Graph algorithms are fundamental tools for deriving valuable insights from complex network structures. As network data grows in scale, and hardware architecture becomes more diverse than ever, the demand for efficient and portable graph algorithms has surged. The Kokkos framework has emerged as a promising solution for achieving high performance and portability in parallel computing applications. This paper presents a thorough evaluation of Kokkos-implemented triangle counting, an important graph kernel. Employing diverse algorithmic and implementation methods, we benchmark Kokkos-enabled graph algorithms targeting CPUs and GPUs. We explore the impact of both graph properties and Kokkos' parallel execution model on algorithmic efficiency. Our results indicate that thread scheduling can improve performance by up to 10×,data structure choice by 6 ×, and configuring the parallel hierarchy based on degree properties can result in a remarkable 300 ×difference in performance over untuned implementations on Kokkos.