale Free Network ◽

Scale Free ◽

Free Network ◽

Law Degree ◽

Analytical Expressions ◽

Good Agreement ◽

The Continuum

The Barabási–Albert (BA) model is extended to include the concept of local world and the microscopic event of adding edges. With probability p, we add a new node with m edges which preferentially link to the nodes presented in the network; with probability 1-p, we add m edges among the present nodes. A node is preferentially selected by its degree to add an edge randomly among its neighbors. Using the continuum theory and the rate equation method we get the analytical expressions of the power-law degree distribution with exponent γ=3 and the clustering coefficient c(k)~k-1+c. The analytical expressions are in good agreement with the numerical calculations.

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

International Journal of Modern Physics C ◽

10.1142/s0129183106009837 ◽

2006 ◽

Vol 17 (09) ◽

pp. 1303-1311 ◽

Cited By ~ 8

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.

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

Complexity ◽

10.1155/2020/1873796 ◽

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.

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Analyses of Complex Networks Based on the Random Walk Model

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.610.850 ◽

2014 ◽

Vol 610 ◽

pp. 850-853

Author(s):

Jing Wei Deng ◽

Kai Ying Deng ◽

Ying Xing Li

Keyword(s):

Theoretical Analysis ◽

Scale Free Network ◽

Theoretical Justification ◽

Scale Free ◽

Proposed Model ◽

Global Meaning ◽

Master Equation Approach ◽

Free Network ◽

Free Behavior ◽

Analytical Expressions

In this letter, we derive the analytical expressions of the degree distributions for a kind of networks model random initializing attractiveness and preferential linking, which analyzed degree evolution by using the master equation approach. We also discuss the theoretical justification of the scale-free behavior about the proposed model. The influencing range of initialization to the degree distribution only related to initialization’s expectation under the global meaning. Finally, a series of theoretical analysis and numerical simulations to the scale-free network model are conducted in this letter. The results of computer simulation is presented to the theoretical analysis.

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Evolving complex networks with logistic property: Global versus local growth

International Journal of Modern Physics B ◽

10.1142/s0217979221502507 ◽

2021 ◽

Vol 35 (24) ◽

Author(s):

Sen Qin ◽

Sha Peng

Keyword(s):

Shortest Paths ◽

Network Models ◽

Logistic Growth ◽

Scale Free Network ◽

Network Growth ◽

Network Nodes ◽

Scale Free ◽

Free Network ◽

Law Degree ◽

Global And Local

Considering the retarding effect of natural resources, environmental conditions, and other factors on network growth, the capacity of network nodes to connect to new edges is generally limited. Inspired by this hindered growth of many real-world networks, two types of evolving network models are suggested with different logistic growth schemes. In the global and local logistic network, the total number of network edges and the number of edges added into the network at each step are in line with the Logistic growth, respectively. The most exciting feature of the Logistic growth network is that the growth rule of network edges is first fast, then slow and finally reaches the saturation value [Formula: see text]. Theoretical analysis and numerical simulation reveal that the node degrees of two new networks converge to the same results of the BA scale-free network, [Formula: see text], as the growth rate [Formula: see text] approaches to 0. The local logistic network follows a bilateral power-law degree distribution with a given value of [Formula: see text]. Meanwhile, for these two networks, it is found that the greater [Formula: see text] and [Formula: see text], the smaller the average shortest paths, the greater the clustering coefficients, and the weaker the disassortativity. Additionally, compared to the local logistic growth network, the clustering feature of the global logistic network is more obvious.

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A Novel BA Complex Network Model on Color Template Matching

The Scientific World JOURNAL ◽

10.1155/2014/918453 ◽

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.

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The Fractional Preferential Attachment Scale-Free Network Model

Entropy ◽

10.3390/e22050509 ◽

2020 ◽

Vol 22 (5) ◽

pp. 509

Author(s):

Rafał Rak ◽

Ewa Rak

Keyword(s):

Network Model ◽

Real World ◽

Degree Distribution ◽

Preferential Attachment ◽

Clustering Coefficient ◽

Node Degree ◽

Scale Free Network ◽

Scale Free ◽

Degree Correlation ◽

Free Network

Many networks generated by nature have two generic properties: they are formed in the process of preferential attachment and they are scale-free. Considering these features, by interfering with mechanism of the preferential attachment, we propose a generalisation of the Barabási–Albert model—the ’Fractional Preferential Attachment’ (FPA) scale-free network model—that generates networks with time-independent degree distributions p ( k ) ∼ k − γ with degree exponent 2 < γ ≤ 3 (where γ = 3 corresponds to the typical value of the BA model). In the FPA model, the element controlling the network properties is the f parameter, where f ∈ ( 0 , 1 ⟩ . Depending on the different values of f parameter, we study the statistical properties of the numerically generated networks. We investigate the topological properties of FPA networks such as degree distribution, degree correlation (network assortativity), clustering coefficient, average node degree, network diameter, average shortest path length and features of fractality. We compare the obtained values with the results for various synthetic and real-world networks. It is found that, depending on f, the FPA model generates networks with parameters similar to the real-world networks. Furthermore, it is shown that f parameter has a significant impact on, among others, degree distribution and degree correlation of generated networks. Therefore, the FPA scale-free network model can be an interesting alternative to existing network models. In addition, it turns out that, regardless of the value of f, FPA networks are not fractal.

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