An ordered pair (V,E), where V is a set of elements called vertices (or nodes) and E is a set of pairs of elements of V, called edges; informally, a set of vertices together with a set edges that join these vertices
A diagram displaying data; in particular one showing the relationship between two or more quantities, measurements or indicative numbers that may or may not have a specific mathematical formula relating them to each other
A diagram displaying data, in particular one showing the relationship between two or more variables; specifically, for a function f(x_1, x_2, \ldots, x_n), the set of all tuples (x_1, x_2, \ldots, x_n, f(x_1, x_2, \ldots, x_n))
A visual representation of the relationship between change in one variable and change in another variable, consisting of a line connecting points plotted on an x and y axis, for the purpose of analysis
In mathematics, a set of elements called vertices or nodes together with a set of unordered pairs of vertices called edges Intuitively speaking, an edge is a line joining two vertices
In one context, this is the functional value and domain: {(x, z): x in X and z=f(x)}, where f: X-->R In another context, this is a (maybe undirected) network In the former context, see also epigraph and hypograph In the latter context, the notation [V,E] is sometimes used to mean a graph with vertex (or node) set V and edge (or link) set E We say an edge is incident with the two nodes that define it, and those two nodes are called the endpoints of the edge The endpoints are said to be adjacent nodes
A diagram displaying data, in particular one showing the relationship between two or more variables; specifically, for a function f(x_1, x_2, ldots, x_n), the set of all tuples (x_1, x_2, ldots, x_n, f(x_1, x_2, ldots, x_n))
A pictorial representation of a numerical relation, where each ordered pair in the relation corresponds to a point in the plane, with the two numbers corresponding to the horizontal and vertical displacement from the origin, respectively
Informally, a graph is a finite set of dots called vertices (or nodes) connected by links called edges (or arcs) More formally: a simple graph is a (usually finite) set of vertices V and set of unordered pairs of distinct elements of V called edges Not all graphs are simple Sometimes a pair of vertices are connected by multiple edge yielding a multigraph At times vertices are even connected to themselves by a edge called a loop, yeilding a pseudograph Finally, edges can also be given a direction yielding a directed graph (or digraph)
a (non-)oriented graph is composed of two sets: a set of vertices, and a set of (non-)oriented edges, where each edge is a (un-)ordered pair of vertices, called "source" and "destination" in the oriented case; an hypergraph may have edges with any number of vertices; a dataflow graph is an oriented hypergraph where each vertex is an operation, and where each edge is a data-dependence with a single source and one or several destinations
a drawing illustrating the relations between certain quantities plotted with reference to a set of axes represent by means of a graph; "chart the data"
When you are given an equation, such as y = x + 1, each value of x has a corresponding y value For example, when x = 0, y = 1; when x = 1, y = 2 A graph lets you look at a large number of values for x, and tells you the value of y for each x on the graph As you look at more examples of graphs, you will begin to be able to analyze the relationship between x and y, based on the shape of the graph
The term "graph" has several meanings In the most general form, it is an incidence structure consisting of a set of vertices and a set of edges, each edge incident with one or two vertices An edge incident with one vertex is called a loop, and an edge incident with two vertices is called a link Multiple edges (incident with the same set of vertices) are allowed A more restricted concept, sometimes called a simple graph, has no loops and no multiple edges In this case, an edge can be identified with an unordered pair of vertices Two vertices are called adjacent if there is an edge incident with that pair of vertices In a directed graph or digraph, edges are ordered (rather than unordered) pairs
A graph is a mathematical diagram which shows the relationship between two or more sets of numbers or measurements. a drawing that uses a line or lines to show how two or more sets of measurements are related to each other chart (graphic formula). Visual representation of a data set or a mathematical equation, inequality, or function to show relationships or tendencies that these formulas can only suggest symbolically and abstractly. Though histograms and pie charts are also graphs, the term usually applies to point plots on a coordinate system. For example, a graph of the relationship between real numbers and their squares matches each real number on a horizontal axis with its square on a vertical axis. The resulting set of points in this case is a parabola. A graph of an inequality is usually a shaded region on one side of a curve, whose shape depends not only on the equation or inequality but on the coordinate system chosen
A grid of lines, with the vertical lines representing one set of information and the horizontal lines representing another A "Curve" superimposed on a graph grid gives information about test results
{i} diagram which uses a series of points or lines to demonstrate a connection between two or more things; number or group of numbers represented by a point or points on a line (Mathematics)
Informally, a graph consists of a finite set of vertices and edges which connect them Graphs are usually depicted pictorially as a set of points representing the vertices with lines (usually straight, but not necessarily so) connecting them to represent the edges Types of graphs are: simple, directed or digraphs, multigraphs or planar A Graph
» In order to accommodate the requirements of signed, gain, and biased graph theory while being technically correct it is sometimes necessary to define a graph in a relatively complicated way Here is one way to produce a satisfactory definition We define a graph as a quadruple of three sets and an incidence relation: Gamma = (V(Gamma), E(Gamma), I(Gamma), IGamma) (as is customary, we may write V, E, I, I; and we also may omit explicit mention of I and I when there will be no confusion), where I = (IV, IE) : I -> E × V is the incidence relation; that is, IV and IE are incidence relations between, respectively, I and V (this is the ``vertex incidence relation'') and I and E (this is the ``edge incidence relation'') The members of V, E, and I are called ``vertices'', ``edges'', and ``ends'' or ``edge ends'' The requirements are that I be a function and that each e in E is edge-incident with at most 2 members of I (which are called the ``ends of e'')
A graph is a visual representation of data that displays the relationship among variables, usually cast along x and y axes Graphs are especially useful in showing the broader trends in the data
Shows one of a variety of plots of the motion of the pendulum (listed in "Graph Type" above) You can capture a plot, combine plots, print plots, save trajectories, using the "Copy Graph" button (above) See the help for graphs
a set of topologically interrelated zero-dimensional (node), one-dimensional (link or chain), and sometimes two-dimensional (GT-polygon) objects that conform to a set of defined constraint rules Numerous rule sets can be used to distinguish different types of graphs Three such types, planar graph, network, and two-dimensional manifold, are used in this standard All three share the following rules: each link or chain is bounded by an ordered pair of nodes, not necessarily distinct; a node may bound one or more links or chains; and links or chains may only intersect at nodes Planar graphs and networks are two specialized types of graphs, and a two-dimensional manifold is an even more specific type of planar graph