Graph data structure and algorithms

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This document discusses graph data structures and algorithms. A graph consists of nodes and edges, where nodes represent entities and edges represent relationships between nodes. There are different types of graphs including undirected, directed, weighted, and cyclic graphs. Graphs can be represented using an adjacency matrix or adjacency list. Graphs are used to model real-world networks and solve problems in areas like social networks, maps, robot path planning, and neural networks.

Graph Data Structure and
Algorithms
Presented by
D.Anandhasilambarasan
KIT - CBE

Graph Data Structure and Algorithms
A Graph is a non-linear data structure consisting of nodes and
edges.
The nodes are sometimes also referred to as vertices and the
edges are lines or arcs that connect any two nodes in the graph.
A Graph consists of a finite set of vertices (or nodes) and set of
Edges which connect a pair of nodes.

 Nodes: These are the most important components in any graph. Nodes are
entities whose relationships are expressed using edges. If a graph comprises
2 nodes A and B and an undirected edge between them, then it expresses a
bi-directional relationship between the nodes and edge.
 Edges: Edges are the components that are used to represent the relationships
between various nodes in a graph. An edge between two nodes expresses a
one-way or two-way relationship between the nodes.

- In the above Graph, the set of vertices V = {0,1,2,3,4}
and the set of edges E = {01, 12, 23, 34, 04, 14, 13}.

Types of graphs
Undirected: An undirected graph is a graph in which all the edges are bi-
directional
i.e. the edges do not point in any specific direction.
Directed: A directed graph is a graph in which all the edges are uni-directional
i.e. the edges point in a single direction.
Weighted: In a weighted graph, each edge is assigned a weight or cost.
Cyclic: A graph is cyclic if the graph comprises a path that starts from a vertex
and ends at the same vertex. That path is called a cycle. An acyclic graph is a
graph that has no cycle.

Graph Representation
You can represent a graph in many ways. The two most common ways of
representing a graph is as follows:
Adjacency matrix
Adjacency list
Adjacency matrix
An adjacency matrix is a VxV binary matrix A. Element Ai,j is 1 if there is an
edge from vertex i to vertex j else Ai,jis 0.
Note: A binary matrix is a matrix in which the cells can have only one of two
possible values - either a 0 or 1.

The adjacency matrix of the following graph is:
i/j: 1 2 3 4
1: 0 1 0 1
2: 1 0 1 0
3: 0 1 0 1
4: 1 0 1 0
Adjacency list
The other way to represent a graph is by using an adjacency list. An adjacency
list is an array A of separate lists. Each element of the array Ai is a list, which
contains all the vertices that are adjacent to vertex i.
1 2
34

Applications of Graphs
 Graphs are used to solve many real-life problems. Graphs are used to
represent networks.
 The networks may include paths in a city or telephone network or circuit
network.
 Graphs are also used in social networks like LinkedIn, Facebook.
 It is used to Document link graphs.
 Scene graphs: Such graphs are very important in the computer games
industry.

 Robot planning: Such graph plans are used in planning paths for
Autonomous vehicles.
 Neural networks
 For example, in Facebook, each person is represented with a vertex (or
node).
 Each node is a structure and contains information like person id, name,
gender, locale etc.

This document defines and provides examples of graphs and their representations. It discusses: - Graphs are data structures consisting of nodes and edges connecting nodes. - Examples of directed and undirected graphs are given. - Graphs can be represented using adjacency matrices or adjacency lists. Adjacency matrices store connections in a grid and adjacency lists store connections as linked lists. - Key graph terms are defined such as vertices, edges, paths, and degrees. Properties like connectivity and completeness are also discussed.

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Graph data structure and algorithms

1. Graph Data Structure and Algorithms Presented by D.Anandhasilambarasan KIT - CBE

2. Graph Data Structure and Algorithms A Graph is a non-linear data structure consisting of nodes and edges. The nodes are sometimes also referred to as vertices and the edges are lines or arcs that connect any two nodes in the graph. A Graph consists of a finite set of vertices (or nodes) and set of Edges which connect a pair of nodes.

3.  Nodes: These are the most important components in any graph. Nodes are entities whose relationships are expressed using edges. If a graph comprises 2 nodes A and B and an undirected edge between them, then it expresses a bi-directional relationship between the nodes and edge.  Edges: Edges are the components that are used to represent the relationships between various nodes in a graph. An edge between two nodes expresses a one-way or two-way relationship between the nodes.

4. - In the above Graph, the set of vertices V = {0,1,2,3,4} and the set of edges E = {01, 12, 23, 34, 04, 14, 13}.

5. Types of graphs Undirected: An undirected graph is a graph in which all the edges are bi- directional i.e. the edges do not point in any specific direction. Directed: A directed graph is a graph in which all the edges are uni-directional i.e. the edges point in a single direction. Weighted: In a weighted graph, each edge is assigned a weight or cost. Cyclic: A graph is cyclic if the graph comprises a path that starts from a vertex and ends at the same vertex. That path is called a cycle. An acyclic graph is a graph that has no cycle.

6. Graph Representation You can represent a graph in many ways. The two most common ways of representing a graph is as follows: Adjacency matrix Adjacency list Adjacency matrix An adjacency matrix is a VxV binary matrix A. Element Ai,j is 1 if there is an edge from vertex i to vertex j else Ai,jis 0. Note: A binary matrix is a matrix in which the cells can have only one of two possible values - either a 0 or 1.

7. The adjacency matrix of the following graph is: i/j: 1 2 3 4 1: 0 1 0 1 2: 1 0 1 0 3: 0 1 0 1 4: 1 0 1 0 Adjacency list The other way to represent a graph is by using an adjacency list. An adjacency list is an array A of separate lists. Each element of the array Ai is a list, which contains all the vertices that are adjacent to vertex i. 1 2 34

9. Applications of Graphs  Graphs are used to solve many real-life problems. Graphs are used to represent networks.  The networks may include paths in a city or telephone network or circuit network.  Graphs are also used in social networks like LinkedIn, Facebook.  It is used to Document link graphs.  Scene graphs: Such graphs are very important in the computer games industry.

10.  Robot planning: Such graph plans are used in planning paths for Autonomous vehicles.  Neural networks  For example, in Facebook, each person is represented with a vertex (or node).  Each node is a structure and contains information like person id, name, gender, locale etc.

Graph data structure and algorithms

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Graph data structure and algorithms