scholarly journals Ultra-small scale-free geometric networks

2006 ◽  
Vol 43 (03) ◽  
pp. 665-677
Author(s):  
J. E. Yukich
Keyword(s):  
Long Range ◽  
Power Law ◽  
Degree Distribution ◽  
Small Scale ◽  
Graph Distance ◽  
Power Law Distribution ◽  
Scale Free

We consider a family of long-range percolation models (G p ) p>0 on ℤ d that allow dependence between edges and have the following connectivity properties for p ∈ (1/d, ∞): (i) the degree distribution of vertices in G p has a power-law distribution; (ii) the graph distance between points x and y is bounded by a multiple of log pd log pd | x - y | with probability 1 - o(1); and (iii) an adversary can delete a relatively small number of nodes from G p (ℤ d ∩ [0, n] d ), resulting in two large, disconnected subgraphs.

scholarly journals Ultra-small scale-free geometric networks

2006 ◽  
Vol 43 (3) ◽  
pp. 665-677 ◽  
Author(s):  
J. E. Yukich
Keyword(s):  
Long Range ◽  
Power Law ◽  
Degree Distribution ◽  
Small Scale ◽  
Graph Distance ◽  
Power Law Distribution ◽  
Scale Free

We consider a family of long-range percolation models (Gp)p>0on ℤdthat allow dependence between edges and have the following connectivity properties forp∈ (1/d, ∞): (i) the degree distribution of vertices inGphas a power-law distribution; (ii) the graph distance between pointsxandyis bounded by a multiple of logpdlogpd|x-y| with probability 1 -o(1); and (iii) an adversary can delete a relatively small number of nodes fromGp(ℤd∩ [0,n]d), resulting in two large, disconnected subgraphs.

scholarly journals Co-Movement in Stock Markets Based on Directed Complex Network

2016 ◽  
Vol 8 (2) ◽  
pp. 179
Author(s):  
Zhen Du ◽  
Pujiang Chen ◽  
Na Luo ◽  
Yingjie Tang
Keyword(s):  
Complex Network ◽  
Power Law ◽  
Degree Distribution ◽  
Path Length ◽  
Stock Exchange ◽  
Small World ◽  
Clustering Coefficient ◽  
Power Law Distribution ◽  
Scale Free ◽  
Set Up

<p>In this paper, directed complex network is applied to the study of A shares in SSE (Shanghai Stock Exchange). In order to discuss the intrinsic attributes and regularities in stock market, we set up a directed complex network, selecting 450 stocks as nodes between 2012 and 2014 and stock yield correlation connected as edges. By discussing out-degree and in-degree distribution, we find essential nodes in stock network, which represent the leading stock,. Moreover, we analyze directed average path length and clustering coefficient in the condition of different threshold, which shows that the network doesn’t have a small- world effect. Furthermore, we see that when threshold is between 0.08 and 0.15, the network follows the power-law distribution and behaves scale-free.</p>

scholarly journals The structure of co-publications multilayer network

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Ghislain Romaric Meleu ◽  
Paulin Yonta Melatagia
Keyword(s):  
Power Law ◽  
Degree Distribution ◽  
Preferential Attachment ◽  
Small World ◽  
Generation Model ◽  
Small World Network ◽  
Power Law Distribution ◽  
Multilayer Networks ◽  
Multilayer Network ◽  
Scientific Papers

AbstractUsing the headers of scientific papers, we have built multilayer networks of entities involved in research namely: authors, laboratories, and institutions. We have analyzed some properties of such networks built from data extracted from the HAL archives and found that the network at each layer is a small-world network with power law distribution. In order to simulate such co-publication network, we propose a multilayer network generation model based on the formation of cliques at each layer and the affiliation of each new node to the higher layers. The clique is built from new and existing nodes selected using preferential attachment. We also show that, the degree distribution of generated layers follows a power law. From the simulations of our model, we show that the generated multilayer networks reproduce the studied properties of co-publication networks.

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.

scholarly journals Power-law energy distributions of small-scale impulsive events on the active Sun: results from IRIS

2020 ◽  
Vol 499 (1) ◽  
pp. 1385-1394
Author(s):  
Nived Vilangot Nhalil ◽  
Chris J Nelson ◽  
Mihalis Mathioudakis ◽  
J Gerry Doyle ◽  
Gavin Ramsay
Keyword(s):  
Energy Range ◽  
Power Law ◽  
Coronal Heating ◽  
Radiative Energy ◽  
Small Scale ◽  
Data Sets ◽  
Imaging Data ◽  
Power Law Distribution ◽  
Energy Distributions ◽  
Power Law Index

ABSTRACT Numerous studies have analysed inferred power-law distributions between frequency and energy of impulsive events in the outer solar atmosphere in an attempt to understand the predominant energy supply mechanism in the corona. Here, we apply a burst detection algorithm to high-resolution imaging data obtained by the Interface Region Imaging Spectrograph to further investigate the derived power-law index, γ, of bright impulsive events in the transition region. Applying the algorithm with a constant minimum event lifetime (of either 60 s or 110 s) indicated that the target under investigation, such as Plage and Sunspot, has an influence on the observed power-law index. For regions dominated by sunspots, we always find γ &lt; 2; however, for data sets where the target is a plage region, we often find that γ &gt; 2 in the energy range (∼1023, ∼1026) erg. Applying the algorithm with a minimum event lifetime of three time-steps indicated that cadence was another important factor, with the highest cadence data sets returning γ &gt; 2 values. The estimated total radiative power obtained for the observed energy distributions is typically 10–25 per cent of what would be required to sustain the corona indicating that impulsive events in this energy range are not sufficient to solve coronal heating. If we were to extend the power-law distribution down to an energy of 1021 erg, and assume parity between radiative energy release and the deposition of thermal energy, then such bursts could provide 25–50 per cent of the required energy to account for the coronal heating problem.

scholarly journals The use of the power law for designing wireless networks

2018 ◽  
Vol 21 ◽  
pp. 00012
Author(s):  
Andrzej Paszkiewicz
Keyword(s):  
Wireless Networks ◽  
Power Law ◽  
Degree Distribution ◽  
Limited Resources ◽  
Random Networks ◽  
New Approach ◽  
Available Bandwidth ◽  
Scale Free ◽  
Scale Free Networks ◽  
Node Removal

The paper concerns the use of the scale-free networks theory and the power law in designing wireless networks. An approach based on generating random networks as well as on the classic Barabási-Albert algorithm were presented. The paper presents a new approach taking the limited resources for wireless networks into account, such as available bandwidth. In addition, thanks to the introduction of opportunities for dynamic node removal it was possible to realign processes occurring in wireless networks. After introduction of these modifications, the obtained results were analyzed in terms of a power law and the degree distribution of each node.

Priority Weighted Fitness Model in Networks

2012 ◽  
Vol 229-231 ◽  
pp. 1854-1857
Author(s):  
Xin Yi Chen
Keyword(s):  
World Wide Web ◽  
Power Law ◽  
Common Property ◽  
World Wide ◽  
Genetic Networks ◽  
Power Law Distribution ◽  
Large Networks ◽  
Scale Free ◽  
The World ◽  
Complex Topology

Systems as diverse as genetic networks or the World Wide Web are best described as networks with complex topology. A common property of many large networks is that the vertex connectivities follow a power-law distribution. This feature was found to be a consequence of three generic mechanisms: (i) networks expand continuously by the addition of new vertices, (ii) new vertex with priority selected different edges of weighted selected that connected to different vertices in the system, and (iii) by the fitness probability that a new vertices attach preferentially to sites that are already well connected. A model based on these ingredients reproduces the observed stationary scale-free distributions, which indicates that the development of large networks is governed by robust self-organizing phenomena. Experiment results show that the model is more close to the actual Internet network.

scholarly journals SYNCHRONIZABILITY AND SYNCHRONIZATION DYNAMICS OF WEIGHED AND UNWEIGHED SCALE FREE NETWORKS WITH DEGREE MIXING

2007 ◽  
Vol 17 (07) ◽  
pp. 2419-2434 ◽  
Author(s):  
FRANCESCO SORRENTINO ◽  
MARIO DI BERNARDO ◽  
FRANCO GAROFALO
Keyword(s):  
Power Law ◽  
Biological Networks ◽  
Optimization Strategy ◽  
Power Law Distribution ◽  
Scale Free ◽  
Degree Correlation ◽  
Topological Features ◽  
Low Degree ◽  
Correlation Properties ◽  
Law Degree

We study the synchronizability and the synchronization dynamics of networks of nonlinear oscillators. We investigate how the synchronization of the network is influenced by some of its topological features such as variations of the power law degree distribution exponent γ and the degree correlation coefficient r. Using an appropriate construction algorithm based on clustering the network vertices in p classes according to their degrees, we construct networks with an assigned power law distribution but changing degree correlation properties. We find that the network synchronizability improves when the network becomes disassortative, i.e. when nodes with low degree are more likely to be connected to nodes with higher degree. We consider the case of both weighed and unweighed networks. The analytical results reported in the paper are then confirmed by a set of numerical observations obtained on weighed and unweighed networks of nonlinear Rössler oscillators. Using a nonlinear optimization strategy we also show that negative degree correlation is an emerging property of networks when synchronizability is to be optimized. This suggests that negative degree correlation observed experimentally in a number of physical and biological networks might be motivated by their need to synchronize better.

scholarly journals Discriminating low frequency components from long range persistent fluctuations in daily atmospheric temperature variability

2009 ◽  
Vol 9 (14) ◽  
pp. 4537-4544 ◽  
Author(s):  
M. Lanfredi ◽  
T. Simoniello ◽  
V. Cuomo ◽  
M. Macchiato
Keyword(s):  
Time Series ◽  
Long Range ◽  
Power Law ◽  
Low Frequency ◽  
Atmospheric Temperature ◽  
Fluctuation Analysis ◽  
Climate Modelling ◽  
Scale Free ◽  
Statistical Confidence ◽  
Frequency Components

Abstract. This study originated from recent results reported in literature, which support the existence of long-range (power-law) persistence in atmospheric temperature fluctuations on monthly and inter-annual scales. We investigated the results of Detrended Fluctuation Analysis (DFA) carried out on twenty-two historical daily time series recorded in Europe in order to evaluate the reliability of such findings in depth. More detailed inspections emphasized systematic deviations from power-law and high statistical confidence for functional form misspecification. Rigorous analyses did not support scale-free correlation as an operative concept for Climate modelling, as instead suggested in literature. In order to understand the physical implications of our results better, we designed a bivariate Markov process, parameterised on the basis of the atmospheric observational data by introducing a slow dummy variable. The time series generated by this model, analysed both in time and frequency domains, tallied with the real ones very well. They accounted for both the deceptive scaling found in literature and the correlation details enhanced by our analysis. Our results seem to evidence the presence of slow fluctuations from another climatic sub-system such as ocean, which inflates temperature variance up to several months. They advise more precise re-analyses of temperature time series before suggesting dynamical paradigms useful for Climate modelling and for the assessment of Climate Change.

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.

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