You don’t need a PhD to choose the right graph representation
You don’t need a PhD to choose the right graph representation.
You just need to know what you’ll do with the graph and pick the structure that makes that fast and easy.
Below is a quick, practical guide you can use today:
1. Edge List:
Start here when you just need “a list of connections.”
An edge list is literally a list of edges: (x, y) for directed graphs, (x, y) and (y, x) for undirected, and (x, y, w) if weighted.
It shines when you process edges globally (e.g., sort by weight for Kruskal’s MST).
It’s also the most compact when your graph is sparse and you don’t need constant-time lookups.
When to use:
• You’ll sort/filter edges (MST, connectivity batches)
• You’re loading data from CSV/logs where edges arrive as rows
• You want minimal structure first and you’ll convert later if needed
Trade-offs:
• Space: O(m)
• Iterate neighbors of x: O(m) (unless you pre-index)
• Check if (x, y) exists: O(m) (or O(1) with an auxiliary hash set you maintain)
2. Adjacency Matrix:
Use this when instant “is there an edge?” matters.
A 2D array G[x][y] stores 1 (or weight) if the edge exists, else 0 (or a sentinel like −1/∞).
You get constant-time edge existence checks and very clean math/linear-algebra operations.
The cost is space: O(n²) even if the graph is tiny.
If memory is fine and you need O(1) membership checks, go matrix.
When to use:
• Dense graphs (m close to n²)
• Fast membership tests dominate your workload
• You’ll leverage matrix ops (spectral methods, transitive closure variations, etc.)
Trade-offs:
• Space: O(n²)
• Check if (x, y) exists: O(1)
• Iterate neighbors of x: O(n)
3. Adjacency List
Choose this when you traverse from nodes to neighbors a lot.
Each node stores its exact neighbors, so traversal is proportional to degree, not n.
This representation is ideal for BFS/DFS, Dijkstra (with weights), and most real-world sparse graphs.
Membership checks are slower than a matrix unless you keep neighbor sets.
For sparse graphs and traversal-heavy algorithms, pick adjacency lists.
When to use:
• Graph is sparse (common in practice)
• You’ll run BFS/DFS, shortest paths, topological sorts
• You need O(n + m) space and fast neighbor iteration
Trade-offs:
• Space: O(n + m)
• Iterate neighbors of x: O(deg(x))
• Check if (x, y) exists: O(deg(x)) (or O(1) if you store a set per node)
~
Pick the representation that optimizes your next operation, not some abstract ideal.
Edge lists for global edge work, matrices for instant membership, lists for fast traversal.
Choose deliberately, and your graph code gets both cleaner and faster.
If you want a deep dive on graph representation, say “Graphs” in the comments and I’ll send it to you on DM. | 15 comments on LinkedIn
You don’t need a PhD to choose the right graph representation
