Adjacency Matrix
An adjacency matrix is a square matrix used in graph theory to represent a finite graph, where each element indicates whether pairs of vertices are adjacent or connected in the graph. It is a two-dimensional array with rows and columns representing vertices, and entries (often 0 or 1) denoting the presence or absence of an edge between them. This data structure is particularly useful for dense graphs and allows for efficient edge lookup and graph operations like connectivity checks.
Developers should learn and use adjacency matrices when working with graph algorithms in applications such as network analysis, social networks, or pathfinding, where quick edge existence queries are needed. They are ideal for dense graphs with many edges relative to vertices, as they provide O(1) time complexity for edge checks, but may be memory-inefficient for sparse graphs. Common use cases include representing relationships in databases, computer networks, or game development for AI navigation.