Graphs
Graph:- A graph consists of a nonempty set of points or vertices, and a set of edges that link together the vertices. A simple real world example of a graph would be your house and the corner store. Where the house and the store are the vertices and the road between them is the edge connecting the two vertices.

Or a graph is a network consisting of vertices (or nodes) and edges (V,E) Simple Graph

A graph can take on many forms: directed or undirected.

Directed Graph:- A directed graph is one in which the direction of any given edge is defined. Or A graph with directed edges = directed graph (digraph)

Directed edges = arcs
Directed Graph

Undirected Graph:- An undirected graph is one in which the direction of any given edge is not defined. Conversely, in an undirected graph you can move in both directions between vertices. Or a graph with undirected edges is called undirected graph. Undirected graph Mixed Graph:- A graph is one in which contains both directed and undirected edges.

Mixed Graph

Null Graph: - A null graph is one that contains only isolated vertices (example no edges). Null Graph

Connected graph:- All vertices are directly or indirectly connected with each other (otherwise we have a graph, consisting of at least two sub graphs).

Connected Graph

Complete graph:- Each vertex is directly connected with every other vertex. Or a simple graph in which every pair of vertices is adjacent.
Complete Graph

...V. Adamchik
1
GraphTheory
Victor Adamchik Fall of 2005
Plan
1. Basic Vocabulary 2. Regular graph 3. Connectivity 4. Representing Graphs
Introduction
A.Aho and J.Ulman acknowledge that “Fundamentally, computer science is a science of abstraction.” Computer scientists must create abstractions of real-world problems that can be represented and manipulated in a computer. Sometimes the process of abstraction is simple. For example, we use...

...
Graphs
1 Introduction
We have studied one non-linear data structure so far i.e Trees. A graph is another non-linear data structure that is widely used to solve many real-life computing problems. For example, we need to use a graph to find out whether two places on a road-map are connected and what is the shortest distance between them. Graphs are used in simulating electrical circuits to find out current flows and voltage drops at...

...Baker Machine Company
Layout
Problem 3.4. (Summary)
Baker Machine is considering two alternative layouts. We will compare the Weighted-Distance Scores using rectilinear distance* of the two block plans to determine which alternative layout is better.
Alternative Layout 1 Alternative Layout 2
3 | 6 | 4 |
5 | 1 | 2 |
3 | 1 | 4 |
5 | 6 | 2 |
* rectilinear distance – the distance between two points with a series 90-degree turns, as along city blocks
Data
Baker Machine...

...Introduction in GraphTheory
(BASIC CONCEPTS)
BASIC CONCEPTS
We used decision trees in Unit DT and used them to study decision making. However,
we did not look at their structure as trees. In fact, we didn’t even define a tree precisely.
What is a tree? It is a particular type of graph, which brings us to the subject of this unit.
What is a Graph?
There are various types of graphs, each with its own...

...LAB # 1
Graph Matching
Principles of Physics I Laboratory
Breanna Wilhite
Introduction
In this lab motion will be represented by graphs that plots distance and velocity vs. time. A motion detector will be used to measure the time it takes for a high frequency sound pulse to travel from the detector to an object and back. By using this method sound can determine the distance to the object, or its position. This device will determine in what direction the...

...Graphs - Introduction
Terminology
Graph ADT
Data Structures
Reading: 12.1-12.2
COSC 2011, Summer 2004
Definition
• A graph is a pair (V, E), where
– V is a set of nodes, called vertices
– E is a collection of pairs of vertices, called edges
• Both are objects (i.e. store data)
G
E
B
F
A
Vertex
city
computer
web page
airport
C
D
COSC 2011, Summer 2004
H
Edge
road
cable
hyperlink
flight
Example Applications
•
•
•
•
•
Electronic circuits...

...tructureResearch on Graphs in Data Structure
Source: http://www.algolist.net/Algorithms/Graph/Undirected/Depth-first_search
Introduction to graphsGraphs are widely-used structure in computer science and different computer applications. We don't say data structurehere and see the difference. Graphs mean to store and analyze metadata, the connections, which present in data. For instance, consider cities in your country....

...Trenerry
§5 GraphTheory
Loosely speaking, a graph is a set of dots and dot-connecting lines. The dots are called vertices and the lines are called edges. Formally, a (ﬁnite) graph G consists of A ﬁnite set V whose elements are called the vertices of G; A ﬁnite set E whose elements are called the edges of G; A function that assigns to each edge e ∈ E an unordered pair of vertices called the endpoints of e. This function is called the...