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Graph algorithms, from first principles to advanced.

Each guide follows the same structure: intuition first, then step-by-step instructions, pseudocode, runnable Python, and real-world applications. Pick a topic to dive in.

Basics

1 topic
Storage: O(V+E) list / O(V²) matrixLvl 00

Graph Basics & Representations

Vertices, edges, adjacency lists vs matrices.

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Traversal

2 topics
O(V + E)Lvl 01

Breadth-First Search (BFS)

Layer-by-layer traversal — shortest path in unweighted graphs.

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O(V + E)Lvl 02

Depth-First Search (DFS)

Dive deep, then backtrack — basis for topo sort & SCC.

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Shortest Path

2 topics
O((V + E) log V)Lvl 03

Dijkstra's Shortest Path

Cheapest route in a non-negative weighted graph.

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O(V · E)Lvl 04

Bellman-Ford

Shortest paths with negative edge weights & cycle detection.

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MST

1 topic
O(E log E)Lvl 05

Kruskal's MST

Greedy minimum spanning tree via Union-Find.

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Advanced

2 topics
O(V + E)Lvl 06

Topological Sort

Linear ordering of a DAG — Kahn's & DFS approaches.

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O(V · E²)Lvl 07

Max Flow (Edmonds-Karp)

Maximum flow from source to sink via BFS augmenting paths.

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