In this paper, we do exactly what the title implies: prove the Čebotarev Density Theorem. This is an extremely valuable theorem because it is a vast generalization of Dirichlet's Theorem on primes in an arithmetic progression. Our theorem goes even further to the case of other number fields; we will show that the prime ideals in an imaginary quadratic field K are virtually equidistributed among the conjugacy classes of Artin symbols in the Galois group of a Galois extension L over K. Note that L need not be abelian over K!
The output of this graph is used as Figure 1 of the paper: Wangyan Li, Zidong Wang, Guoliang Wei, Lifeng Ma, Jun Hu, and Derui Ding, “A Survey on Multisensor Fusion and Consensus Filtering for Sensor Networks,” Discrete Dynamics in Nature and Society, vol. 2015, Article ID 683701, 12 pages, 2015. doi:10.1155/2015/683701.
It's based on http://www.texample.net/tikz/examples/hierarchical-diagram/.
Relevant link: http://tex.stackexchange.com/questions/226461/how-to-draw-hierarchical-graph-like-this-one.