What are the most efficient algorithms for detecting cycles in a directed graph?

Question

I am working on a problem where I need to detect cycles in a directed graph. The graph is represented using an adjacency list, and it can have a large number of nodes and edges. I am looking for the most efficient algorithm to detect cycles, considering both time complexity and space complexity. I have come across several approaches, such as Depth-First Search (DFS) and Kahn's algorithm, but I am not sure which is the best fit for my scenario.

I have implemented the basic DFS approach, where I maintain a recursion stack to detect back edges, which indicate a cycle. The algorithm works for small graphs, but as the size of the graph increases, I notice a significant drop in performance. Additionally, I tried using Kahn's algorithm for topological sorting, but I am not confident if it's the best approach for all types of graphs, especially those with a large number of nodes.

I expected the DFS approach to be efficient enough for larger graphs, but the performance issues suggest that it might not be the best approach in my case. I am looking for guidance on whether there are more efficient algorithms or optimizations that I can apply to my existing approach. Specifically, I would like to know if there are any techniques to reduce the time complexity or handle large graphs more effectively.