The Formation of Social Network Assortativity: A Cultural Trait-Matching 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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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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SCALE-FREE EVOLVING NETWORKS WITH ACCELERATED ATTACHMENT

Advances in Complex Systems ◽

10.1142/s0219525907001033 ◽

2007 ◽

Vol 10 (02) ◽

pp. 143-154 ◽

Cited By ~ 3

Author(s):

SEN QIN ◽

GUANZHONG DAI ◽

LIN WANG ◽

MING FAN

Keyword(s):

Growth Model ◽

Preferential Attachment ◽

Time Step ◽

Scale Free ◽

Evolving Networks ◽

Power Law Decay ◽

Free Network ◽

Accelerated Growth ◽

Attachment Mechanism ◽

Aging Network

A new evolving network based on the scale-free network of Barabási and Albert (BA) is studied, and the accelerated attachment of new edges is considered in its evolving process. The accelerated attachment is different from the previous accelerated growth of edges and has two particular meanings in this paper. One is that a new vertex with the edges is inserted into the network with acceleration at each time step; the other is that, with a given probability, some additional edges are linked with the vertices in proportion to the number of their obtained edges in the latest evolving periods. The new model describes the cases of those complex networks with a few exceptional vertices. The attachment mechanism of the new adding edges for these vertices does not follow the preferential attachment rule. Comparing with the linear edge growth model, the characteristics of the accelerated growth model are studied theoretically and numerically. We show that the degree distributions of these models have a power law decay and the exponents are larger than that of the BA model. We point out that the characteristics of the exceptional vertices and the aging vertices in an aging network are not identical. The reasons for neglecting this attachment in most of evolving networks are also summarized.

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COMPLEX NETWORK SIMULATION OF FOREST NETWORK SPATIAL PATTERN IN PEARL RIVER DELTA

ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences ◽

10.5194/isprs-archives-xlii-2-w7-1445-2017 ◽

2017 ◽

Vol XLII-2/W7 ◽

pp. 1445-1449

Author(s):

Y. Zeng

Keyword(s):

Power Law ◽

Pearl River Delta ◽

Pearl River ◽

Network Node ◽

Scale Free Network ◽

Power Law Distribution ◽

Network Nodes ◽

Scale Free ◽

Node Distribution ◽

Free Network

Forest network-construction uses for the method and model with the scale-free features of complex network theory based on random graph theory and dynamic network nodes which show a power-law distribution phenomenon. The model is suitable for ecological disturbance by larger ecological landscape Pearl River Delta consistent recovery. Remote sensing and GIS spatial data are available through the latest forest patches. A standard scale-free network node distribution model calculates the area of forest network’s power-law distribution parameter value size; The recent existing forest polygons which are defined as nodes can compute the network nodes decaying index value of the network’s degree distribution. The parameters of forest network are picked up then make a spatial transition to GIS real world models. Hence the connection is automatically generated by minimizing the ecological corridor by the least cost rule between the near nodes. Based on scale-free network node distribution requirements, select the number compared with less, a huge point of aggregation as a future forest planning network’s main node, and put them with the existing node sequence comparison. By this theory, the forest ecological projects in the past avoid being fragmented, scattered disorderly phenomena. The previous regular forest networks can be reduced the required forest planting costs by this method. For ecological restoration of tropical and subtropical in south China areas, it will provide an effective method for the forest entering city project guidance and demonstration with other ecological networks (water, climate network, etc.) for networking a standard and base datum.

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Random Immunization Algorithm to Energy Consumption in Optical Network

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.926-930.1993 ◽

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.

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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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EVOLVING SCALE-FREE NETWORK MODEL

International Journal of Modern Physics B ◽

10.1142/s0217979208039307 ◽

2008 ◽

Vol 22 (13) ◽

pp. 2139-2149

Author(s):

QIONG QIN ◽

ZHIPING WANG ◽

FANG ZHANG ◽

PENGYUAN XU

Keyword(s):

Time Evolution ◽

Preferential Attachment ◽

Continuum Theory ◽

Scale Free Network ◽

Scale Free ◽

Long Time ◽

Free Network ◽

Law Degree ◽

Analytical Expressions ◽

The Continuum

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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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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