论文标题
一维软随机几何图中的连通性
Connectivity in One-Dimensional Soft Random Geometric Graphs
论文作者
论文摘要
在本文中，我们研究了一维软随机几何图（RGG）的连通性。图是通过将点随机放置在有界线段中的，并以概率取决于它们之间的距离的概率来生成。我们通过分析断开连接的关键模式完全连接图形的概率来得出界限。特别是，给出了分析表达式的均匀淋巴结数量的平均值和方差，并为其出现而建立了急剧的阈值。界限也针对无跨度的间隙得出，并且在分析上显示，在出现隔离节点的缩放缩放范围内，无差的间隙具有可忽略的概率。这与在考虑网络连接时最重要的因素是最重要的因素形成鲜明对比。
In this paper, we study the connectivity of a one-dimensional soft random geometric graph (RGG). The graph is generated by placing points at random on a bounded line segment and connecting pairs of points with a probability that depends on the distance between them. We derive bounds on the probability that the graph is fully connected by analysing key modes of disconnection. In particular, analytic expressions are given for the mean and variance of the number of isolated nodes, and a sharp threshold established for their occurrence. Bounds are also derived for uncrossed gaps, and it is shown analytically that uncrossed gaps have negligible probability in the scaling at which isolated nodes appear. This is in stark contrast to the hard RGG in which uncrossed gaps are the most important factor when considering network connectivity.
