scholarly journals Contact processes on random graphs with power law degree distributions have critical value 0

2009 ◽  
Vol 37 (6) ◽  
pp. 2332-2356 ◽  
Author(s):  
Shirshendu Chatterjee ◽  
Rick Durrett
Keyword(s):  
Random Graphs ◽  
Power Law ◽  
Critical Value ◽  
Contact Processes ◽  
Law Degree

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

Investigating the Properties of a Social Bookmarking and Tagging Network

2010 ◽  
Vol 6 (1) ◽  
pp. 1-19 ◽  
Author(s):  
Ralitsa Angelova ◽  
Marek Lipczak ◽  
Evangelos Milios ◽  
Pawel Pralat
Keyword(s):  
Social Networks ◽  
Social Network ◽  
Random Graphs ◽  
Power Law ◽  
Information Dissemination ◽  
Collaborative Tagging ◽  
Social Bookmarking ◽  
Primary Means ◽  
Common Interests ◽  
Law Degree

Social networks and collaborative tagging systems are rapidly gaining popularity as a primary means for storing and sharing data among friends, family, colleagues, or perfect strangers as long as they have common interests. del.icio.us3 is a social network where people store and share their personal bookmarks. Most importantly, users tag their bookmarks for ease of information dissemination and later look up. However, it is the friendship links that make del.icio.us a social network. They exist independently of the set of bookmarks that belong to the users and have no relation to the tags typically assigned to the bookmarks. To study the interaction among users, the strength of the existing links and their hidden meaning, we introduce implicit links in the network. These links connect only highly “similar” users. Here, similarity can reflect different aspects of the user’s profile that makes her similar to any other user, such as number of shared bookmarks, or similarity of their tags clouds. The authors investigate the question whether friends have common interests, they gain additional insights on the strategies that users use to assign tags to their bookmarks, and they demonstrate that the graphs formed by implicit links have unique properties differing from binomial random graphs or random graphs with an expected power-law degree distribution.

Investigating the Properties of a Social Bookmarking and Tagging Network

2011 ◽  
pp. 1-16
Author(s):  
Ralitsa Angelova ◽  
Marek Lipczak ◽  
Evangelos Milios ◽  
Pawel Pralat
Keyword(s):  
Social Networks ◽  
Social Network ◽  
Random Graphs ◽  
Power Law ◽  
Degree Distribution ◽  
Information Dissemination ◽  
Social Bookmarking ◽  
Primary Means ◽  
Common Interests ◽  
Law Degree

Social networks and collaborative tagging systems are rapidly gaining popularity as a primary means for storing and sharing data among friends, family, colleagues, or perfect strangers as long as they have common interests. del.icio.us3 is a social network where people store and share their personal bookmarks. Most importantly, users tag their bookmarks for ease of information dissemination and later look up. However, it is the friendship links, that make del.icio.us a social network. They exist independently of the set of bookmarks that belong to the users and have no relation to the tags typically assigned to the bookmarks. To study the interaction among users, the strength of the existing links and their hidden meaning, we introduce implicit links in the network. These links connect only highly “similar” users. Here, similarity can reflect different aspects of the user’s profile that makes her similar to any other user, such as number of shared bookmarks, or similarity of their tags clouds. The authors investigate the question whether friends have common interests, they gain additional insights on the strategies that users use to assign tags to their bookmarks, and they demonstrate that the graphs formed by implicit links have unique properties differing from binomial random graphs or random graphs with an expected power-law degree distribution.

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.

Dense subgraphs of power-law random graphs

2021 ◽  
Vol 10 (1) ◽  
pp. 1-11
Author(s):  
Denis O. Lazarev ◽  
Nikolay N. Kuzyurin
Keyword(s):  
Random Graphs ◽  
Power Law ◽  
Dense Subgraphs
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