Explaining the Power-Law Degree Distribution in a Social Commerce Network

2009 ◽  
Author(s):  
Andrew T. Stephen ◽  
Olivier Toubia
Keyword(s):  
Power Law ◽  
Degree Distribution ◽  
Social Commerce ◽  
Law Degree

Explaining the power-law degree distribution in a social commerce network

2009 ◽  
Vol 31 (4) ◽  
pp. 262-270 ◽  
Author(s):  
Andrew T. Stephen ◽  
Olivier Toubia
Keyword(s):  
Power Law ◽  
Degree Distribution ◽  
Social Commerce ◽  
Law Degree

scholarly journals Models And Mining Of On-Line Social Networks

2021 ◽  
Author(s):  
Yanhua Tian
Keyword(s):  
Social Networks ◽  
Power Law ◽  
Degree Distribution ◽  
Small World ◽  
Spectral Expansion ◽  
On Line ◽  
Simulation Results ◽  
Small World Property ◽  
P Type ◽  
Law Degree

Power law degree distribution, the small world property, and bad spectral expansion are three of the most important properties of On-line Social Networks (OSNs). We sampled YouTube and Wikipedia to investigate OSNs. Our simulation and computational results support the conclusion that OSNs follow a power law degree distribution, have the small world property, and bad spectral expansion. We calculated the diameters and spectral gaps of OSNs samples, and compared these to graphs generated by the GEO-P model. Our simulation results support the Logarithmic Dimension Hypothesis, which conjectures that the dimension of OSNs is m = [log N]. We introduced six GEO-P type models. We ran simulations of these GEO-P-type models, and compared the simulated graphs with real OSN data. Our simulation results suggest that, except for the GEO-P (GnpDeg) model, all our models generate graphs with power law degree distributions, the small world property, and bad spectral expansion.

scholarly journals Multistage Random Growing Small-World Networks with Power-Law Degree Distribution

2006 ◽  
Vol 23 (3) ◽  
pp. 746-749 ◽  
Author(s):  
Liu Jian-Guo ◽  
Dang Yan-Zhong ◽  
Wang Zhong-Tuo
Keyword(s):  
Power Law ◽  
Degree Distribution ◽  
Small World ◽  
Small World Networks ◽  
Law Degree

GROWING HIERARCHICAL SCALE-FREE NETWORKS BY MEANS OF NONHIERARCHICAL PROCESSES

2007 ◽  
Vol 17 (07) ◽  
pp. 2447-2452 ◽  
Author(s):  
S. BOCCALETTI ◽  
D.-U. HWANG ◽  
V. LATORA
Keyword(s):  
Power Law ◽  
Degree Distribution ◽  
Preferential Attachment ◽  
Rate Equations ◽  
Scale Free ◽  
Scale Free Networks ◽  
Degree Correlations ◽  
Law Degree ◽  
Hierarchical Scale

We introduce a fully nonhierarchical network growing mechanism, that furthermore does not impose explicit preferential attachment rules. The growing procedure produces a graph featuring power-law degree and clustering distributions, and manifesting slightly disassortative degree-degree correlations. The rigorous rate equations for the evolution of the degree distribution and for the conditional degree-degree probability are derived.

scholarly journals Sparse Maximum-Entropy Random Graphs with a Given Power-Law Degree Distribution

2017 ◽  
Vol 173 (3-4) ◽  
pp. 806-844 ◽  
Author(s):  
Pim van der Hoorn ◽  
Gabor Lippner ◽  
Dmitri Krioukov
Keyword(s):  
Maximum Entropy ◽  
Random Graphs ◽  
Power Law ◽  
Degree Distribution ◽  
Law Degree

A Distributed and Local-World Topology Evolution Model for Wireless Sensor Network

2015 ◽  
Vol 7 (2) ◽  
pp. 45-55
Author(s):  
Changlun Zhang ◽  
Chao Li ◽  
Haibing Mu
Keyword(s):  
Wireless Sensor Network ◽  
Sensor Network ◽  
Power Law ◽  
Degree Distribution ◽  
Fixed Number ◽  
Evolution Model ◽  
Wireless Sensor ◽  
Distribution Analysis ◽  
Cluster Heads ◽  
Law Degree

In this paper, a new evolution model based on complex network among the cluster heads in wireless sensor network is proposed. The evolution model considered distributed and local-world mechanism during the evolving process. The theoretical analysis of this model exhibits a power-law degree distribution with mean-field theory, which provides good fault-tolerance. The degree exponent is not a fixed number, which changes with the distribution of the cluster heads and the energy as well as the communication radius. Furthermore, the degree exponent can lead to an upper limit -2 when the distribution of the cluster heads and the energy are both uniform distribution. Analysis and simulation show that the network exhibits well robustness and a power-law degree distribution.

scholarly journals Scale-Free Property for Degrees and Weights in a Preferential Attachment Random Graph Model

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
István Fazekas ◽  
Bettina Porvázsnyik
Keyword(s):  
Asymptotic Behaviour ◽  
Random Graph ◽  
Power Law ◽  
Degree Distribution ◽  
Preferential Attachment ◽  
Graph Model ◽  
Random Graph Model ◽  
Scale Free ◽  
Attachment Model ◽  
Law Degree

A random graph evolution mechanism is defined. The evolution studied is a combination of the preferential attachment model and the interaction of four vertices. The asymptotic behaviour of the graph is described. It is proved that the graph exhibits a power law degree distribution; in other words, it is scale-free. It turns out that any exponent in(2,∞)can be achieved. The proofs are based on martingale methods.

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