论文标题
重新评估球体边缘交叉数的分布
Reappraising the distribution of the number of edge crossings of graphs on a sphere
论文作者
论文摘要
许多真实的运输和移动性网络都将其顶点放在地球表面上。在这样的嵌入中，铺设在该表面上的边缘可能会交叉。在他的开创性研究中，月亮分析了在完整图和完整的两部分图上的交叉数分布，其顶点均匀地位于球体表面上，假设顶点位置彼此独立。在这里，我们根据有关交叉和计算机模拟方差的最新理论发展修改他对这种差异的推导。我们表明，月亮的公式在预测真实方差并提供精确公式方面是不准确的。
Many real transportation and mobility networks have their vertices placed on the surface of the Earth. In such embeddings, the edges laid on that surface may cross. In his pioneering research, Moon analyzed the distribution of the number of crossings on complete graphs and complete bipartite graphs whose vertices are located uniformly at random on the surface of a sphere assuming that vertex placements are independent from each other. Here we revise his derivation of that variance in the light of recent theoretical developments on the variance of crossings and computer simulations. We show that Moon's formulae are inaccurate in predicting the true variance and provide exact formulae.
