scholarly journals Truncation of Power Law Behavior in “Scale-Free” Network Models due to Information Filtering

2002 ◽  
Vol 88 (13) ◽  
Author(s):  
Stefano Mossa ◽  
Marc Barthélémy ◽  
H. Eugene Stanley ◽  
Luís A. Nunes Amaral
Keyword(s):  
Power Law ◽  
Information Filtering ◽  
Network Models ◽  
Scale Free Network ◽  
Scale Free ◽  
Free Network

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.

THE RELEVANCE-STRENGTH IN A SCALE-FREE NETWORK

2008 ◽  
Vol 22 (31) ◽  
pp. 3053-3059 ◽  
Author(s):  
HYUN-JOO KIM
Keyword(s):  
Network Model ◽  
Shortest Path ◽  
Power Law ◽  
Path Length ◽  
Scale Free Network ◽  
Scale Free ◽  
Free Network ◽  
The Mean

We introduce a new quantity, relevance-strength which describes the relevance of a node to the others in a scale-free network. We define a weight between two nodes i and j based on the shortest path length between them and the relevance-strength of a node is defined as the sum of the weights between it and others. For the Barabási and Albert model which is a well-known scale-free network model, we measure the relevance-strength of each node and study the correlations with other quantities, such as the degree, the mean degree of neighbors of a node, and the mean relevance-strength of neighbors. We find that the relevance-strength shows power law behaviors and the crossover behaviors for the degree and the mean relevance-strength of neighbors. Also, we study the scaling behaviors of the relevance-strength for various average relevance-strength for all nodes.

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 IMMUNIZATION FOR COMPLEX NETWORK BASED ON THE EFFECTIVE DEGREE OF VERTEX

2012 ◽  
Vol 26 (06) ◽  
pp. 1250052 ◽  
Author(s):  
KE HU ◽  
YI TANG
Keyword(s):  
Network Models ◽  
Scale Free Network ◽  
Scale Free ◽  
Immunization Strategies ◽  
Degree Of Vertex ◽  
Free Network ◽  
Immunization Procedure ◽  
Degree Correlations ◽  
Effective Immunization ◽  
Effective Degree

The basic idea of many effective immunization strategies is to first rank the importance of vertices according to the degrees of vertices and then remove the vertices from highest importance to lowest until the network becomes disconnected. Here we define the effective degrees of vertex, i.e., the number of its connections linking to un-immunized nodes in current network during the immunization procedure, to rank the importance of vertex, and modify these strategies by using the effective degrees of vertices. Simulations on both the scale-free network models with various degree correlations and two real networks have revealed that the immunization strategies based on the effective degrees are often more effective than those based on the degrees in the initial network.

AVALANCHES OF BAK–SNEPPEN COEVOLUTION MODEL ON DIRECTED SCALE-FREE NETWORK

Fractals ◽  
2009 ◽  
Vol 17 (02) ◽  
pp. 233-237 ◽  
Author(s):  
KYOUNG EUN LEE ◽  
JAE WOO LEE
Keyword(s):  
Probability Distribution ◽  
Power Law ◽  
Critical Exponents ◽  
Return Time ◽  
Scale Free Network ◽  
Avalanche Size ◽  
Scale Free ◽  
Free Network ◽  
First Return Time ◽  
Physical Quantities

We study the critical properties of the Bak–Sneppen coevolution model on scale-free networks by Monte Carlo method. We report the distribution of the avalanche size and fractal activity through the branching process. We observe that the critical fitness fc(N) depends on the number of the node such as fc(N) ~ 1/ log (N) for both the scale-free network and the directed scale-free network. Near the critical fitness many physical quantities show power-law behaviors. The probability distribution P(s) of the avalanche size at the critical fitness shows a power-law like P(s) ~ s-τ with τ = 1.53(5) regardless of the scale-free network and the directed scale free network. The probability distribution Pf(t) of the first return time also shows a power-law such as Pf(t) ~ t-τf. The critical exponents τf are equivalent for both the scale-free network and the directed scale-free network. We obtain the critical exponents as τf = 1.776(5) at the scalinge regime. The directionality of the network does not change the universality on the network.

scholarly journals Characterizing the intrinsic correlations of scale-free networks

2016 ◽  
Vol 27 (03) ◽  
pp. 1650024 ◽  
Author(s):  
J. B. de Brito ◽  
C. I. N. Sampaio Filho ◽  
A. A. Moreira ◽  
J. S. Andrade
Keyword(s):  
Extreme Values ◽  
Network Models ◽  
Network Size ◽  
Scale Free Network ◽  
Scale Free ◽  
Scale Free Networks ◽  
Free Network ◽  
Degree Correlations ◽  
Multiple Edges ◽  
Random Scale

When studying topological or dynamical properties of random scale-free networks, it is tacitly assumed that degree–degree correlations are not present. However, simple constraints, such as the absence of multiple edges and self-loops, can give rise to intrinsic correlations in these structures. In the same way that Fermionic correlations in thermodynamic systems are relevant only in the limit of low temperature, the intrinsic correlations in scale-free networks are relevant only when the extreme values for the degrees grow faster than the square root of the network size. In this situation, these correlations can significantly affect the dependence of the average degree of the nearest neighbors of a given vertex on this vertices degree. Here, we introduce an analytical approach that is capable to predict the functional form of this property. Moreover, our results indicate that random scale-free network models are not self-averaging, that is, the second moment of their degree distribution may vary orders of magnitude among different realizations. Finally, we argue that the intrinsic correlations investigated here may have profound impact on the critical properties of random scale-free networks.

ANALYSIS OF A COMPLEX NETWORK OF PHYSICS CONCEPTS

2012 ◽  
Vol 26 (28) ◽  
pp. 1250186 ◽  
Author(s):  
HYUN-JOO KIM
Keyword(s):  
Power Law ◽  
Betweenness Centrality ◽  
Random Network ◽  
The Other ◽  
Topological Properties ◽  
Scale Free Network ◽  
Scale Free ◽  
Energy Concept ◽  
Physics Concepts ◽  
Free Network

We construct the physics concepts network in which the physics concepts is considered as nodes. We find that this network is clearly not a random network but a scale-free network in which the distribution P(k) of the degree k follows a power law, P(k) ~ k-γ with exponent γ ≈ 2.41. The relevance between the physics concepts and the important concepts are studied by measuring the degree, the betweenness centrality, and the relevance strength and we find that the energy concept is most important. Also we find that the relevance strength s(k) as a function of the degree k exhibits a power-law behavior, s(k) ~ kα with the exponent α ≈ 0.15 and s(knn) as a function of the average neighbor's degree knn follows a power-law behavior, [Formula: see text] with the exponent δ ≈ 0.17 for small knn. We also measured the other quantities which describe the topological properties of the network and find that it has the hierarchical property and tree-like patterns.

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