Act as a senior software engineer with 10+ years of experience in data structures and algorithms. Explain how to implement a graph data structure in [LANGUAGE], focusing on [ADJACENCY_LIST or ADJACENCY_MATRIX] representation. Cover key operations like adding nodes, adding edges, and traversals (BFS/DFS). Provide [BEGINNER or ADVANCED] level code examples with clear comments. Address common pitfalls like handling cycles in directed graphs or optimizing for sparse/dense graphs. Tailor the explanation for [AUDIENCE_TYPE: students, developers, or researchers].