Reinterpretaion of the friendship paradox

2017 ◽  
Vol 28 (02) ◽  
pp. 1750024
Author(s):  
Jingcheng Fu ◽  
Jianliang Wu
Keyword(s):  
Social Networks ◽  
Random Network ◽  
Network Models ◽  
Mean Value ◽  
Clustering Coefficient ◽  
Probability Method ◽  
Price Model ◽  
Power Law Exponent ◽  
The Mean ◽  
Shed Light

The friendship paradox (FP) is a sociological phenomenon stating that most people have fewer friends than their friends do. It is to say that in a social network, the number of friends that most individuals have is smaller than the average number of friends of friends. This has been verified by Feld. We call this interpreting method mean value version. But is it the best choice to portray the paradox? In this paper, we propose a probability method to reinterpret this paradox, and we illustrate that the explanation using our method is more persuasive. An individual satisfies the FP if his (her) randomly chosen friend has more friends than him (her) with probability not less than [Formula: see text]. Comparing the ratios of nodes satisfying the FP in networks, [Formula: see text], we can see that the probability version is stronger than the mean value version in real networks both online and offline. We also show some results about the effects of several parameters on [Formula: see text] in random network models. Most importantly, [Formula: see text] is a quadratic polynomial of the power law exponent [Formula: see text] in Price model, and [Formula: see text] is higher when the average clustering coefficient is between [Formula: see text] and [Formula: see text] in Petter–Beom (PB) model. The introduction of the probability method to FP can shed light on understanding the network structure in complex networks especially in social networks.

Word-of-Mouth Recommendations in an Automobile Market System

2019 ◽  
Author(s):  
Amineh Zadbood ◽  
Nicholas Russo ◽  
Steven Hoffenson
Keyword(s):  
Social Networks ◽  
Word Of Mouth ◽  
Consumer Preferences ◽  
Random Network ◽  
Network Models ◽  
System Level ◽  
Purchasing Decisions ◽  
Eigenvector Centrality ◽  
Agent Based ◽  
Consumer Interactions

Abstract Improving design in the context of market systems requires an understanding of how consumers learn about and evaluate competing products. Marketing models frequently assume that consumers choose the product with the highest utility, which provides businesses insights into how to design and price their products to maximize profits. While recent research has shown the impacts of consumer interactions within social networks on their purchasing decisions, they typically model market systems using a top-down approach. This paper applies an agent-based modeling approach with social network models to investigate the extent to which word-of-mouth (WOM) communications are influential in changing consumer preferences and producer market performance. Using a random network, we study the effects of the number of referrals for a product and the degrees of similarity between the senders and receivers of referrals on purchase decisions. In addition, the eigenvector centrality metric is used to analyze the spread of WOM referrals. The simulation results show that the most influential consumers in the network can create significant shifts in the market share, and a statistical analysis reveals a significant change in the system-level metrics of interest for the competing firms when WOM recommendations are included. The findings incentivize producers to invest in supporting their product development efforts with rigorous social networks analysis so as to increase their market success.

scholarly journals Snowdrift Game on Topologically Alterable Complex Networks

2015 ◽  
Vol 2015 ◽  
pp. 1-5
Author(s):  
Zhe Wang ◽  
Hong Yao ◽  
Jun Du ◽  
Xingzhao Peng ◽  
Chao Ding
Keyword(s):  
Complex Networks ◽  
Power Law ◽  
Network Models ◽  
Average Degree ◽  
Clustering Coefficient ◽  
Topological Parameters ◽  
Snowdrift Game ◽  
Cooperation Level ◽  
Optimal Value ◽  
Power Law Exponent

In order to study the influence of network’s structure on cooperation level of repeated snowdrift game, in the frame of two kinds of topologically alterable network models, the relation between the cooperation density and the topological parameters was researched. The results show that the network’s cooperation density is correlated reciprocally with power-law exponent and positively with average clustering coefficient; in other words, the more homogenous and less clustered a network, the lower the network’s cooperation level; and the relation between average degree and cooperation density is nonmonotonic; when the average degree deviates from the optimal value, the cooperation density drops.

scholarly journals Analysis of Basic Features in Dynamic Network Models

Entropy ◽  
2018 ◽  
Vol 20 (9) ◽  
pp. 681 ◽  
Author(s):  
Pedro Zufiria ◽  
Iker Barriales-Valbuena
Keyword(s):  
Random Network ◽  
Density Ratio ◽  
Dynamic Network ◽  
Network Models ◽  
Clustering Coefficient ◽  
Edge Density ◽  
Mathematical Framework ◽  
Complexity Measures ◽  
Dynamic Network Models ◽  
Link Density

Time evolving Random Network Models are presented as a mathematical framework for modelling and analyzing the evolution of complex networks. This framework allows the analysis over time of several network characterizing features such as link density, clustering coefficient, degree distribution, as well as entropy-based complexity measures, providing new insight on the evolution of random networks. First, some simple dynamic network models, based only on edge density, are analyzed to serve as a baseline reference for assessing more complex models. Then, a model that depends on network structure with the aim of reflecting some characteristics of real networks is also analyzed. Such model shows a more sophisticated behavior with two different regimes, one of them leading to the generation of high clustering coefficient/link density ratio values when compared with the baseline values, as it happens in many real networks. Simulation examples are discussed to illustrate the behavior of the proposed models.

Wealth distribution under Yard–Sale exchange with proportional taxes

2016 ◽  
Vol 27 (08) ◽  
pp. 1650094 ◽  
Author(s):  
R. Bustos-Guajardo ◽  
Cristian F. Moukarzel
Keyword(s):  
Asymptotic Behavior ◽  
Power Law ◽  
Wealth Distribution ◽  
Mean Value ◽  
Recent Analysis ◽  
Return Distribution ◽  
Power Law Exponent ◽  
Extensive Numerical Simulation ◽  
The Mean ◽  
Parameter Dependent

Recent analysis of a Yard–Sale (YS) exchange model supplemented with redistributive proportional taxation suggested an asymptotic behavior [Formula: see text] for the wealth distribution, with a parameter-dependent exponent [Formula: see text]. Revisiting this problem, it is here shown analytically, and confirmed by extensive numerical simulation, that the asymptotic behavior of [Formula: see text] is not power-law but rather a Gaussian. When taxation is weak, we furthermore show that a restricted-range power-law behavior appears for wealths around the mean value. The corresponding power-law exponent equals 3/2 when the return distribution has zero mean.

scholarly journals Impact of gray matter signal regression in resting state and language task functional networks

2016 ◽  
Author(s):  
Luis C. T. Herrera ◽  
Gabriela Castellano ◽  
Ana C. Coan ◽  
M. Ludwing ◽  
C. L. César
Keyword(s):  
Community Structure ◽  
Gray Matter ◽  
Resting State ◽  
Mean Value ◽  
Clustering Coefficient ◽  
Data Sets ◽  
Before And After ◽  
The Mean ◽  
Graph Parameters ◽  
The Impact

AbstractA network analysis of the resting state (RS) and language task (LT) of fRMI data sets is presented. Specifically, the analysis compares the impact of the global signal regression of gray matter signal on the graph parameters and community structure derived of functional data. It was found that, without gray matter signal regression (GSR), the group comparison showed no significant changes of the global metrics between the two conditions studied. With gray matter signal regression, significant differences between the global (local) metrics for the conditions were obtained. The mean degree, the clustering coefficient of the network and the mean value of the local efficiency were metrics with significant changes. The community structure of group connectivity matrices was explored for both conditions (RS and LT) and for different preprocessing steps. When gray matter signal regression was performed, small changes of the community structure were observed. Approximately, the same regions were classified in the same communities before and after GSR. This means, that the community structure of the data is weakly affected by this preprocessing step. The modularity index presented significant changes between conditions (RS and LT) and between different preprocessing pipeline.

Application of Lattice Imaging Techniques to Amorphous Films

1975 ◽  
Vol 33 ◽  
pp. 8-9
Author(s):  
S. R. Herd ◽  
P. Chaudhari
Keyword(s):  
Nearest Neighbor ◽  
Random Network ◽  
Imaging Techniques ◽  
Network Models ◽  
Accurate Method ◽  
Direct Transmission ◽  
Lattice Imaging ◽  
Transmission Electron ◽  
Lattice Planes ◽  
Nearest Neighbor Distances

Electron diffraction and direct transmission have been used extensively to study the local atomic arrangement in amorphous solids and in particular Ge. Nearest neighbor distances had been calculated from E.D. profiles and the results have been interpreted in terms of the microcrystalline or the random network models. Direct transmission electron microscopy appears the most direct and accurate method to resolve this issue since the spacial resolution of the better instruments are of the order of 3Å. In particular the tilted beam interference method is used regularly to show fringes corresponding to 1.5 to 3Å lattice planes in crystals as resolution tests.

Long-period modulated superstructures in Pd-12.5 at.%Ce and Pd-15 at.%Ce alloys

1990 ◽  
Vol 48 (4) ◽  
pp. 164-165
Author(s):  
Noriyuki Kuwano ◽  
Masaru Itakura ◽  
Kensuke Oki
Keyword(s):  
Electron Microscopy ◽  
Mean Value ◽  
Heavy Elements ◽  
Arc Furnace ◽  
X Ray ◽  
Long Period ◽  
Ultra High Purity ◽  
Heat Treated ◽  
Atomic Scattering ◽  
The Mean

Pd-Ce alloys exhibit various anomalies in physical properties due to mixed valences of Ce, and the anomalies are thought to be strongly related with the crystal structures. Since Pd and Ce are both heavy elements, relative magnitudes of (fcc-fpd) are so small compared with <f> that superlattice reflections, even if any, sometimes cannot be detected in conventional x-ray powder patterns, where fee and fpd are atomic scattering factors of Ce and Pd, and <f> the mean value in the crystal. However, superlattices in Pd-Ce alloys can be analyzed by electron microscopy, thanks to the high detectability of electron diffraction. In this work, we investigated modulated superstructures in alloys with 12.5 and 15.0 at.%Ce.Ingots of Pd-Ce alloys were prepared in an arc furnace under atmosphere of ultra high purity argon. The disc specimens cut out from the ingots were heat-treated in vacuum and electrothinned to electron transparency by a jet method.

Partition Coefficient Ratios and Tumour Perfusion Studied with 85mKr and 133Xe

1987 ◽  
Vol 26 (06) ◽  
pp. 253-257
Author(s):  
M. Mäntylä ◽  
J. Perkkiö ◽  
J. Heikkonen
Keyword(s):  
Partition Coefficient ◽  
Partition Coefficients ◽  
Regional Blood Flow ◽  
Blood Perfusion ◽  
Compartmental Analysis ◽  
Malignant Tumour ◽  
Mean Value ◽  
Perfusion Rate ◽  
Biological Variables ◽  
The Mean

The relative partition coefficients of krypton and xenon, and the regional blood flow in 27 superficial malignant tumour nodules in 22 patients with diagnosed tumours were measured using the 85mKr- and 133Xe-clearance method. In order to minimize the effect of biological variables on the measurements the radionuclides were injected simultaneously into the tumour. The distribution of the radiotracers was assumed to be in equilibrium at the beginning of the experiment. The blood perfusion was calculated by fitting a two-exponential function to the measuring points. The mean value of the perfusion rate calculated from the xenon results was 13 ± 10 ml/(100 g-min) [range 3 to 38 ml/(100 g-min)] and from the krypton results 19 ± 11 ml/(100 g-min) [range 5 to 45 ml/(100 g-min)]. These values were obtained, if the partition coefficients are equal to one. The equations obtained by using compartmental analysis were used for the calculation of the relative partition coefficient of krypton and xenon. The partition coefficient of krypton was found to be slightly smaller than that of xenon, which may be due to its smaller molecular weight.

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