Topology properties of a weighted multi-local-world evolving network

2015 ◽  
Vol 93 (3) ◽  
pp. 353-360 ◽  
Author(s):  
Meifeng Dai ◽  
Danping Zhang ◽  
Lei Li
Keyword(s):  
Real World ◽  
Weight Distribution ◽  
Preferential Attachment ◽  
Mean Field ◽  
Field Method ◽  
Strength Distribution ◽  
Power Law Distribution ◽  
World Model ◽  
The Mean ◽  
Theoretical Results

Many real-world networks, ranging from the world trade web to the Internet network, have been described by multi-local-worlds. It is obvious that the nodes within a local world are much more connected to each other than to the others outside the local world. A multi-local-world model can capture and describe these real-world networks’ topological properties. Based on the local-world model, a weighted multi-local-world evolving network model is presented. This model combines selected nodes with preferential attachment and three kinds of local changes of weights. Using a rate equation and the mean-field method, we study the network’s properties: the weight distribution and the strength distribution. We theoretically prove that the weight distribution and the strength distribution follow a power-law distribution in some conditions. Numerical simulations are in agreement with the theoretical results.

A WEIGHTED EVOLVING NETWORK WITH AGING-NODE-DELETING AND LOCAL REARRANGEMENTS OF WEIGHTS

2014 ◽  
Vol 25 (02) ◽  
pp. 1350093 ◽  
Author(s):  
MEIFENG DAI ◽  
DANPING ZHANG
Keyword(s):  
Rate Equation ◽  
Mean Field ◽  
Evolutionary Model ◽  
Field Method ◽  
Strength Distribution ◽  
Power Law Distribution ◽  
Time Step ◽  
Binary State ◽  
State Present ◽  
The Relationship

In previous study of complex network, researchers generally considered the increase of the un-weighted network by the method of adding new nodes and new links. However, most of real networks are weighted and characterized by capacities or strength instead of a binary state (present or absent), and their nodes and links experience both increase and deletion. Barrat, Barthlemy and Vespignani, Phys. Rev. Lett.92, 228701 (2004) presented an evolutionary model (BBV model) to investigate weighted networks. We present a weighted evolution network model based on BBV model, which not only considers to add a new node and m links, but also to remove an old node and corresponding links with probability at each time step. By using rate equation and mean-field method, we study the network's properties: The weight, strength and their distributions. We find that the relationship between weight and strength is nonlinear. In addition, we theoretically prove that the weight distribution and the strength distribution follow a power-law distribution, respectively.

scholarly journals Dynamically Weighted Clique Evolution Model in Clique Networks

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Zhang-Wei Li ◽  
Xu-Hua Yang ◽  
Feng-Ling Jiang ◽  
Guang Chen ◽  
Guo-Qing Weng ◽  
...  
Keyword(s):  
Real World ◽  
Mean Field Theory ◽  
Mean Field ◽  
Strength Distribution ◽  
Evolution Model ◽  
Edge Weight ◽  
Time Step ◽  
Complete Subgraph ◽  
Scale Free ◽  
The Mean

This paper proposes a weighted clique evolution model based on clique (maximal complete subgraph) growth and edge-weight driven for complex networks. The model simulates the scheme of real-world networks that the evolution of networks is likely to be driven by the flow, such as traffic or information flow needs, as well as considers that real-world networks commonly consist of communities. At each time step of a network’s evolution progress, an edge is randomly selected according to a preferential scheme. Then a new clique which contains the edge is added into the network while the weight of the edge is adjusted to simulate the flow change brought by the new clique addition. We give the theoretical analysis based on the mean field theory, as well as some numerical simulation for this model. The result shows that the model can generate networks with scale-free distributions, such as edge weight distribution and node strength distribution, which can be found in many real-world networks. It indicates that the evolution rule of the model may attribute to the formation of real-world networks.

scholarly journals Friendship paradox in growth networks: analytical and empirical analysis

2021 ◽  
Vol 6 (1) ◽  
Author(s):  
Sergei P. Sidorov ◽  
Sergei V. Mironov ◽  
Alexey A. Grigoriev
Keyword(s):  
Real World ◽  
Preferential Attachment ◽  
Empirical Studies ◽  
Mean Field ◽  
Network Models ◽  
Average Degree ◽  
Closure Model ◽  
Triadic Closure ◽  
Attachment Mechanism ◽  
Over Time

AbstractMany empirical studies have shown that in social, citation, collaboration, and other types of networks in real world, the degree of almost every node is less than the average degree of its neighbors. This imbalance is well known in sociology as the friendship paradox and states that your friends are more popular than you on average. If we introduce a value equal to the ratio of the average degree of the neighbors for a certain node to the degree of this node (which is called the ‘friendship index’, FI), then the FI value of more than 1 for most nodes indicates the presence of the friendship paradox in the network. In this paper, we study the behavior of the FI over time for networks generated by growth network models. We will focus our analysis on two models based on the use of the preferential attachment mechanism: the Barabási–Albert model and the triadic closure model. Using the mean-field approach, we obtain differential equations describing the dynamics of changes in the FI over time, and accordingly, after obtaining their solutions, we find the expected values of this index over iterations. The results show that the values of FI are decreasing over time for all nodes in both models. However, for networks constructed in accordance with the triadic closure model, this decrease occurs at a much slower rate than for the Barabási–Albert graphs. In addition, we analyze several real-world networks and show that their FI distributions follow a power law. We show that both the Barabási–Albert and the triadic closure networks exhibit the same behavior. However, for networks based on the triadic closure model, the distributions of FI are more heavy-tailed and, in this sense, are closer to the distributions for real networks.

The Applicability of the Mean Field Method in the Optical Bistability

1986 ◽  
pp. 173-177
Author(s):  
I. M. Popescu ◽  
E. N. Stefanescu ◽  
P. E. Sterian
Keyword(s):  
Optical Bistability ◽  
Mean Field ◽  
Field Method ◽  
The Mean

Superconducting and other phases in organic high polymers of polyacenic carbon skeletons. II. The mean field method

1986 ◽  
Vol 85 (5) ◽  
pp. 3097-3102 ◽  
Author(s):  
M. Kimura ◽  
H. Kawabe ◽  
K. Nishikawa ◽  
S. Aono
Keyword(s):  
Mean Field ◽  
Field Method ◽  
The Mean ◽  
High Polymers

scholarly journals An analytical framework for consensus-based global optimization method

2018 ◽  
Vol 28 (06) ◽  
pp. 1037-1066 ◽  
Author(s):  
José A. Carrillo ◽  
Young-Pil Choi ◽  
Claudia Totzeck ◽  
Oliver Tse
Keyword(s):  
Global Optimization ◽  
Optimization Problems ◽  
Mean Field ◽  
Optimization Method ◽  
Analytical Framework ◽  
Global Minimizer ◽  
Global Optimization Method ◽  
The Mean ◽  
Class Of Functions ◽  
Theoretical Results

In this paper, we provide an analytical framework for investigating the efficiency of a consensus-based model for tackling global optimization problems. This work justifies the optimization algorithm in the mean-field sense showing the convergence to the global minimizer for a large class of functions. Theoretical results on consensus estimates are then illustrated by numerical simulations where variants of the method including nonlinear diffusion are introduced.

GENERALIZATION OF THE MEAN-FIELD METHOD FOR POWER-LAW DISTRIBUTIONS

2006 ◽  
Vol 16 (01) ◽  
pp. 129-135 ◽  
Author(s):  
TARO TOYOIZUMI ◽  
KAZUYUKI AIHARA
Keyword(s):  
Computational Complexity ◽  
Financial Markets ◽  
Mean Field ◽  
Field Method ◽  
World Systems ◽  
Developed Turbulence ◽  
Binary State ◽  
The Mean ◽  
Generalized Mean ◽  
Power Law Distributions

Recently much attention has been paid to the nonextensive canonical distributions: the α-families. Such distributions have been found in many real-world systems such as fully developed turbulence and financial markets. In this paper, a generalized mean-field method to approximate the expectations of the α-families is proposed. We calculate the α′-projection of a probability distribution to find that the computational complexity to approximate the expectations is greatly reduced with a proper choice of the projection-index α′. We apply this method to a simple binary-state system and compare the results with direct numerical calculations.

scholarly journals A Weighted Multi-Local-World Network Evolving Model and Its Application in Software Network Modeling

2018 ◽  
Vol 2018 ◽  
pp. 1-9
Author(s):  
Zengyang Li ◽  
Hui Liu ◽  
Jun-An Lu ◽  
Bing Li
Keyword(s):  
Power Law ◽  
Network Modeling ◽  
Real Life ◽  
Strength Distribution ◽  
Software Systems ◽  
Distribution Analysis ◽  
Power Law Distribution ◽  
Software Network ◽  
Evolving Model ◽  
Theoretical Results

The phenomenon of local worlds (also known as communities) exists in numerous real-life networks, for example, computer networks and social networks. We proposed the Weighted Multi-Local-World (WMLW) network evolving model, taking into account (1) the dense links between nodes in a local world, (2) the sparse links between nodes from different local worlds, and (3) the different importance between intra-local-world links and inter-local-world links. On topology evolving, new links between existing local worlds and new local worlds are added to the network, while new nodes and links are added to existing local worlds. On weighting mechanism, weight of links in a local world and weight of links between different local worlds are endowed different meanings. It is theoretically proven that the strength distribution of the generated network by the WMLW model yields to a power-law distribution. Simulations show the correctness of the theoretical results. Meanwhile, the degree distribution also follows a power-law distribution. Analysis and simulation results show that the proposed WMLW model can be used to model the evolution of class diagrams of software systems.

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