Difference Between the Adjacency Matrix and Adjacency List

Implementation of Graph Data Structure in C++

There are two primary ways to implement or represent graph data structures in C++:...

Adjacency Matrix Representation of Graph in C++

An adjacency matrix is a square matrix (2D vector in C++) used to represent a finite graph. It provides a straightforward way to describe the relationships between nodes (vertices) in a graph....

Adjacency List Representation of Graph in C++

An Adjacency List is a common way to represent a graph in computer science. Specifically, it’s a way of representing a graph as a map from vertices to lists of edges. The adjacency list representation of a graph is linked to the degree of the vertices, and hence is quite space efficient. It only uses space proportional to the number of edges, which can be much less than the square of the number of vertices (which is the space complexity of the adjacency matrix representation)....

Difference Between the Adjacency Matrix and Adjacency List

AspectAdjacency MatrixAdjacency ListMemory UsageRequires O(V^2) spaceRequires O(V + E) spaceEdge Existence QueryQuick O(1) checkO(degree(v)) check for adjacency of vSpace EfficiencyInefficient for sparse graphsEfficient for sparse graphsAdding/Removing EdgesO(1) for adding/removing edges Depends on data structure, typically O(1)Iterating Over EdgesInefficient, potentially O(V^2) for traversalEfficient, O(V + E) for traversalSuitabilitySuitable for dense graphsSuitable for sparse graphs...