Abstract: Generalized sparse matrix-matrix multiplication (SpGEMM) is a key primitive kernel for many high-performance graph algorithms as well as for machine learning, and data analysis algorithms. Although many SpGEMM algorithms have been proposed, such as ESC and SPA, there is currently no SpGEMM kernel optimized for vector engines (VEs). NEC SX-Aurora is the new vector computing system that can achieve high performance by leveraging high bandwidth memory of 1.2TB/s and long vector of VEs, where the execution of scientific applications is limited by memory bandwidth. In this paper, we demonstrate significant initial work of SpGEMM kernel for a vector engine and implement it to vectorize several essential graph analysis algorithms: Butterfly counting and Triangle counting. We propose a SpGEMM algorithm with a novel hybrid method based on sparse vectors and loop raking to maximize the length of vectorizable code for vector machine architectures. The experimental results show that the vector engine has advantages on more massive data sets. This work contributes to high performance and portability of the SpGEMM kernel to a new family of heterogeneous computing systems, which is Vector Host (VH) equipped with different accelerators or VEs.