DYNAMICS BEHAVIORS OF WEIGHTED LOCAL-WORLD EVOLVING NETWORKS WITH EXTENDED LINKS

2009 ◽  
Vol 20 (11) ◽  
pp. 1719-1735 ◽  
Author(s):  
GUANGHUI WEN ◽  
ZHISHENG DUAN
Keyword(s):  
Weak Interactions ◽  
Small World ◽  
Local Information ◽  
Scale Free ◽  
Evolving Networks ◽  
Free Behavior ◽  
Small World Property ◽  
Evolving Model ◽  
Analytical Expressions ◽  
Good Agreement

In this paper, we present a local-world evolving model to characterize weighted networks. By introducing the extended links to mimic the weak interactions between the nodes in different local-worlds, the model yields scale-free behavior as well as the small-world property, as confirmed in many real networks. With the increase of the local information, the generated network undergoes a transition from assortative to disassortative, meanwhile the small-world property is preserved. It indicates that the small-world property is a universal characteristic in our model. The numerical simulation results are in good agreement with the analytical expressions.

EVOLVING MODEL OF SCALE-FREE NETWORKS WITH INTRINSIC LINKS

2008 ◽  
Vol 19 (07) ◽  
pp. 1129-1144 ◽  
Author(s):  
XIANMIN GENG ◽  
GUANGHUI WEN ◽  
YING WANG ◽  
JINXIA LI
Keyword(s):  
Numerical Simulation ◽  
Preferential Attachment ◽  
Scaling Exponent ◽  
Scale Free ◽  
Scale Free Networks ◽  
Free Behavior ◽  
Simulation Results ◽  
Evolving Model ◽  
Analytical Expressions ◽  
Good Agreement

In this paper, we introduce the concept of intrinsic link, which is used to describe the intrinsic interactions between the individuals in complex systems. Furthermore, we present a model for the evolution of complex networks, in which the system dynamics motivated by four mechanisms: the addition of new nodes with preferential attachment, the addition of new nodes with intrinsic attachment, the addition of new links with preferential attachment and the addition of new intrinsic links. The model yields scale-free behavior for the degree distributions as confirmed in many real networks. With continumm theory, we get the analytical expressions of the degree distribution and the scaling exponent γ. The analytical expressions are in good agreement with the numerical simulation results.

STOCHASTIC EVOLVING MODEL FOR COMPLEX NETWORKS

2004 ◽  
Vol 18 (23) ◽  
pp. 1157-1164 ◽  
Author(s):  
HYUN-JOO KIM ◽  
YEON-MU CHOI ◽  
JIN MIN KIM
Keyword(s):  
Control Parameter ◽  
Small World ◽  
Network Size ◽  
Clustering Coefficient ◽  
Scale Free ◽  
Hierarchical Topology ◽  
Free Behavior ◽  
Small World Property ◽  
Evolving Model ◽  
High Degree

We introduce an evolving complex network model, where a new vertex is added and new edges between already existing vertices are added with a control parameter p. The model shows the characteristics of real networks such as small-world property, high degree of clustering, scale-free behavior in degree distribution, and hierarchical topology. We obtain the various values of degree exponent γ in the range 2<γ≤3 by adjusting the parameter p and find that the degree exponent decreases logarithmically with p. In addition, the clustering coefficient is tunable by changing the control parameter p, and the average path length L is proportional to ln ( ln N) with nonzero p, where N is the network size.

SMALL-WORLD AND SCALE-FREE PROPERTIES OF FRACTAL NETWORKS MODELED ON n-DIMENSIONAL SIERPINSKI PYRAMID

Fractals ◽  
2017 ◽  
Vol 25 (06) ◽  
pp. 1750057 ◽  
Author(s):  
CHENG ZENG ◽  
MENG ZHOU
Keyword(s):  
Small World ◽  
The Self ◽  
Scale Free ◽  
Evolving Networks ◽  
Self Similar

In this paper, we construct evolving networks based on the construction of the [Formula: see text]-dimensional Sierpinski pyramid by the self-similar structure. We show that such networks have scale-free and small-world effects.

SMALL-WORLD AND SCALE-FREE PROPERTIES OF THE n-DIMENSIONAL SIERPINSKI CUBE NETWORKS

Fractals ◽  
2020 ◽  
Vol 28 (01) ◽  
pp. 2050001
Author(s):  
CHENG ZENG ◽  
MENG ZHOU ◽  
YUMEI XUE
Keyword(s):  
Small World ◽  
The Self ◽  
Self Similarity ◽  
Scale Free ◽  
Evolving Networks

In this paper, we construct evolving networks from [Formula: see text]-dimensional Sierpinski cube. Using the self-similarity of Sierpinski cube, we show the evolving networks have scale-free and small-world properties.

scholarly journals Directed random geometric graphs

2019 ◽  
Vol 7 (5) ◽  
pp. 792-816
Author(s):  
Jesse Michel ◽  
Sushruth Reddy ◽  
Rikhav Shah ◽  
Sandeep Silwal ◽  
Ramis Movassagh
Keyword(s):  
Real World ◽  
Word Association ◽  
Graph Model ◽  
Small World ◽  
Geometric Graph ◽  
Clustering Coefficient ◽  
Random Geometric Graph ◽  
Random Geometric Graphs ◽  
Scale Free ◽  
Small World Property

Abstract Many real-world networks are intrinsically directed. Such networks include activation of genes, hyperlinks on the internet and the network of followers on Twitter among many others. The challenge, however, is to create a network model that has many of the properties of real-world networks such as power-law degree distributions and the small-world property. To meet these challenges, we introduce the Directed Random Geometric Graph (DRGG) model, which is an extension of the random geometric graph model. We prove that it is scale-free with respect to the indegree distribution, has binomial outdegree distribution, has a high clustering coefficient, has few edges and is likely small-world. These are some of the main features of aforementioned real-world networks. We also empirically observed that word association networks have many of the theoretical properties of the DRGG model.

Epidemic spreading on evolving networks

2019 ◽  
Vol 33 (23) ◽  
pp. 1950266 ◽  
Author(s):  
Jin-Xuan Yang
Keyword(s):  
Preferential Attachment ◽  
Small World ◽  
Network Evolution ◽  
Epidemic Spreading ◽  
Epidemic Threshold ◽  
Scale Free ◽  
Evolving Networks ◽  
Power Law Exponent ◽  
Free Network ◽  
Over Time

Network structure will evolve over time, which will lead to changes in the spread of the epidemic. In this work, a network evolution model based on the principle of preferential attachment is proposed. The network will evolve into a scale-free network with a power-law exponent between 2 and 3 by our model, where the exponent is determined by the evolution parameters. We analyze the epidemic spreading process as the network evolves from a small-world one to a scale-free one, including the changes in epidemic threshold over time. The condition of epidemic threshold to increase is given with the evolution processes. The simulated results of real-world networks and synthetic networks show that as the network evolves at a low evolution rate, it is more conducive to preventing epidemic spreading.

scholarly journals Complex network description of the ionosphere

2018 ◽  
Vol 25 (1) ◽  
pp. 233-240
Author(s):  
Shikun Lu ◽  
Hao Zhang ◽  
Xihai Li ◽  
Yihong Li ◽  
Chao Niu ◽  
...  
Keyword(s):  
Complex Network ◽  
Hypothesis Test ◽  
Small World ◽  
Dynamic Processes ◽  
Electron Content ◽  
Vertical Total Electron Content ◽  
Total Electron ◽  
Scale Free ◽  
Probabilistic Graph ◽  
Small World Property

Abstract. Complex networks have emerged as an essential approach of geoscience to generate novel insights into the nature of geophysical systems. To investigate the dynamic processes in the ionosphere, a directed complex network is constructed, based on a probabilistic graph of the vertical total electron content (VTEC) from 2012. The results of the power-law hypothesis test show that both the out-degree and in-degree distribution of the ionospheric network are not scale-free. Thus, the distribution of the interactions in the ionosphere is homogenous. None of the geospatial positions play an eminently important role in the propagation of the dynamic ionospheric processes. The spatial analysis of the ionospheric network shows that the interconnections principally exist between adjacent geographical locations, indicating that the propagation of the dynamic processes primarily depends on the geospatial distance in the ionosphere. Moreover, the joint distribution of the edge distances with respect to longitude and latitude directions shows that the dynamic processes travel further along the longitude than along the latitude in the ionosphere. The analysis of “small-world-ness” indicates that the ionospheric network possesses the small-world property, which can make the ionosphere stable and efficient in the propagation of dynamic processes.

WEIGHTED EVOLVING NETWORKS WITH INTRINSIC STRENGTH

2007 ◽  
Vol 18 (09) ◽  
pp. 1435-1442 ◽  
Author(s):  
XIANMIN GENG ◽  
GUANGHUI WEN
Keyword(s):  
Preferential Attachment ◽  
Dynamical Evolution ◽  
Intrinsic Property ◽  
Network Growth ◽  
Evolving Networks ◽  
Attachment Model ◽  
Analytical Expressions ◽  
Power Law Distributions ◽  
Intrinsic Strength ◽  
Good Agreement

In this paper, we introduce the concept of intrinsic strength which is used to describe the node's intrinsic property. Furthermore, we present a single preferential attachment model for the evolution of weighted networks in which the network growth is coupled with dynamical evolution of weights and intrinsic strength. The model yields a nontrivial time evolution of nodes' properties and generalized power law distributions for the weight, strength and degree, as confirmed in many real networks. The numerical simulation results are in good agreement with the analytical expressions.

scholarly journals Navigation in small-world networks: a scale-free continuum model

2006 ◽  
Vol 43 (04) ◽  
pp. 1173-1180 ◽  
Author(s):  
Massimo Franceschetti ◽  
Ronald Meester
Keyword(s):  
Social Sciences ◽  
Scale Invariance ◽  
Small World ◽  
Local Information ◽  
Engineering Systems ◽  
Small World Networks ◽  
Social Contacts ◽  
Scale Free ◽  
Free Model ◽  
Random Connection Model

The small-world phenomenon, the principle that we are all linked by a short chain of intermediate acquaintances, has been investigated in mathematics and social sciences. It has been shown to be pervasive both in nature and in engineering systems like the World Wide Web. Work of Jon Kleinberg has shown that people, using only local information, are very effective at finding short paths in a network of social contacts. In this paper we argue that the underlying key to finding short paths is scale invariance. In order to appreciate scale invariance we suggest a continuum setting, since true scale invariance happens at all scales, something which cannot be observed in a discrete model. We introduce a random-connection model that is related to continuum percolation, and we prove the existence of a unique scale-free model, among a large class of models, that allows the construction, with high probability, of short paths between pairs of points separated by any distance.

A SMALL-WORLD AND SCALE-FREE NETWORK GENERATED BY SIERPINSKI TETRAHEDRON

Fractals ◽  
2016 ◽  
Vol 24 (01) ◽  
pp. 1650001 ◽  
Author(s):  
JIN CHEN ◽  
FEI GAO ◽  
ANBO LE ◽  
LIFENG XI ◽  
SHUHUA YIN
Keyword(s):  
Small World ◽  
Scale Free Network ◽  
Fractal Scaling ◽  
Scale Free ◽  
Evolving Networks ◽  
Free Network

The Sierpinski tetrahedron is used to construct evolving networks, whose vertexes are all solid regular tetrahedra in the construction of the Sierpinski tetrahedron up to the stage [Formula: see text] and any two vertexes are neighbors if and only if the corresponding tetrahedra are in contact with each other on boundary. We show that such networks have the small-world and scale-free effects, but are not fractal scaling.

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