The classical Graph Twiddling (GT) algorithm is the MapReduce implementation of triangle parallel enumeration algorithm. However, the GT algorithm can only enumerate the triangle structure of whole graph and can not enumerate the triangle structure of candidate vertexes directly. To solve the problem, a parallel algorithm was proposed for directly enumerating the triangle structure of candidate vertexes. Firstly, the set of all the combinations of candidate vertexes for forming triangle was given by analyzing the distribution of candidate vertexes. Then, through the screening of the set, the triangle structure of candidate vertexes was directly enumerated. Finally, the proposed algorithm was implemented on Spark to achieve high efficiency and popularity. The contrast experiment was completed on artificial datasets and real datasets. The experimental results show that, compared with the GT algorithm, the running time of the proposed algorithm is only 1/3 of the running time of GT algorithm, and the running time on Spark is only 1/7 of the running time on Hadoop. The proposed algorithm can be used to generate the triangle dataset of any candidate vertex directly and efficiently.