Which representation tends to be more space-efficient for sparse graphs?

Which representation tends to be more space-efficient for sparse graphs?

• A. Adjacency Matrix
• B. Adjacency List
• C. Both are space-efficient
• D. Neither is space-efficient

Answer: (B)

When a graph is sparse, most possible connections don’t exist, so you want a representation that doesn’t waste space on those missing edges. An adjacency matrix allocates space for every possible pair of vertices, resulting in O(n^2) space regardless of how many edges there actually are. An adjacency list, on the other hand, stores only the real edges, giving O(n + m) space, where m is the number of edges. Since sparse graphs have m much smaller than n^2, the adjacency list uses far less memory. That’s why it’s the more space-efficient choice for sparse graphs. For dense graphs, the matrix can be more practical, but not for sparse ones.

When a graph is sparse, most possible connections don’t exist, so you want a representation that doesn’t waste space on those missing edges. An adjacency matrix allocates space for every possible pair of vertices, resulting in O(n^2) space regardless of how many edges there actually are. An adjacency list, on the other hand, stores only the real edges, giving O(n + m) space, where m is the number of edges. Since sparse graphs have m much smaller than n^2, the adjacency list uses far less memory. That’s why it’s the more space-efficient choice for sparse graphs. For dense graphs, the matrix can be more practical, but not for sparse ones.