多类型优先依恋树

Q3 Mathematics
Sebastian Rosengren
{"title":"多类型优先依恋树","authors":"Sebastian Rosengren","doi":"10.24166/im.05.2018","DOIUrl":null,"url":null,"abstract":"A multi-type preferential attachment tree is introduced, and studied using general multi-type branching processes. For the $p$-type case we derive a framework for studying the tree where a type $i$ vertex generates new type $j$ vertices with rate $w_{ij}(n_1,n_2,\\ldots, n_p)$ where $n_k$ is the number of type $k$ vertices previously generated by the type $i$ vertex, and $w_{ij}$ is a non-negative function from $\\mathbb{N}^p$ to $\\mathbb{R}$. The framework is then used to derive results for trees with more specific attachment rates. \nIn the case with linear preferential attachment---where type $i$ vertices generate new type $j$ vertices with rate $w_{ij}(n_1,n_2,\\ldots, n_p)=\\gamma_{ij}(n_1+n_2+\\dots +n_p)+\\beta_{ij}$, where $\\gamma_{ij}$ and $\\beta_{ij}$ are positive constants---we show that under mild regularity conditions on the parameters $\\{\\gamma_{ij}\\}, \\{\\beta_{ij}\\}$ the asymptotic degree distribution of a vertex is a power law distribution. The asymptotic composition of the vertex population is also studied.","PeriodicalId":38105,"journal":{"name":"Internet Mathematics","volume":"2018 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2017-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"9","resultStr":"{\"title\":\"A Multi-type Preferential Attachment Tree\",\"authors\":\"Sebastian Rosengren\",\"doi\":\"10.24166/im.05.2018\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A multi-type preferential attachment tree is introduced, and studied using general multi-type branching processes. For the $p$-type case we derive a framework for studying the tree where a type $i$ vertex generates new type $j$ vertices with rate $w_{ij}(n_1,n_2,\\\\ldots, n_p)$ where $n_k$ is the number of type $k$ vertices previously generated by the type $i$ vertex, and $w_{ij}$ is a non-negative function from $\\\\mathbb{N}^p$ to $\\\\mathbb{R}$. The framework is then used to derive results for trees with more specific attachment rates. \\nIn the case with linear preferential attachment---where type $i$ vertices generate new type $j$ vertices with rate $w_{ij}(n_1,n_2,\\\\ldots, n_p)=\\\\gamma_{ij}(n_1+n_2+\\\\dots +n_p)+\\\\beta_{ij}$, where $\\\\gamma_{ij}$ and $\\\\beta_{ij}$ are positive constants---we show that under mild regularity conditions on the parameters $\\\\{\\\\gamma_{ij}\\\\}, \\\\{\\\\beta_{ij}\\\\}$ the asymptotic degree distribution of a vertex is a power law distribution. The asymptotic composition of the vertex population is also studied.\",\"PeriodicalId\":38105,\"journal\":{\"name\":\"Internet Mathematics\",\"volume\":\"2018 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2017-04-11\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"9\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Internet Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.24166/im.05.2018\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Internet Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.24166/im.05.2018","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 9

摘要

介绍了一种多类型优先连接树,并利用一般的多类型分支过程进行了研究。对于$p$类型的情况,我们导出了一个研究树的框架,其中类型$i$顶点生成新的类型$j$顶点,速率为$w_{ij}(n_1,n2,\ldots,n_p)$,其中$n_k$是以前由类型$i$顶点生成的类型$k$顶点的数量,$w_{ij}$是从$\mathbb{n}^p$到$\mathbb{R}$的非负函数。然后使用该框架来导出具有更具体附着率的树的结果。在线性优先附着的情况下——其中类型$i$顶点生成新类型$j$顶点,速率为$w_,顶点的渐近度分布是幂律分布。还研究了顶点总体的渐近组成。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
A Multi-type Preferential Attachment Tree
A multi-type preferential attachment tree is introduced, and studied using general multi-type branching processes. For the $p$-type case we derive a framework for studying the tree where a type $i$ vertex generates new type $j$ vertices with rate $w_{ij}(n_1,n_2,\ldots, n_p)$ where $n_k$ is the number of type $k$ vertices previously generated by the type $i$ vertex, and $w_{ij}$ is a non-negative function from $\mathbb{N}^p$ to $\mathbb{R}$. The framework is then used to derive results for trees with more specific attachment rates. In the case with linear preferential attachment---where type $i$ vertices generate new type $j$ vertices with rate $w_{ij}(n_1,n_2,\ldots, n_p)=\gamma_{ij}(n_1+n_2+\dots +n_p)+\beta_{ij}$, where $\gamma_{ij}$ and $\beta_{ij}$ are positive constants---we show that under mild regularity conditions on the parameters $\{\gamma_{ij}\}, \{\beta_{ij}\}$ the asymptotic degree distribution of a vertex is a power law distribution. The asymptotic composition of the vertex population is also studied.
求助全文
通过发布文献求助,成功后即可免费获取论文全文。 去求助
来源期刊
Internet Mathematics
Internet Mathematics Mathematics-Applied Mathematics
自引率
0.00%
发文量
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信