1. Graphs in ‘C’ Language
By
Dr. C. Saritha
Lecturer in Electronics
SSBN Degree College, Anantapur
2. Data Structure
• Data structure is a particular way of
sorting and organizing data in a
computer. So that it can be used
efficiently.
• Different kinds of data structures are
suited to different kinds of applications.
3. Types of Data Structure
• Linear Data Structure: A data structure
is said to be linear data structure if its
elements form a sequence.
Ex: Array, Stack , Queue and linked list.
• Non-Linear Data Structure: Elements in
a non-linear data structure do not form
a sequence.
Ex: Tree and Graph.
4. Types of data structure
Data Structures
Linear Non-Linear
Arrays Linked lists Stack Queue Trees Graphs
5. Trees
• A tree is hierarchical collection of
nodes. One of the nodes, known as the
root, is at the top of the hierarchical.
• Each node can have utmost one link
coming into it.
• The node where the link originates is
called the parent node. The root node
has no parent.
6. Continue…
• The links leaving a node (any number
of links are allowed) point to child
nodes.
A
B C D
E F G H I J
7. Graphs
• A graph is a set of nodes (also called
vertices) and a set of arcs (also called
edges). A sample graph is as fallows:
A B
C
D
E
8. Edges & Vertices
• Each node in a graph is known as a
vertex of the graph.
• The Each edge of a graph contains two
vertices.
9. Types of Graphs
• The Graphs can be classified into two
types. They are:
Undirected graphs
Directed graph
10. Continue…
Undirected graphs: In an undirected
graph the order of pair is unimportant.
Hence the pairs (v1,v2)and (v2,v1)
represent same edge.
Directed graph: In this the order of the
vertices representing an edge is
important. This pair is represented as
<v1,v2> where v1 is the tail and v2 is
head of v2. Thus <v1,v2> and <v2,v1>
represents different edges.
11. Undirected graph
1 2
5
3 4
• Set of vertices={1,2,3,4,5}
• Set of edges= {(1,2),(1,3),(1,4),(2,3),
(2,4),(2,5),(3,4),(4,5)}
12. Directed Graphs
1
2
3
• Set of vertices={1,2,3}
• Set of edges= {<1,2>, <2,1>, <2,3>,
<3,2>}
13. Adjacent Vectors & Incident Edges
• In an undirected graph if (v1,v2) is an
edge in the set of edges, then the
vertices v1 and v2 are said to be
adjacent and the edge (v1,v2) is
incident on vertices v1 and v2.
• If <v1,v2> is a directed edge, then
vertex v1 is said to be adjacent to v2
while v2 is adjacent from v1.
• The edge <v1,v2> is incident to v1 and
v2.
14. Continue…
• The vertex 2 in the
shown undirected
graph is adjacent to 1 2
vertices 1,3,4 and
5.The edges incident 5
on vertex 3 are
(1,3),(2,3) and 3 4
(3,4).
15. Continue…
• In the shown
directed graph the 1
edges incident to
vertex 2 are 2
<1,2>,<2,1>,<2,3>
and <3,2>.
3
16. Terminology of Graphs
• Weighted graph: A
graph is said to be
weighted graph if
it’s edges have been 2
2
assigned some non- 1
negative value as
5
weight. A weighted 6
graph is known as
network. 3 4
3
17. Continue…
• Degree: In an
undirected graph,
the number of edges 1 2
connected to a node
is called the degree
of that node. Where
is in digraph, there 4
3
are two degrees for
every node they are
indegree and
outdegree.
18. Continue…
• Indegree: The
indegree of node is
the number of edges 1 2
coming to that
node.
• Out degree: The out
degree of node is 3 4
the number of edges
going outside that
node.
19. Continue…
• Isolated node: If any node has no
edges connected with any other node
then its degree will be zero (0) and it
will be called as isolated node.
A B
C
D
E
20. Continue…
• Source: A node,
which has no
incoming edges, but 1 2
has outgoing edges,
is called a source.
3 4
21. Continue…
• Connected graph:
An undirected graph B
A
is said to be
connected if there is
a path from any C
node of graph to D
any other node. E
22. Continue…
• Complete graph: An
undirected graph 1
will contain n(n-1)/2 1
edges is called a
complete graph 2 2
where as in the case
of digraph will
contain n(n-1) 3
3
edges, where n is
the total number of
nodes in the graph.
23. Continue…
• Loop: An edge will
be called loop or self
edge if it starts and 1 2
ends on the same
node.
3 4
24. Breadth first search
• The general idea
behind a breadth
first traversal A B C
beginning at a
starting node A is as D E
following. We first
examine the starting
node A, and then its F G
neighbors after that
the neighbors of its
neighbors. • A BDE CFG
25. Depth first search
• In Depth first search
technique also we take T H A
one node as starting
node. Then go to the K Y N
path which from
starting node and visit
all the nodes which are O
in the path. When we
reach at the last node U
then we traverse
another path starting THANK YOU
from that node
