Connectivity of networks with general connection functions
Connectivity of networks with general connection functions
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DOI：
10.1103/physreve.93.032313
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发表时间：
2014-11
期刊：
影响因子：
--
通讯作者：
C. Dettmann;Orestis Georgiou
中科院分区：
文献类型：
--
作者：
C. Dettmann;Orestis Georgiou
在原始（1961）的吉尔伯特（Gilbert）随机几何图模型中，节点是根据泊松点过程放置的，以及固定范围内的节点。最近引入了由无线临时网络“软”或“概率”连接模型的动机，其中涉及“连接函数” H（r），该函数使距离r的两个节点链接（直接连接）。在许多应用程序（不仅是无线网络）中，需要连接该图。也就是说，每个节点都以多跃波方式链接到其他所有节点。在这里，在两个或三个维度中，在凸域中密集网络的连接概率是根据一个非常通用的连接函数的边界组件的贡献来表达的。事实证明，仅出现了几个数量，例如连接函数的矩。与以前的研究和数值模拟的特殊情况发现了良好的一致性。
In the original (1961) Gilbert model of random geometric graphs, nodes are placed according to a Poisson point process, and links formed between those within a fixed range. Motivated by wireless ad hoc networks "soft" or "probabilistic" connection models have recently been introduced, involving a "connection function" H(r) that gives the probability that two nodes at distance r are linked (directly connect). In many applications (not only wireless networks), it is desirable that the graph is connected; that is, every node is linked to every other node in a multihop fashion. Here the connection probability of a dense network in a convex domain in two or three dimensions is expressed in terms of contributions from boundary components for a very general class of connection functions. It turns out that only a few quantities such as moments of the connection function appear. Good agreement is found with special cases from previous studies and with numerical simulations.