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The power of choice combined with preferential attachement


 
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1. Title Title of document The power of choice combined with preferential attachement
 
2. Creator Author's name, affiliation, country Yury Malyshkin; Moscow State University; Russian Federation
 
2. Creator Author's name, affiliation, country Elliot Paquette; Weizmann Institute of Science; Israel
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) preferential attachment; choice; stochastic approximation
 
3. Subject Subject classification 05C80
 
4. Description Abstract

We prove almost sure convergence of the maximum degree in an evolving tree model combining local choice and preferential attachment. At each step in the growth of the graph, a new vertex is introduced. A fixed, finite number of possible neighbors are sampled from the existing vertices with probability proportional to degree. Of these possibilities, the new vertex attaches to the vertex from the sample that has the highest degree. The maximal degree in this model has linear or near-linear behavior. This behavior contrasts sharply with the behavior in the same choice model with uniform attachment as well as the preferential attachment model without choice. The proof is based on showing the tree has a persistent hub by comparison with the standard preferential attachment model, as well as martingale and stochastic approximation arguments.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) NSF
 
7. Date (YYYY-MM-DD) 2014-07-12
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ecp.ejpecp.org/article/view/3461
 
10. Identifier Digital Object Identifier 10.1214/ECP.v19-3461
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 19
 
12. Language English=en en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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