Pattern Studioalgorithmic thinking
All patterns

Graph Representation

Graphs
Intermediate
Interactive

Build adjacency lists from node-to-node relationships.

Time
O(V + E) build
Space
O(V + E)
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The idea

Graphs model arbitrary relationships with vertices and edges. An adjacency list stores each vertex's neighbors, providing the representation used by BFS, DFS, shortest paths, and connectivity algorithms.

Analogy

A reusable way to think about organizing and navigating structured data efficiently.

When to reach for it

  • The relationships between values drive the algorithm.
  • You need efficient traversal, lookup, or updates.
  • An interview problem names or implies this structure.

Language-independent template

adj = map(node -> [])
for (u, v) in edges:
    adj[u].append(v)
    adj[v].append(u)

Complexity — time O(V + E) build, space O(V + E).

Common mistakes

  • Losing a pointer before saving its next target.
  • Breaking the structure invariant during an update.
  • Forgetting empty and single-node cases.

Practice progression

Canonical interview problems, ordered from foundation to advanced application.

Easy
Find Center of Star GraphLC 1791

Return the node incident to every edge in a star.

Medium
Clone GraphLC 133

Create a deep copy of every node and edge in a connected graph.

Hard
Critical Connections in a NetworkLC 1192

Find every edge whose removal disconnects the graph.

Variations

Traversal
Insertion and deletion
Search and reconstruction