Types:

1. Undirected Graph:

• Description: A graph where edges have no direction, meaning the connection between nodes is bidirectional.
• Usage: Modeling symmetric relationships, like friendships in a social network.

2. Directed Graph:

• Description: A graph where edges have a direction, meaning the connection between nodes is unidirectional.
• Usage: Representing one-way relationships, such as follower-following relationships on social media.

3. Unweighted Graph

• Description: A graph where edges do not have any weights.
• Usage: Simple connections where all edges are considered equal.

4. Weighted Graph:

• Description: A graph where edges have weights representing costs, distances, or capacities.
• Usage: Finding the shortest path, as in network routing algorithms.

5. Simple Graph:

• Description: A graph where there are no multiple edges and no loops.It can be either directed or undirected.

6. Non-Simple Graphs:

• Description: A graph which has loops and more than one edge between any pair of vertices.

7. Sparse Graphh:

• Description: A graph with relatively few edges compared to the number of vertices.
• Usage: Efficient storage and computation for large networks with few connections.

8. Dense Graph:

• Description: A graph with a large number of edges compared to the number of vertices.
• Usage: Networks with high connectivity, such as certain social networks.

9. Acyclic Graph:

• Description: A graph that does not contain any cycles.
• Usage: Representing hierarchical structures, such as organizational charts.

10. Cyclic Graph:

• Description: A graph that contains at least one cycle, where a cycle is a path that starts and ends at the same vertex.
• Usage: Modeling processes with feedback loops, such as in electrical circuits.

11.Unlabeled Graph:

• Description: A graph where vertices (and edges) are not assigned unique identifiers. The focus is on the structure rather than on the identities of the vertices.
• Usage: Unlabeled graphs are used when the specific identity of vertices is not important, and only the structure of the graph matters. Often used in theoretical research and certain types of combinatorial problems.

12.Labeled Graph:

• Description: A graph where each vertex (and optionally each edge) is assigned a unique identifier or label.
• Usage: Labeled graphs are used when the identity of each vertex is important and must be distinguished from others. Common in practical applications where nodes represent specific entities, like cities in a network, people in a social network, or components in a circuit.