Graphs are basic objects in combinatorics.

Graph ( mathematics ) | Graphs like this are among the objects studied by discrete mathematics, for their interesting graph property | mathematical properties, their usefulness as models of real-world problems, and their importance in developing computer algorithm s.

Graphs are one of the prime objects of study in discrete mathematics.

Graphs are among the most ubiquitous models of both natural and human-made structures.

Graphs with weights, or weighted graphs, are used to represent structures in which pairwise connections have some numerical values.

Graphs are represented graphically by drawing a dot or circle for every vertex, and drawing an arc between two vertices if they are connected by an edge.

Graphs that have vertices representing events, and edges representing causal relations between events, are often acyclic.

Graphs whose edges or vertices have names or labels are known as labeled, those without as unlabeled.

Graphs with labeled vertices only are vertex-labeled, those with labeled edges only are edge-labeled.

Graphs are the basic subject studied by graph theory.

Graphs are frequently drawn as node-link diagrams in which the vertices are represented as disks or boxes and the edges are represented as line segments, polylines, or curves in the Euclidean plane.

( Graphs which show just the length of the rule in the two dynasties are the most widely known ; however, Fomenko's conclusions are also based on other parameters, as described above.

Graphs are converted into factor graph form to perform belief propagation.

* Graphs are used to visualize relationships between different quantities.

Current research activities of the Department are in the areas of Analysis, Algebra, Operator Theory, Functional Analysis, General topology, Fuzzy mathematics, Graph Theory, Combinations, Convexity Theory, Fluid Dynamics, Non-linear waves, Stability, Stochastic Processes in general and Random Graphs, Operations Research and the History of Mathematics.

Graphs showing this trade-off are available from folds. net.

Graphs are an expressive, visual and mathematically precise formalism for modelling of objects ( entities ) linked by relations ; objects are represented by nodes and relations between them by edges.

The optional modules are Number Patterns, Geometry and Trigonometry, Graphs and Relations, Business-Related Mathematics, Networks and Decision Mathematics, or Matrices.

Graphs similar to the one on the right result.

Graphs are switching equivalent if one can be obtained from the other by switching.

40 Graphs, w species pictures, also Tables, Photos, etc.

Mikhalev, Monoids, Acts and Categories: with Applications to Wreath Products and Graphs, De Gruyter Expositions in Mathematics vol.

A Discussion of the Two qi 其 Graphs in the First Chapter of the Daodejing .” PEW 60. 3 ( 2010 ): 391-421

Free groups of higher rank: Graphs or punctured plane.

* Chein, M., Mugnier, M .- L. ( 2009 ), Graph-based Knowledge Representation: Computational Foundations of Conceptual Graphs, Springer, 2009, ISBN 978-1-84800-285-2.

It is also possible to represent logical descriptions using semantic networks such as the existential Graphs of Charles Sanders Peirce or the related Conceptual Graphs of John F. Sowa.

Stirling Numbers of the First Kind., § 24. 1. 3 in Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing.

* Milton Abramowitz and Irene A. Stegun, eds., Handbook of Mathematical Functions ( with Formulas, Graphs and Mathematical Tables ), U. S. Dept.

Coxeter, R. Frucht and D. L. Powers, Zero-Symmetric Graphs, ( 1981 ) Academic Press.

And, as a matter of fact, Nicolas had slept in the park only part of one night, when he discovered that Munich's early mornings even in summer are laden with dew.

But in our case -- and neither my wife nor I have extreme views on integration, nor are we given to emotional outbursts -- the situation has ruined one or two valued friendships and come close to wrecking several more.

It is one of the ironic quirks of history that the viability and usefulness of nationalism and the territorial state are rapidly dissipating at precisely the time that the nation-state attained its highest number ( approximately 100 ).

Accidental war is so sensitive a subject that most of the people who could become directly involved in one are told just enough so they can perform their portions of incredibly complex tasks.

Only one rule prevailed in my conversations with these men: The more highly placed they are -- that is, the more they know -- the more concerned they have become.

( There are two receivers in case one should be dropped and damaged.

Now we must become vague, for we are approaching one of the nation's most guarded secrets.

They are mere fragments, just one portion of preprepared messages.

The one apparent connection between the two is a score of buildings which somehow or other have survived and which naturally enough are called `` historical monuments ''.

Often it is recognized that all the details of the pattern may not be essential to the outcome but, because the pattern was empirically determined and not developed through theoretical understanding, one is never quite certain which behavior elements are effective, and the whole pattern becomes ritualized.

Two thieves are crucified with Christ, one saved and the other damned.

Again, the sufferings and disasters produced by any transgression against the commandment not to love are almost invariably associated in one way or another with childhood, with the figure of a child.

In a certain perfectly definite way, the method and the theme of his stories are one and the same.

He is a widower, his three children are dead, he has no one left on earth ; ;

Whatever pole of this contrast one emphasizes and whatever the tension between these two approaches to understanding the artistic imagination, it will be readily seen that they are not mutually exclusive, that they belong together.

they are fields of force exerting a unique influence on the sensibilities and a unique relatedness to one another.

In its place is a passionate consciousness grasped and molded to feelings of positive or negative values even as the actions of one's life are determined by constellations of process in which one is caught.

The party is usually in a room small enough so that all guests are within sight and hearing of one another.

For the occasion on which everyone already knows everyone else and the host wishes them to meet one or a few honored newcomers, then the `` open house '' system is advantageous because the honored guests are fixed connective points and the drifting guests make and break connections at the door.

The networks for military communications are one of the best examples of networks which not only must be changed with the changes in objectives but also must be changed with the addition of new machines of war.

These assumptions lead to an organization with one man at the top, six directly under him, six under each of these, and so on until there are six levels of personnel.

What I want to point out here is that all of them are ex-liberals, or modified liberals, with perhaps one exception.

The men who speculate on these institutions have, for the most part, come to at least one common conclusion: that many of the great enterprises and associations around which our democracy is formed are in themselves autocratic in nature, and possessed of power which can be used to frustrate the citizen who is trying to assert his individuality in the modern world ''.

They tell us, sir, that we are free, because we have in one hand a ballot, and in the other a stock certificate.

The continuities, contrasts, and similarities discernible when past and present are surveyed together are inexhaustible and the one is often understood through the other.