Graphs — Part 4 — Adjacency List vs Adjacency Matrix

In this post, let me explain the applications of adjacency list and adjacency matrix implementations and provide guidance on when to use each of them.

Adjacency List Implementation

The adjacency list representation is a widely used approach for graph representation due to its efficiency in terms of both memory usage and certain graph algorithms. It is particularly useful in scenarios where the graph is sparse, meaning it has relatively fewer edges compared to the number of vertices.

Here are some key points about the applications and advantages of the adjacency list implementation:

1. Memory Efficiency: The adjacency list implementation requires less memory compared to the adjacency matrix, especially for sparse graphs. This is because it only stores the connections (edges) explicitly, rather than allocating memory for all possible edges.
2. Efficient Iteration: The adjacency list allows for efficient iteration over the neighbors of a vertex. It maintains a list of neighbors for each vertex, which makes it straightforward to traverse the graph and perform operations on its neighbors.
3. Dynamic Graphs: The adjacency list is suitable for graphs that are subject to frequent updates and modifications. Adding or removing edges or vertices can be done efficiently by simply updating the corresponding lists.
4. Complex Graph Structures: When dealing with complex graph…