1. Directed Graphs (Digraphs):

Definition: Directed graphs, also known as digraphs, are graphs in which edges have a direction. Each edge connects two vertices and has an associated direction indicating a one-way relationship between them.

Example:

    A --> B
   /  ↗   ↘
  ↓   C --> D
   \  ↘   ↗
    └---> E

2. Undirected Graphs:
Definition: Undirected graphs are graphs in which edges have no direction. The relationship between vertices is symmetric, and edges connect vertices bidirectionally.

    A --- B
   /  \    \
  C -- D -- E

3. Weighted Graphs:
Definition: Weighted graphs are graphs in which edges have weights or costs associated with them. These weights can represent distances, costs, or any other relevant metric.

    A -4- B
   / |   /|
  2  |1  |6
 /   | / |
D -3-C -7- E

4. Unweighted Graphs:
Definition: Unweighted graphs are graphs in which edges have no weights associated with them. The edges are only present or absent.

    A --- B
   /  \    \
  C -- D -- E

5 Cyclic Graphs:
Definition: Cyclic graphs are graphs containing one or more cycles, i.e., closed paths.

    A --- B
   /  \    \
  C -- D -- E
   \  /    /
    └----─┘

6. Acyclic Graphs:
Definition: Acyclic graphs are graphs without any cycles.

    A --> B
   /  ↗   ↘
  ↓   C    D
   \  ↘   ↗
    └----─┘

7. Connected Graphs:
Definition: Connected graphs are graphs in which there is a path between every pair of vertices.

    A --- B
   /  \    \
  C -- D -- E

8. Disconnected Graphs:
Definition: Disconnected graphs are graphs in which there are one or more isolated subgraphs, and there is no path between vertices in different subgraphs.

    A --- B       G    H
   /  \    \          /
  C -- D -- E       I

9. Bipartite Graphs:
Definition: Bipartite graphs are graphs whose vertices can be divided into two disjoint sets such that every edge connects a vertex from one set to a vertex in the other set.

    A       B
   /  \    / |
  C    D  /  E
   \  /  /   |
    F    G   H

10. Complete Graphs:
Definition: Complete graphs are graphs in which every pair of distinct vertices is connected by a unique edge.

    A --- B
   /  \ / |
  C --- D  |
   \  / \ |
    E --- F