scholarly journals Minimum vertex cover in generalized random graphs with power law degree distribution

2016 ◽  
Vol 647 ◽  
pp. 101-111
Author(s):  
André L. Vignatti ◽  
Murilo V.G. da Silva
Keyword(s):  
Random Graphs ◽  
Power Law ◽  
Degree Distribution ◽  
Vertex Cover ◽  
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

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 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.

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