What makes a graph discrete or continuous? 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 a discrete graph look like?
Properties :
- (1) A Hamiltonianc irbuitc ontainsa Hamiltonian path but a graph , Containing a Hamiltonian path need not have a Hamiltonian cycle.
- (2) By deleting any one edge from Hamiltonian cycle,we can get Hamiltonian path.
- (3) A graph may contain more than one Hamiltonian cycle.
- (4) A complete graph kn, will always have a Hamiltonian cycle, when n>=3
What kind of graph is use to show discrete data?
#9 Area Graph
- Use stacked area
- Graph data that is cumulative
- Use colors carefully
What is the difference between discrete and continuous graphs?
What is the difference between continuous and discrete graph? A discrete function is a function with distinct and separate values. A continuous function, on the other hand, is a function that can take on any number within a certain interval. Discrete functions have scatter plots as graphs and continuous functions have lines or curves as graphs.
What is the best graphical format for showing discrete data?
Discrete data is best represented using bar charts. Temperature graphs would usually be line graphs because the data is continuous . When you are graphing percentages of a distribution a pie chart would be suitable.
What makes a graph continuous or 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 does it mean for a graph to be discreet?
Graph: A discrete graph is a series of unconnected points (a scatter plot). Domain: a set of input values consisting of all numbers in an interval. Domain: a set of input values consisting of only certain numbers in an interval.
Are graphs discrete?
The two discrete structures that we will cover are graphs and trees. A graph is a set of points, called nodes or vertices, which are interconnected by a set of lines called edges....What is a Graph?VertexDegreeEven / Oddd1odd3 more rows
How do you know if its discrete or continuous?
The key differences are: Discrete data is the type of data that has clear spaces between values. Continuous data is data that falls in a constant sequence. Discrete data is countable while continuous — measurable.
What do you mean by discrete?
Definition of discrete 1 : constituting a separate entity : individually distinct several discrete sections. 2a : consisting of distinct or unconnected elements : noncontinuous. b : taking on or having a finite or countably infinite number of values discrete probabilities a discrete random variable.
What does discrete mean in maths?
Discrete mathematics is the branch of mathematics dealing with objects that can assume only distinct, separated values.
What is graph in discrete structure?
In discrete mathematics, a graph is a collection of points, called vertices, and lines between those points, called edges. There are many different types of graphs, such as connected and disconnected graphs, bipartite graphs, weighted graphs, directed and undirected graphs, and simple graphs.
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 makes 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 is an example of a discrete graph?
Discrete functions are used for things that can be counted. For example, the number of televisions or the number of puppies born. The graph of discrete functions is usually a scatter plot with scattered points like the one you just saw.
What does discrete mean in statistics?
A discrete distribution is one in which the data can only take on certain values, for example integers. A continuous distribution is one in which data can take on any value within a specified range (which may be infinite).
What does it mean to graph something against something?
Usually, plotting against x is a plot of function f(x) against a horizontal value of x: f(x) Therefore, plotting y against x. y = f(x) which is a mapping of y values against a range of x values related thro the function f(x).
How do you label a graph in a lab report?
–A title should be placed at the top of the graph if the graph is to be placed in the laboratory notebook. This helps the reader immediately know what the graph is. The title should be a concise description of what is being graphed (e. g., “Pressure as a Function of Temperature for Nitrogen”).
How do you label a graph?
To properly label a graph, you should identify which variable the x-axis and y-axis each represent. Don't forget to include units of measure (called scale) so readers can understand each quantity represented by those axes. Finally, add a title to the graph, usually in the form "y-axis variable vs. x-axis variable."
What does it mean to plot something against something?
To join together to form a scheme or plot to foil or defeat someone or something. The group was arrested for plotting against the monarch. His two younger brothers plotted against him to have him removed from the head of the company.
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 is a multigraph in text?
A multigraph is a generalization that allows multiple edges to have the same pair of endpoints. In some texts, multigraphs are simply called graphs.
What is the difference between a directed and undirected graph?
In contrast, if any edge from a person A to a person B corresponds to A owes money to B, then this graph is directed, because owing money is not necessarily reciprocated. The former type of graph is called an undirected graph while the latter type of graph is called a directed graph .
What is a graph in math?
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 ...
How many vertices are there in a weighted graph?
A weighted graph with ten vertices and twelve edges.
How many vertices can an edge join?
In a hypergraph, an edge can join more than two vertices.
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 graph made of?
The graph is made up of vertices (nodes) that are connected by the edges (lines). The applications of the linear graph are used not only in Maths but also in other fields such as Computer Science, Physics and Chemistry, Linguistics, Biology, etc. In real-life also the best example of graph structure is GPS, where you can track the path or know the direction of the road.
What is a graph with finite number of vertices called?
A graph that has finite number of vertices and edges is called finite graph.
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 degree in graph?
Degree: A degree in a graph is mentioned to be the number of edges connected to a vertex. It is denoted deg (v), where v is a vertex of the graph. So basically it the measure of the vertex.
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 the same types of nodes are connected to one another, the graph is known as?
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.
How to generate a symbolic function on a graph?
To generate a symbolic (vertex and/or edge) function on a given graph the makeVertexFunction and makeEdgeFunction can be used.
What does the notation A[g] mean?
The notation or A[g] will denote incidence matrix of the graph g. Note that our incidence matrix is the edge-vertex matrix and not the vertex-edge matrix of Mathematica (i.e. the transposed).
What does W[g] mean in mathematica?
The notation or W[g] will denote the adjacency matrix of the graph g. The Mathematica implementation takes the directed edges into account but for our purposes the adjacency matrix needs to be symmetric.
Which symbols can be executed in Mathematica?
Note: each of the gothic symbols L, T, G … can be executed and really are just aliases to Mathematica functions.
Is a metric a weight?
The metric can both be seen as a coupling factor in the inner product and as a weight on the vertices and edges. Especially on the edge level it’s interesting that the metric can be taken from the weight of the weighted graph. This means that the metric is usually taken as to be a diagonal matrix with orthogonality; only edge-edge and vertex-vertex coupling are considered.
Is differential calculus on graphs?
This is an overview of the discrete differential calculus on graphs with an emphasis on the usage of Mathematica to perform related calculations. While the calculus is more generic and can also be applied to generic simplices, it’s more complex to program since it involves concepts which are not directly deduced from the algebraic properties of graphs (e.g. orientation). We, hence, focus mainly on graphs and the usage of matrix methods.
Why is discrete math important in data science?
Most of the students think that is why it is needed for data science. The major reason for the use of discrete math is dealing with continuous values. With the help of discrete math, we can deal with any possible set of data values and the necessary degree of precision. The math in computers is based on discrete mathematics. The reason is that computers work in machine language.
When to avoid using line graphs?
Its recommended to avoid using Line Graphs when a variable is dependent on qualitative variable (X-axis).
What is stacked line graph?
A stacked line graph will follow the same structure — x-axis, independent, y-axis, dependent, plot and connect — but will consist of more than one line plotted on the same graph. Each line represents a different “thing” that was studied. A good
What are all curves composed of?
It’s more like… all curves are composed of straight lines.
What are the green lines in a parabola?
The green lines are all straight lines. They’re all tangent to a parabola. The parabola itself is not drawn, but it is determined by the lines.
How many lines are there in a line graph?
A line graph only has one line of data. To be more explicit, the independent variable, usually time, is marked on the x-axis, and the dependent variable, whatever it is you’re studying over time to monitor changes, is marked on the y-axis. Once all points are plotted, a single line is drawn through the points from left to right to show change over time.
Can a family of straight lines be a curve?
Yes, many curves can be represented by a family of straight lines, but not in a way that the straight lines are part of the curve but, nonetheless, somehow describe the curve. One way is that the straight lines are tangent lines to a curve. That curve is called the envelope of the family of straight lines. (The concept of envelope has been generalized so that the family needn’t be of straight lines but could be a family of curves.)
Why is an undirected graph more restrictive than a directed graph?
The undirected graph is more restrictive as compared to the directed graph because if the relationships have a hierarchical nature, then an undirected graph will not allow modeling them. The undirected graph is very common in practice. With the help of undirected graphs, we can easily model many real-world relationships. The relationship "is a friend of" can be called the typical symmetric relationship, for instance. This relationship is symmetric because if there is a case that "Mary is a friend of Harry", then "Harry is a friend of Mary" is also true.
Why is an undirected graph important?
The undirected graph is used to model those types of relationship for which it is important that the graph is existed or not, but they are not intrinsically transitive. Pedestrian paths are a good example of an undirected graph because, in pedestrian paths, we can go in both ways. That's why with the help of an undirected graph, the pathways are able to model.
What is the graph of a 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. Arrow (→) is used to represent the edges. According to the direction of arrow, the graph will traverse. The edge of the graph sometimes contains the Weights, which is used to show the strength of each connection between vertices.
Why do we need to select between directed and undirected graphs?
The programmer has to carefully select between the directed and undirected graph according to the problem because both the graphs are mathematical abstractions over real-world phenomena. On the basis of the relation, we will use the graph to model it. If it is reciprocal, then we will use the undirected graph. Otherwise, we will use the directed graph.
What is directed path?
The directed path in a directed graph can be described as a sequence of vertices and a directed edge. Where, the edge is pointing from each vertex in the sequence to its successor in the sequence. The directed path will not contain repeated edges. If there are no repeated vertices, then the directed path will be simple.
What is the relationship between vertices?
Suppose there are two vertices, 'x' and 'y'. If there is a directed path from 'x' to 'y', then the vertex 'x' is reachable from vertex 'y'. If the vertices 'x' and 'y' both are mutually reachable, the vertices will be known as strongly connected. The mutually connected means that the vertex 'x' has a directed path from vertex 'y' and vertex 'y' also has a directed path from vertex 'x'.
How to express an undirected graph?
In the field of computer science, the most popular undirected graph can be expressed by the topology of connections in a computer network. If one system in a graph is connected to the other system, then the second system will also be connected with the first system in an undirected graph.
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
What Is Graph
History
- The history of graph theory states it was introduced by the famous Swiss mathematician named Leonhard Euler, to solve many mathematical problems by constructing graphs based on given data or a set of points. The graphical representationshows different types of data in the form of bar graphs, frequency tables, line graphs, circle graphs, line plots, etc.
Definition
- Graph Theory is the study of points and lines. In Mathematics, it is a sub-field that deals with the study of graphs. It is a pictorial representation that represents the Mathematical truth. Graph theory is the study of relationship between the vertices (nodes) and edges (lines). Formally, a graph is denoted as a pair G(V, E). Where V represents th...
Types of Graph
- The graphs are basically of two types, directed and undirected. It is best understood by the figure given below. The arrow in the figure indicates the direction.
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.
- When all the pairs of nodes are connected by a single edge it forms a complete graph.