论文标题
具有任意度序列和边缘长度分布的空间网络的顺序构建
Sequential construction of spatial networks with arbitrary degree sequence and edge length distribution
论文作者
论文摘要
从软材料到无线通信的复杂系统通常被组织为随机几何网络，在该网络中，节点和边缘均匀地填充了某些空间的体积。研究此类网络很困难，因为它们从嵌入空间以及通过设计对网络结构施加的约束（例如度序列）继承了其属性。在这里，我们考虑具有给定分布的几何图和边缘长度的给定分布，并提出了这种图形无偏采样的数值方法。我们表明，该方法将所需的目标分布重现至渐近误差，这是一些边界情况，只有网络的正分数可以保证可以构造。
Complex systems, ranging from soft materials to wireless communication, are often organised as random geometric networks in which nodes and edges evenly fill up the volume of some space. Studying such networks is difficult because they inherit their properties from the embedding space as well as from the constraints imposed on the network's structure by design, for example, the degree sequence. Here we consider geometric graphs with a given distribution for vertex degrees and edge lengths and propose a numerical method for unbiased sampling of such graphs. We show that the method reproduces the desired target distributions up to a small error asymptotically, and that is some boundary cases only a positive fraction of the network is guaranteed to possible to construct.
