Graph Adjacency Matrix

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Figure: Adjacency Matrix

Shows a graph represented as an adjacency matrix, where each cell indicates whether two vertices are connected (1) or not (0). This matrix form provides fast edge lookups but uses more space for large, sparse graphs.

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🔥 Breadth First Search → BFS can be implemented over an adjacency matrix by scanning each row A[u][*] to enumerate neighbors of u and using O(1) edge-existence checks, enabling straightforward traversal on dense or small graphs (typically yielding O(n^2) time).

🔥 Adjacency List → An adjacency list can be constructed by scanning each row of the adjacency matrix and collecting columns with nonzero entries (and their weights) as neighbors; understanding the matrix form ensures correct derivation and interpretation of the list and its complexity trade-offs.

Weighted Graph →

Dijkstra →

Depth First Search →

Floyd-Warshall Algorithm →

Introduction To Weighted Graphs →