Graphs

1. Welcome To Our
Presentation

2. Our Presentation Topics:
Graphs

3. Group members:
Md.Afzal Hossain
ID:171-15-1193
Md.Yusuf Khan
ID:171-15-1202
Md. Mahbobur Rahman
Salman
ID:171-15-1217

4. What is a Graph?
A graph is a structure that consists of a set of nodes
(vertices) and a set of edges that relate the nodes to each
other.
A graph G is defined as follows:
G=(V,E)
V: set of vertices
E: set of edges connecting the vertices in
V

5. Example:

6. Types of Graphs:
Though there are a lot of different types of graphs in
data structure. There are some common graphs given
below:
Bipartite Graph:
Complete Graph:
Cycle Graph:

7. Bipartite Graph:

8. Complete Graph:

9. Cycle Graph:

10. Graph Variation

11. Connected & Disconnected graph:
A graph is connected when there is a path between
every pair of vertices. In a connected graph, there
are no unreachable vertices. A graph that is not
connected is disconnected.
A B

12. Undirected Graph:
Which graph has no specific direction between the
vertices is called undirected graph.
• Edge (u,v) = edge (v,u)
• No self-loops
We uses undirected edges as to represent symmetrical
relationship.
→Two way streets
→Network traffic
→Mazes

13. Directed Graph:
A directed graph has edges that are “One way”. We
can go from one vertices to another, but not vice
versa.
Edge (u,v) goes from vertex u to vertex v, notated
u→v

14. Weighted Graph:
A weighted graph has weights associated with each
edge. The weight can represent distance, cost etc.
→A road map.

15. Multigraph:
A multigraph is a directed graph which is permitted to
have multiple edges, e.g. edges with the own, source
and target vertices.

16. Graph Representation:
Popular computer representations of a graph.

17. Following representations:
• Two are most popular computer representations of a
graph.
• 1: Adjacency Matrix
• 2: Adjacency List
• But it has one other representation:
• 3: Incidence Matrix

18. Adjacency Matrix
For example, consider the following undirected graph
representation...

19. Adjacency Matrix
Directed graph representation...

20. Adjacency List
In this representation, every vertex of graph contains list of its adjacent
vertices.

21. Adjacency List
For example, consider the following directed graph representation
implemented using linked list...

22. Adjacency List
Other example of Adjacency
List:

23. Thank you