graph terminology , MFC

1. GRAPH-
TERMINOLOGY

2. CONTENTS:
1.Overview of Graphs in Data Structure
2.Graph Terminologies in Data Structure
3.Types of Graphs in Data Structure

3. Overview of Graphs in Data Structure
Let us understand what is a graph in the data structure. Graphs
are non-linear data structures that are made up of a set of nodes
(or vertices), connected by edges (or arcs). Nodes are entities
where the data is stored and their relationships are expressed
using edges. Edges may be directed or undirected. Graphs
demonstrate complicated relationships with ease and are used to
solve many real-life problems.

4. For example, Facebook uses a
graph data structure that consists
of a group of entities and their
relationships. On Facebook, every
user, photo, post, page, place, etc.
that has data is represented with a
node. Every edge from one node to
another represents their
relationships, friendships,
ownerships, tags, etc. Whenever a
user posts a photo, comments on a
post, etc., a new edge is created for
that relationship. Both nodes and
edges have meta-data associated
with them.

5. Graph Terminologies in
Data Structure:
• Vertex
• Every individual data element is
called a vertex or a node. In the above
image, A, B, C, D & E are the vertices.
• Edge (Arc)
• It is a connecting link between
two nodes or vertices. Each edge has two
ends and is represented as starting
Vertex , ending Vertex .
5

6. Directed Edge It is a unidirectional edge.
Weighted Edge An edge with value (cost) on it.
Degree
The total number of edges connected to a
vertex in a graph.
Indegree
The total number of incoming edges connected
to a vertex.
Outdegree
The total number of outgoing edges connected
to a vertex.
Self-loop
An edge is called a self-loop if its two endpoints
coincide with each other.
Adjacency
Vertices are said to be adjacent to one another
if there is an edge connecting them

7. Types of Graphs in Data Structure
The most common types of graphs in the data structure are
mentioned below:
DIRECTED GRAPH UNDIRECTED GRAPH WEIGHTED GRAPH UNWEIGHTED GRAPH

8. DIRECTED -
GRAPH

9. UNDIRECTED-GRAPH
• An undirected graph is graph, i.e.,
a set of objects (called vertices or
nodes) that are connected together,
where all the edges are
bidirectional. An undirected graph is
sometimes called an
undirected network. In contrast, a
graph where the edges point in a
direction is called a directed graph.
• When drawing an undirected
graph, the edges are typically drawn
as lines between pairs of nodes, as
illustrated in the following figure.

11. WEIGHTED-GRAPH
• In many applications, each edge of a graph has
an associated numerical value, called a weight.
Usually, the edge weights are nonnegative
integers. Weighted graphs may be either directed
or undirected.
• The weight of an edge is often referred to as the
"cost" of the edge. In applications, the weight may
be a measure of the length of a route, the capacity
of a line, the energy required to move between
locations along a route, etc.

12. WEIGHTED GRAPH
It is not mandatory in a weighted
graph that all nodes have distinct
weight, i.e. some edges may
have same weights.

13. UNWEIGHTED-
GRAPH
It is not mandatory in a weighted graph
that all nodes have distinct weight, i.e.
some edges may have same weights.
Applications of Unweighted Graph:
•Unweighted graphs are used to represent data that
are not related in terms of magnitude.
•Unweighted graphs are used to represent
computation flow.
Real-Time Applications of Unweighted
Graph:
•Unweighted graphs can be used to solve puzzles.
•It can be used to represent a circuit diagram.
•It can be used in social media sites to find whether
two users are connected or not.
•It is used in Hamiltonian graphs which have many
practical applications like genome mapping to
combine many tiny fragments of genetic code.

14. UNWEIGHTED
GRAPH
• Advantages of Unweighted Graph:
• Unweighted graphs can be used to implement
tree data structures.
• Unweighted graphs are used in many
algorithms like DFS and BFS.
• Helps in optimal visualization of interrelated
problems which are not related in terms of
magnitude.
• Disadvantages:
• The unweighted graphs do not have edge
weight. Hence, cannot be used for shortest path
evaluation or applications which require the
distance between the nodes.