scholarly journals Engineering Uniform Sampling of Graphs with a Prescribed Power-law Degree Sequence

2022 ◽  
pp. 27-40
Author(s):  
Daniel Allendorf ◽  
Ulrich Meyer ◽  
Manuel Penschuck ◽  
Hung Tran ◽  
Nick Wormald
Keyword(s):  
Power Law ◽  
Degree Sequence ◽  
Uniform Sampling ◽  
Law Degree

scholarly journals A Fast Algorithm to Find All High-Degree Vertices in Graphs with a Power-Law Degree Sequence

2014 ◽  
Vol 10 (1-2) ◽  
pp. 137-161 ◽  
Author(s):  
Colin Cooper ◽  
Tomasz Radzik ◽  
Yiannis Siantos
Keyword(s):  
Power Law ◽  
Fast Algorithm ◽  
Degree Sequence ◽  
Law Degree ◽  
High Degree

scholarly journals The diameter of KPKVB random graphs

2019 ◽  
Vol 51 (2) ◽  
pp. 358-377 ◽  
Author(s):  
Tobias Müller ◽  
Merlijn Staps
Keyword(s):  
Complex Networks ◽  
Power Law ◽  
Degree Sequence ◽  
Graph Model ◽  
Clustering Coefficient ◽  
Maximum Diameter ◽  
Hyperbolic Distance ◽  
Random Graph Model ◽  
Power Law Exponent ◽  
Law Degree

AbstractWe consider a random graph model that was recently proposed as a model for complex networks by Krioukov et al. (2010). In this model, nodes are chosen randomly inside a disk in the hyperbolic plane and two nodes are connected if they are at most a certain hyperbolic distance from each other. It has previously been shown that this model has various properties associated with complex networks, including a power-law degree distribution and a strictly positive clustering coefficient. The model is specified using three parameters: the number of nodes N, which we think of as going to infinity, and $\alpha, \nu > 0$, which we think of as constant. Roughly speaking, $\alpha$ controls the power-law exponent of the degree sequence and $\nu$ the average degree. Earlier work of Kiwi and Mitsche (2015) has shown that, when $\alpha \lt 1$ (which corresponds to the exponent of the power law degree sequence being $\lt 3$), the diameter of the largest component is asymptotically almost surely (a.a.s.) at most polylogarithmic in N. Friedrich and Krohmer (2015) showed it was a.a.s. $\Omega(\log N)$ and improved the exponent of the polynomial in $\log N$ in the upper bound. Here we show the maximum diameter over all components is a.a.s. $O(\log N),$ thus giving a bound that is tight up to a multiplicative constant.

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 Modeling and Analysis of New Products Diffusion on Heterogeneous Networks

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Shuping Li ◽  
Zhen Jin
Keyword(s):  
Decision Making ◽  
Numerical Analysis ◽  
Power Law ◽  
Heterogeneous Networks ◽  
New Products ◽  
Positive Equilibrium ◽  
Modeling And Analysis ◽  
Scale Free ◽  
Scale Free Networks ◽  
Law Degree

We present a heterogeneous networks model with the awareness stage and the decision-making stage to explain the process of new products diffusion. If mass media is neglected in the decision-making stage, there is a threshold whether the innovation diffusion is successful or not, or else it is proved that the network model has at least one positive equilibrium. For networks with the power-law degree distribution, numerical simulations confirm analytical results, and also at the same time, by numerical analysis of the influence of the network structure and persuasive advertisements on the density of adopters, we give two different products propagation strategies for two classes of nodes in scale-free networks.

scholarly journals Quantitative analysis of cryptocurrencies transaction graph

2019 ◽  
Vol 4 (1) ◽  
Author(s):  
Amir Pasha Motamed ◽  
Behnam Bahrak
Keyword(s):  
Growth Rate ◽  
Statistical Analysis ◽  
Quantitative Analysis ◽  
Power Law ◽  
Degree Sequence ◽  
Power Law Distribution ◽  
Comprehensive Comparison ◽  
Statistical Studies ◽  
Financial Transactions ◽  
Over Time

AbstractCryptocurrencies as a new way of transferring assets and securing financial transactions have gained popularity in recent years. Transactions in cryptocurrencies are publicly available, hence, statistical studies on different aspects of these currencies are possible. However, previous statistical analysis on cryptocurrencies transactions have been very limited and mostly devoted to Bitcoin, with no comprehensive comparison between these currencies. In this study, we intend to compare the transaction graph of Bitcoin, Ethereum, Litecoin, Dash, and Z-Cash, with respect to the dynamics of their transaction graphs over time, and discuss their properties. In particular, we observed that the growth rate of the nodes and edges of the transaction graphs, and the density of these graphs, are closely related to the price of these currencies. We also found that the transaction graph of these currencies is non-assortative, i.e. addresses do not tend for transact with a particular type of addresses of higher or lower degree, and the degree sequence of their transaction graph follows the power law distribution.

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