On Random k-Out Graphs with Preferential Attachment
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2013
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| Online Access: | http://rave.ohiolink.edu/etdc/view?acc_num=osu1370527839 |
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ndltd-OhioLink-oai-etd.ohiolink.edu-osu13705278392021-08-03T05:24:02Z On Random k-Out Graphs with Preferential Attachment Peterson, Nicholas Richard Mathematics Combinatorial probability random graphs random mappings Hansen and Jaworski digraphs functional digraph vertex connectivity minimum vertex degree k-core total variation distance In a series of papers, Hansen and Jaworski explored a very general model for choosing random mappings with exchangeable in-degrees. The special case in which the in-degrees are obtained by conditioning independent random variables with a specially chosen negative binomial distribution on their sum corresponds in distribution to a process for choosing random mappings which exhibits preferential attachment - images are chosen one at a time, and vertices chosen as images earlier in the process are more likely to be chosen again. They consider the functional digraph as a random object, and study its properties.We generalize Hansen and Jaworski’s preferential attachment model to a new setting: our model produces digraphs with labeled arcs and uniform out-degree k; other than a few technical wrinkles, the graph obtained by ignoring arc directions, loops, and multiple arcs is essentially a preferential attachment version of the k-out graph model first studied by Fenner and Frieze. This dissertation splits nicely in to three parts: first, we build a collection of analytical tools for studying our mapping; second, we study structural properties of its induced graph, including minimum vertex degree, vertex connectivity, and the k-core; finally, we present a very strong measurement of the differences and similarities between our model and a limiting case that is uniformly random. 2013-08-28 English text The Ohio State University / OhioLINK http://rave.ohiolink.edu/etdc/view?acc_num=osu1370527839 http://rave.ohiolink.edu/etdc/view?acc_num=osu1370527839 unrestricted This thesis or dissertation is protected by copyright: all rights reserved. It may not be copied or redistributed beyond the terms of applicable copyright laws. |
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NDLTD |
| language |
English |
| sources |
NDLTD |
| topic |
Mathematics Combinatorial probability random graphs random mappings Hansen and Jaworski digraphs functional digraph vertex connectivity minimum vertex degree k-core total variation distance |
| spellingShingle |
Mathematics Combinatorial probability random graphs random mappings Hansen and Jaworski digraphs functional digraph vertex connectivity minimum vertex degree k-core total variation distance Peterson, Nicholas Richard On Random k-Out Graphs with Preferential Attachment |
| author |
Peterson, Nicholas Richard |
| author_facet |
Peterson, Nicholas Richard |
| author_sort |
Peterson, Nicholas Richard |
| title |
On Random k-Out Graphs with Preferential Attachment |
| title_short |
On Random k-Out Graphs with Preferential Attachment |
| title_full |
On Random k-Out Graphs with Preferential Attachment |
| title_fullStr |
On Random k-Out Graphs with Preferential Attachment |
| title_full_unstemmed |
On Random k-Out Graphs with Preferential Attachment |
| title_sort |
on random k-out graphs with preferential attachment |
| publisher |
The Ohio State University / OhioLINK |
| publishDate |
2013 |
| url |
http://rave.ohiolink.edu/etdc/view?acc_num=osu1370527839 |
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AT petersonnicholasrichard onrandomkoutgraphswithpreferentialattachment |
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