How do you know if its discrete or continuous?
A discrete variable is a variable whose value is obtained by counting. A continuous variable is a variable whose value is obtained by measuring.
When should a graph be discrete?
When figuring out if a graph is continuous or discrete we see if all the points are connected. If the line is connected between the start and the end, we say the graph is continuous. If the points are not connected it is discrete.
What is discrete data on a graph?
Choosing the right type of chart helps you display discrete data more effectively. Discrete data consists of whole numbers that are counted rather than measured. For example, when you track items sold, the data is considered discrete -- you don't normally sell half an item.
Why is a graph continuous?
A function is continuous if its graph is an unbroken curve; that is, the graph has no holes, gaps, or breaks.
What makes a function discrete?
a discrete function is one where a domain is countable (this will be shown as a bunch of points that are not connected together) and which meets the requirement of a function (each input has at most one output). In discrete functions, many inputs will have no outputs.
What is a discrete data?
Discrete data is information that can only take certain values. These values don't have to be whole numbers (a child might have a shoe size of 3.5 or a company may make a profit of £3456.25 for example) but they are fixed values – a child cannot have a shoe size of 3.72!
What is discrete and continuous graph?
A discrete graph is one with scattered points. They may or may not show a direction or trend. They don't have data in between the points already given. A continuous graph has a line because there is data in between the points already given.
What does discrete mean in math?
Discrete mathematics is the branch of mathematics dealing with objects that can assume only distinct, separated values.
Which graphs can be used for discrete data?
Discrete data is best represented using bar charts. Temperature graphs would usually be line graphs because the data is continuous .
Is discontinuous and discrete the same?
The points of discontinuity for a function are the input values of the function where the function is discontinuous. A relation is said to be discrete if there are a finite number of data points on its graph.
What makes a graph continuous but not differentiable?
The absolute value function is continuous (i.e. it has no gaps). It is differentiable everywhere except at the point x = 0, where it makes a sharp turn as it crosses the y-axis. A cusp on the graph of a continuous function. At zero, the function is continuous but not differentiable.
How do you know if a function is continuous or not?
2:188:44Calculus - Continuous functions - YouTubeYouTubeStart of suggested clipEnd of suggested clipInto the function if you actually get something back so does F of C actually exist. You can alsoMoreInto the function if you actually get something back so does F of C actually exist. You can also check to see if the limit exists as X is approaching that C value and lastly.
What is directed graph?
A directed graph or digraph is a graph in which edges have orientations. , a set of edges (also called directed edges, directed links, directed lines, arrows or arcs) which are ordered pairs of vertices (that is, an edge is associated with two distinct vertices).
What is a graph of a function?
For graphs of mathematical functions, see Graph of a function. For other uses, see Graph (disambiguation). Mathematical structure consisting of vertices and edges connecting some pairs of vertices. A graph with six vertices and seven edges. In mathematics, and more specifically in graph theory, a graph is a structure amounting to a set ...
What are the edges of a graph called?
Two edges of a graph are called adjacent if they share a common vertex. Two edges of a directed graph are called consecutive if the head of the first one is the tail of the second one. Similarly, two vertices are called adjacent if they share a common edge ( consecutive if the first one is the tail and the second one is the head of an edge), in which case the common edge is said to join the two vertices. An edge and a vertex on that edge are called incident .
What is a regular graph?
Regular graph. Main article: Regular graph. A regular graph is a graph in which each vertex has the same number of neighbours, i.e., every vertex has the same degree. A regular graph with vertices of degree k is called a k ‑regular graph or regular graph of degree k .
What is a path graph?
A path graph or linear graph of order n ≥ 2 is a graph in which the vertices can be listed in an order v1, v2, …, vn such that the edges are the {vi, vi+1} where i = 1, 2, …, n − 1. Path graphs can be characterized as connected graphs in which the degree of all but two vertices is 2 and the degree of the two remaining vertices is 1. If a path graph occurs as a subgraph of another graph, it is a path in that graph.
What is an undirected pair of vertices called?
In an undirected graph, an unordered pair of vertices {x, y} is called connected if a path leads from x to y. Otherwise, the unordered pair is called disconnected .
What is a hypergraph?
Generalizations. In a hypergraph, an edge can join more than two vertices. An undirected graph can be seen as a simplicial complex consisting of 1- simplices (the edges) and 0-simplices (the vertices). As such, complexes are generalizations of graphs since they allow for higher-dimensional simplices.
What are the properties of a graph?
Properties of Graph. The starting point of the network is known as root. When the same types of nodes are connected to one another, then the graph is known as an assortative graph, else it is called a disassortative graph. A cycle graph is said to be a graph that has a single cycle.
What is an undirected graph?
The undirected graph is defined as a graph where the set of nodes are connected together, in which all the edges are bidirectional. Sometimes, this type of graph is known as the undirected network.
What is a null graph?
Null Graph: A graph that does not have edges. Simple graph: A graph that is undirected and does not have any loops or multiple edges. Multigraph: A graph with multiple edges between the same set of vertices. It has loops formed. Connected graph: A graph where any two vertices are connected by a path.
What is graph in math?
In Mathematics, a graph is a pictorial representation of any data in an organised manner. The graph shows the relationship between variable quantities. In a graph theory, the graph represents the set of objects, that are related in some sense to each other. The objects are basically mathematical concepts, expressed by vertices or nodes and ...
What is graph theory?
Graph Theory, in discrete mathematics, is the study of the graph. A graph is determined as a mathematical structure that represents a particular function by connecting a set of points. It is used to create a pairwise relationship between objects. The graph is made up of vertices (nodes) that are connected by the edges (lines).
When all the pairs of nodes are connected by a single edge, it forms a complete graph?
When all the pairs of nodes are connected by a single edge it forms a complete graph. A graph is said to be in symmetry when each pair of vertices or nodes are connected in the same direction or in the reverse direction. When a graph has a single graph, it is a path graph.
When was the graph tree invented?
It was introduced by British mathematician Arthur Cayley in 1857. The graph trees have only straight lines between the nodes in any specific direction but do not have any cycles or loops. Therefore trees are the directed graph. Degree: A degree in a graph is mentioned to be the number of edges connected to a vertex.
What is discrete data?
The mini-lesson targeted the fascinating concept of discrete data. The math journey around discrete data starts with what a student already knows, and goes on to creatively crafting a fresh concept in the young minds. Done in a way that not only it is relatable and easy to grasp, but also will stay with them forever. Here lies the magic with Cuemath.
What are the two categories of data?
Data can be divided into two categories- Qualitative data and Quantitative data. Among these two categories, quantitative data can be further classified into two types, discrete and continuous data. Now, let us look at discrete data definition. When values in a data set are countable and can only take certain values, it is called discrete data.
Is salary a continuous variable?
Salary can be both discrete or continuous variable. It is discrete for organizations where there is a fixed salary for employees. But most commonly, we consider salary as a continuous variable as there is no defined range of salary.
Is the number of workers in a company a continuous variable?
Number of workers in a company - It is a discrete data variable , as the value is countable and finite. Annual salary of all the workers in a company - It is a continuous data variable, as the annual salary is different for different employees in a company.
Graph
The graph is a mathematical and pictorial representation of a set of vertices and edges. It consists of the non-empty set where edges are connected with the nodes or vertices. The nodes can be described as the vertices that correspond to objects. The edges can be referred to as the connections between objects.
Types of Graph
Now we will describe the two types of graph: Directed graph, undirected graph.
Selection between Directed Graph and Undirected Graph
Here we will describe some points that will help us choose either a directed graph or an undirected graph.
What are the dots on a graph called?
Graphs are made up of a collection of dots called vertices and lines connecting those dots called edges. When two vertices are connected by an edge, we say they are adjacent. The nice thing about looking at graphs instead of pictures of rivers, islands and bridges is that we now have a mathematical object to study.
Who is the first person to study graph theory?
Graph Theory is a relatively new area of mathematics, first studied by the super famous mathematician Leonhard Euler in 1735. Since then it has blossomed in to a powerful tool used in nearly every branch of science and is currently an active area of mathematics research.
Overview
In mathematics, and more specifically in graph theory, a graph is a structure amounting to a set of objects in which some pairs of the objects are in some sense "related". The objects correspond to mathematical abstractions called vertices (also called nodes or points) and each of the related pairs of vertices is called an edge (also called link or line). Typically, a graph is depicted in diagra…
Definitions
Definitions in graph theory vary. The following are some of the more basic ways of defining graphs and related mathematical structures.
A graph (sometimes called undirected graph for distinguishing from a directed graph, or simple graph for distinguishing from a multigraph) is a pair G = (V, E), where V is a set whose elements are called vertices (singular: vertex), and E is …
Types of graphs
One definition of an oriented graph is that it is a directed graph in which at most one of (x, y) and (y, x) may be edges of the graph. That is, it is a directed graph that can be formed as an orientation of an undirected (simple) graph.
Some authors use "oriented graph" to mean the same as "directed graph". Some authors use "oriented graph" to mean any orientation of a given undirected gra…
Properties of graphs
Two edges of a graph are called adjacent if they share a common vertex. Two edges of a directed graph are called consecutive if the head of the first one is the tail of the second one. Similarly, two vertices are called adjacent if they share a common edge (consecutive if the first one is the tail and the second one is the head of an edge), in which case the common edge is said to join the two vertices. An edge and a vertex on that edge are called incident.
Examples
• The diagram is a schematic representation of the graph with vertices and edges
• In computer science, directed graphs are used to represent knowledge (e.g., conceptual graph), finite state machines, and many other discrete structures.
• A binary relation R on a set X defines a directed graph. An element x of X is a direct predecessor of an element y of X if and only if xRy.
Graph operations
There are several operations that produce new graphs from initial ones, which might be classified into the following categories:
• unary operations, which create a new graph from an initial one, such as:
• binary operations, which create a new graph from two initial ones, such as:
Generalizations
In a hypergraph, an edge can join more than two vertices.
An undirected graph can be seen as a simplicial complex consisting of 1-simplices (the edges) and 0-simplices (the vertices). As such, complexes are generalizations of graphs since they allow for higher-dimensional simplices.
Every graph gives rise to a matroid.
See also
• Conceptual graph
• Graph (abstract data type)
• Graph database
• Graph drawing
• List of graph theory topics