Graphs are fundamental data structures that represent relationships between objects. Representing them efficiently is critical for algorithm performance.
Adjacency Matrices: O(1) Lookup
An adjacency matrix uses an N x N grid to show connections. It's fast for checking if two nodes are connected, but it consumes O(N^2) space even if the graph has very few edges.
Adjacency Lists: Space-Saving King
Adjacency lists only store the edges that actually exist, making them ideal for sparse graphs. They use O(V + E) space and are generally the preferred choice for most graph algorithms.
Choosing the Right Format
If your graph is dense (nearly every node connects to every other), use a matrix. For sparse graphs, an adjacency list is almost always better for speed and memory.