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A graph is a type of non-linear data structure made up of nodes and edges. The nodes are also known as vertices, and edges are lines or arcs that connect any two nodes in the graph.
The following are the two most common graph representations:
1. Adjacency Matrix: Adjacency Matrix is a two-dimensional array with the dimensions V x V, where V is the number of vertices in a graph. Representation is simpler to implement and adhere to. It takes O(1) time to remove an edge. Queries such as whether there is an edge from vertex ‘u’ to vertex ‘v’ are efficient and can be completed in O(1).
2. Adjacency List: In this method, each Node holds a list of Nodes that are directly connected to that vertex. Each node at the end of the list is connected with null values to indicate that it is the last node in the list. This saves space O(|V|+|E|). In the worst-case scenario, a graph can have C(V, 2) edges, consuming O(V^2) space. It is simpler to add a vertex. It takes the least amount of time to compute all of a vertex’s neighbours.