How is a graph represented using an adjacency list?

A graph is represented using an adjacency list by associating each vertex in the graph with a list of its neighbouring vertices.

In more detail, an adjacency list is a data structure that is used to represent a graph in computer science. It is a collection of unordered lists, one for each vertex in the graph. Each list describes the set of neighbours of a vertex in the graph. This means that for every edge in the graph, the edge connects the vertex to each of the vertices in its list.

For example, consider a graph with vertices A, B, C and D. If A is connected to B and C, B is connected to A and D, C is connected to A, and D is connected to B, the adjacency list representation of this graph would be as follows:

A: B, C
B: A, D
C: A
D: B

The adjacency list is an efficient way to represent a graph because it uses space proportional to the number of edges, which can be significantly less than the number of potential edges for dense graphs. It also allows for efficient traversal of the graph, as you can easily access all neighbours of a given vertex.

In terms of implementation, the adjacency list can be represented using a variety of data structures such as an array of lists, a dictionary with vertices as keys and lists as values, or even a linked list of linked lists. The choice of data structure will depend on the specific requirements of the problem at hand, such as whether the graph is directed or undirected, and whether you need to perform operations like adding or removing vertices and edges.

In summary, an adjacency list is a simple and efficient way to represent a graph in computer science, associating each vertex with a list of its neighbours. It allows for efficient traversal and manipulation of the graph, and can be implemented using a variety of data structures depending on the specific needs of the problem.