Graph Algorithms Every Developer Should Know for DSA Interviews

Graph algorithms are a cornerstone of data structures and algorithms interviews. Many real-world problems, from social networks to navigation systems, can be modeled as graphs, making graph traversal and pathfinding essential skills for any software engineer.

A graph consists of vertices (nodes) and edges connecting them. Graphs can be directed or undirected, weighted or unweighted, and cyclic or acyclic. Before diving into algorithms, you need to understand how to represent graphs in code. The two primary representations are adjacency matrices and adjacency lists. An adjacency matrix is a 2D array where matrix[i][j] indicates whether there is an edge from node i to node j. This uses O(V^2) space and allows O(1) edge lookups but wastes space for sparse graphs. An adjacency list uses a dictionary or array of lists, where each node maps to its neighbors. This uses O(V + E) space and is more efficient for sparse graphs, which are common in interview problems.

Breadth-First Search (BFS) explores a graph level by level, starting from a source node. It uses a queue to process nodes in the order they are discovered. BFS is ideal for finding the shortest path in an unweighted graph because it guarantees that when a node is first visited, the path to it is the shortest. Common BFS problems include finding the shortest path in a maze, the minimum number of moves for a knight on a chessboard, and the number of islands in a grid. The time complexity of BFS is O(V + E) for adjacency lists.