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中文摘要：
随机网络中的大连通分支能体现一个网络的连通情况，是几何随机图研究的一个热点，具有重要的理论意义和应用价值．本文利用渗流理论，研究了几何随机图大连通分支覆盖面积所具有的性质，并将理论结果应用到大型无线传感器网络中，研究了无线传感器网络覆盖的性质．研究结果表明，对于节点服从泊松分布的大型无线传感器网络，其大连通分支覆盖区域大小与总区域大小的比值趋于一个常数，且并估计出了2维空间中没有被大连通分支所覆盖的连通区域（本文称为空洞）的大小．这些结果为衡量无线传感器网络性能提供了理论基础，对实际布网和网络优化等具有一定的指导意义．
英文摘要：
The largest component of RGG（random geometric graph） has always been one of the most popular concerns in the research of RGG because it can reflect the connectivity of the whole network, and the study for the largest component has demonstrated theoretical as well as practical values. In this article, based on percolation theory, we investigate the theoretical properties of the coverage of the largest component of RGG, which are then applied in large wireless sensor networks. It is concluded that for a large sensor network following poisson distribution, the size of the area covered by the largest component is asymptotic constant w.h.p（with high probability） compared to the full space. Specifically to R^2, the size of the connected areas not covered by the largest component（we call cavities） is estimated. These results provide theoretical basis for measuring network performance, and can serve as a guideline in sensor network layout and optimization.
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