Use an adjacency list for sparse graphs because it uses O(V + E) memory and iterates neighbors efficiently. Use an adjacency matrix for dense graphs or when you need O(1) edge‑existence checks; it costs O(V^2) memory.
Advanced answer
Deep dive
Expanding on the short answer — what usually matters in practice:
Context (tags): graph, adjacency-list, adjacency-matrix, space
Complexity: compare typical operations (average vs worst-case).
Invariants: what must always hold for correctness.
When the choice is wrong: production symptoms (latency, GC, cache misses).
Explain the "why", not just the "what" (intuition + consequences).
Trade-offs: what you gain/lose (time, memory, complexity, risk).
Edge cases: empty inputs, large inputs, invalid inputs, concurrency.
Examples
A tiny example (an explanation template):
// Example: discuss trade-offs for "adjacency-list-vs-adjacency-matrix:-when-do-you-"
function explain() {
// Start from the core idea:
// Use an adjacency list for sparse graphs because it uses O(V + E) memory and iterates neigh
}
Common pitfalls
Too generic: no concrete trade-offs or examples.
Mixing average-case and worst-case (e.g., complexity).