Lecture 369:- Representation of Directed Graphs

Similar to undirected graphs, there are several ways to represent a directed graph in computer memory. The three common representations for directed graphs are:

1. Adjacency Matrix: An adjacency matrix for a directed graph is a 2D array of size V x V, where V is the number of vertices in the graph. The entry at position (i, j) in the matrix represents whether there is a directed edge from vertex i to vertex j. If there is an edge, the value at (i, j) will be 1 (or the weight of the edge, if the graph is weighted). If there is no edge, the value will be 0.

Advantages and Disadvantages are similar to undirected graphs.

1. Adjacency List: An adjacency list for a directed graph is an array of linked lists (or vectors) where each element of the array represents a vertex, and the linked list (or vector) contains the vertices that are reachable from it (i.e., connected by an outgoing edge). In the case of weighted graphs, each element of the linked list can store a pair of the reachable vertex and the weight of the edge.

Advantages and Disadvantages are similar to undirected graphs.

1. Edge List: An edge list for a directed graph is a list of all the directed edges in the graph. Each directed edge is represented as a pair (u, v), where u is the source vertex and v is the destination vertex of the edge. If the graph is weighted, the pair can also contain the weight of the edge.

Advantages and Disadvantages are similar to undirected graphs.

In summary, the representation of directed graphs is similar to undirected graphs, with the main difference being that directed graphs have edges with a specific direction, indicating one-way relationships between vertices. The choice of representation depends on the specific use case, the size and density of the graph, and the operations that need to be performed on the graph. Each representation has its trade-offs in terms of space complexity and time complexity for various operations.