scholarly journals A Mixture Model of Truncated Zeta Distributions with Applications to Scientific Collaboration Networks

Entropy ◽  
2021 ◽  
Vol 23 (5) ◽  
pp. 502
Author(s):  
Hohyun Jung ◽  
Frederick Kin Hing Phoa
Keyword(s):  
Mixture Model ◽  
Power Law ◽  
Goodness Of Fit ◽  
Scientific Collaboration ◽  
Model Parameters ◽  
Collaboration Networks ◽  
Power Law Distribution ◽  
Scale Free ◽  
Five Disciplines ◽  
Continuous Power

The degree distribution has attracted considerable attention from network scientists in the last few decades to have knowledge of the topological structure of networks. It is widely acknowledged that many real networks have power-law degree distributions. However, the deviation from such a behavior often appears when the range of degrees is small. Even worse, the conventional employment of the continuous power-law distribution usually causes an inaccurate inference as the degree should be discrete-valued. To remedy these obstacles, we propose a finite mixture model of truncated zeta distributions for a broad range of degrees that disobeys a power-law behavior in the range of small degrees while maintaining the scale-free behavior. The maximum likelihood algorithm alongside the model selection method is presented to estimate model parameters and the number of mixture components. The validity of the suggested algorithm is evidenced by Monte Carlo simulations. We apply our method to five disciplines of scientific collaboration networks with remarkable interpretations. The proposed model outperforms the other alternatives in terms of the goodness-of-fit.

Scale-Free Networks Based on the Value of Interest

2013 ◽  
Vol 753-755 ◽  
pp. 2959-2962
Author(s):  
Jun Tao Yang ◽  
Hui Wen Deng
Keyword(s):  
Network Model ◽  
Power Law ◽  
Scale Free Network ◽  
Power Law Distribution ◽  
Scale Free ◽  
Distribution Property ◽  
Scale Free Networks ◽  
Free Model ◽  
Free Network ◽  
Interest Model

Assigning the value of interest to each node in the network, we give a scale-free network model. The value of interest is related to the fitness and the degree of the node. Experimental results show that the interest model not only has the characteristics of the BA scale-free model but also has the characteristics of fitness model, and the network has a power-law distribution property.

Priority Weighted Fitness Model in Networks

2012 ◽  
Vol 229-231 ◽  
pp. 1854-1857
Author(s):  
Xin Yi Chen
Keyword(s):  
World Wide Web ◽  
Power Law ◽  
Common Property ◽  
World Wide ◽  
Genetic Networks ◽  
Power Law Distribution ◽  
Large Networks ◽  
Scale Free ◽  
The World ◽  
Complex Topology

Systems as diverse as genetic networks or the World Wide Web are best described as networks with complex topology. A common property of many large networks is that the vertex connectivities follow a power-law distribution. This feature was found to be a consequence of three generic mechanisms: (i) networks expand continuously by the addition of new vertices, (ii) new vertex with priority selected different edges of weighted selected that connected to different vertices in the system, and (iii) by the fitness probability that a new vertices attach preferentially to sites that are already well connected. A model based on these ingredients reproduces the observed stationary scale-free distributions, which indicates that the development of large networks is governed by robust self-organizing phenomena. Experiment results show that the model is more close to the actual Internet network.

scholarly journals SYNCHRONIZABILITY AND SYNCHRONIZATION DYNAMICS OF WEIGHED AND UNWEIGHED SCALE FREE NETWORKS WITH DEGREE MIXING

2007 ◽  
Vol 17 (07) ◽  
pp. 2419-2434 ◽  
Author(s):  
FRANCESCO SORRENTINO ◽  
MARIO DI BERNARDO ◽  
FRANCO GAROFALO
Keyword(s):  
Power Law ◽  
Biological Networks ◽  
Optimization Strategy ◽  
Power Law Distribution ◽  
Scale Free ◽  
Degree Correlation ◽  
Topological Features ◽  
Low Degree ◽  
Correlation Properties ◽  
Law Degree

We study the synchronizability and the synchronization dynamics of networks of nonlinear oscillators. We investigate how the synchronization of the network is influenced by some of its topological features such as variations of the power law degree distribution exponent γ and the degree correlation coefficient r. Using an appropriate construction algorithm based on clustering the network vertices in p classes according to their degrees, we construct networks with an assigned power law distribution but changing degree correlation properties. We find that the network synchronizability improves when the network becomes disassortative, i.e. when nodes with low degree are more likely to be connected to nodes with higher degree. We consider the case of both weighed and unweighed networks. The analytical results reported in the paper are then confirmed by a set of numerical observations obtained on weighed and unweighed networks of nonlinear Rössler oscillators. Using a nonlinear optimization strategy we also show that negative degree correlation is an emerging property of networks when synchronizability is to be optimized. This suggests that negative degree correlation observed experimentally in a number of physical and biological networks might be motivated by their need to synchronize better.

scholarly journals Ultra-small scale-free geometric networks

2006 ◽  
Vol 43 (3) ◽  
pp. 665-677 ◽  
Author(s):  
J. E. Yukich
Keyword(s):  
Long Range ◽  
Power Law ◽  
Degree Distribution ◽  
Small Scale ◽  
Graph Distance ◽  
Power Law Distribution ◽  
Scale Free

We consider a family of long-range percolation models (Gp)p>0on ℤdthat allow dependence between edges and have the following connectivity properties forp∈ (1/d, ∞): (i) the degree distribution of vertices inGphas a power-law distribution; (ii) the graph distance between pointsxandyis bounded by a multiple of logpdlogpd|x-y| with probability 1 -o(1); and (iii) an adversary can delete a relatively small number of nodes fromGp(ℤd∩ [0,n]d), resulting in two large, disconnected subgraphs.

A Small-World Model of Scale-Free Networks: Features and Verifications

2011 ◽  
Vol 50-51 ◽  
pp. 166-170 ◽  
Author(s):  
Wen Jun Xiao ◽  
Shi Zhong Jiang ◽  
Guan Rong Chen
Keyword(s):  
Complex Networks ◽  
Power Law ◽  
Degree Sequence ◽  
Small World ◽  
Static Condition ◽  
Vertex Degree ◽  
Power Law Distribution ◽  
Least Common Multiple ◽  
Scale Free ◽  
Vertex Degrees

It is now well known that many large-sized complex networks obey a scale-free power-law vertex-degree distribution. Here, we show that when the vertex degrees of a large-sized network follow a scale-free power-law distribution with exponent  2, the number of degree-1 vertices, if nonzero, is of order N and the average degree is of order lower than log N, where N is the size of the network. Furthermore, we show that the number of degree-1 vertices is divisible by the least common multiple of , , . . ., , and l is less than log N, where l = < is the vertex-degree sequence of the network. The method we developed here relies only on a static condition, which can be easily verified, and we have verified it by a large number of real complex networks.

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

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.

scholarly journals Ultra-small scale-free geometric networks

2006 ◽  
Vol 43 (03) ◽  
pp. 665-677
Author(s):  
J. E. Yukich
Keyword(s):  
Long Range ◽  
Power Law ◽  
Degree Distribution ◽  
Small Scale ◽  
Graph Distance ◽  
Power Law Distribution ◽  
Scale Free

We consider a family of long-range percolation models (G p ) p&gt;0 on ℤ d that allow dependence between edges and have the following connectivity properties for p ∈ (1/d, ∞): (i) the degree distribution of vertices in G p has a power-law distribution; (ii) the graph distance between points x and y is bounded by a multiple of log pd log pd | x - y | with probability 1 - o(1); and (iii) an adversary can delete a relatively small number of nodes from G p (ℤ d ∩ [0, n] d ), resulting in two large, disconnected subgraphs.

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