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 one of the objects of study in discrete mathematics.

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.

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.

Furthermore, the network in Figure 3 is only the basic net through which other networks pertaining to logistics and the like are interlaced.

We are reminded, however, that freedom of thought and discussion, the unfettered exchange of ideas, is basic under our form of government.

Within this context of spontaneous and unanalyzed responses to the experience of civilizational crisis, two basic organizations of response are observable: reaction and ideological progressivism.

When the reactionary response is thus bolstered by an intellectual defense, the characteristics of that defense are explicable only in terms of the basic attitudes of unanalyzed reaction.

The selective and directional qualities of basic value-orientations are clearly evident in these data: the `` success-oriented '' students choose vocational preparation, the `` other-directed '' choose goals of social adjustment ( `` getting along with people '' ), the `` intellectuals '' choose a liberal arts emphasis.

The students who are most willing to acquiesce in the suppression of civil liberties are also those who are most likely to be prejudiced against minority groups, to be conformist and traditionalistic in general social attitudes, and to lack a basic faith in people.

Pohl and Kornbluth's ad men have long since thrown out appeals to reason and developed techniques of advertising which tie in with `` every basic trauma and neurosis in American life '', which work on the libido of consumers, which are linked to the `` great prime motivations of the human spirit ''.

Now the basic question to be asked in this situation is what motivates the manipulators, that is, what are their values??

In still others which are barely on the threshold of the transition into modernity, the decade can bring significant progress in launching the slow process of developing their human resources and their basic services to the point where an expanded range of developmental activities is possible.

The long-range aspects of this program are divided into four distinct phases: basic mapping, inventory, analysis and plan and policy formation.

In addition to the basic programs in wavelength standards, spectroscopy, solid state physics, interactions of the free electron and atomic constants which are necessary to provide the foundation for technological progress, the Bureau has strengthened its activities in laboratory astrophysics.

But he takes his bearings from the great guidelines of policy, well-established precedents, the commitments of the United States under international charters and treaties, basic statutes, and well-understood notions of the American people about how we are to conduct ourselves, in policy literature such as country papers and National Security Council papers accumulated in the Department.

If the reserve components are to serve effectively in time of war, their basic organization and objectives must conform to the changing character and missions of the active forces.

There are other basic rules.

The basic costs are generally pretty much the same regardless of the agency through which you reserve your car, but some of them offer supplementary advantages.

Important as these differences are, they should not obscure the basic fact that by shifting the hypothalamic balance sufficiently to the parasympathetic side, we produce depressions, whereas a shift in the opposite direction causes excitatory effects and, eventually, maniclike changes.

Thus, although the agenda of external assistance in the economic sphere are cumulative, and many of the policies suggested for nations in the earlier stages remain relevant, the basic purpose of American economic policy during the later stages of development should be to assure that movement into a stage of self-sustaining growth is not prevented by lack of foreign exchange.

There are also more basic problems.

Additional courses can readily be added and special cooperative programs worked out with any new industry if the basic facilities, staff and program are in being.

The model of this paper considers an industry which is not characterized by vigorous price competition, but which is so basic that its wage-price policies are held in check by continuous critical public scrutiny.

We are abstracting from the fact of strikes here, but it should be obvious that the extent to which the public-limit price is raised by a given increase in the basic wage rate is also a function of the show of resistance put up by the industry.

Changes in the basic wage rate are cost-raising, and they constitute an argument for raising prices.

However, it is not known to either the union or the public precisely how much of a cost increase is caused by a given change in the basic wage rate, although the companies are presumed to have reliable estimates of this magnitude.