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

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

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 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.

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

Graphs that admit exact colorings have been classified.

Graphs may be presented, for example, of coincidence rate against the difference between the settings a and b, but if a more comprehensive set of experiments had been done it might have become clear that the rate depended on a and b separately.

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 are one of the objects of study in discrete mathematics.

Graphs are the basic subject studied by graph theory.

( 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.

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.

and buggies and wagons and chugging Fords kept gathering all morning, until the edges of the field were packed thick and small boys kept scampering out on the playing field to make fun of the visitors -- whose pitcher was a formidable looking young man with the only baseball cap.

The most common geometric arrangement is where some convex polyhedron is in its canonical form, which is to say that the all its edges must be tangent to a certain sphere whose centre coincides with the centre of gravity ( average position ) of the tangent points.

" Raclette scrapers " are notable for their particular form, being blades or flakes whose edges have been sharply retouched until they are semicircular or even shapeless.

Then 2-polytopes ( polygons ) are defined as plane objects whose bounding facets ( edges ) are 1-polytopes, 3-polytopes ( polyhedra ) are defined as solids whose facets ( faces ) are 2-polytopes, and so forth.

Some explain a red – black tree as a binary search tree whose edges, instead of nodes, are colored in red or black, but this does not make any difference.

This is formalized by studying the Ext functor and describing the module category in various ways including quivers ( whose nodes are the simple modules and whose edges are composition series of non-semisimple modules of length 2 ) and Auslander – Reiten theory where the associated graph has a vertex for every indecomposable module.

Barbed tape or razor wire is a mesh of metal strips with sharp edges whose purpose is to prevent passage by humans.

* Every connected graph G admits a spanning tree, which is a tree that contains every vertex of G and whose edges are edges of G.

" This fits well with more general textual themes that consider Nephthys to be a goddess whose unique domain was darkness, or the perilous edges of the desert.

The collection of bridges in a local area network ( LAN ) can be depicted as a graph whose nodes are bridges and LAN segments ( or cables ), and whose edges are the interfaces connecting the bridges to the segments.

It features a wider than normal bit, whose outside edges are sharply turned up, so that when gazing directly down the adze, from bit to eye, the cutting edge resembles an extremely wide and often very flat U. This adze was mainly used for shaping cross grain, such as for joining planks.

The proboscis was striated like a vacuum cleaner's hose and probably flexible, and it ended with a claw-like structure whose inner edges bore spines that projected inwards and forwards.

This also is a special case of Ramsey's theorem, which says that for any given integer c, any given integers n < sub > 1 </ sub >,..., n < sub > c </ sub >, there is a number, R ( n < sub > 1 </ sub >,..., n < sub > c </ sub >), such that if the edges of a complete graph of order R ( n < sub > 1 </ sub >,..., n < sub > c </ sub >) are coloured with c different colours, then for some i between 1 and c, it must contain a complete subgraph of order n < sub > i </ sub > whose edges are all colour i. The special case above has c

More formally, a spin network is a ( directed ) graph whose edges are associated with irreducible representations of a compact Lie group and whose vertices are associated with intertwiners of the edge representations adjacent to it.

For two colours, Ramsey's theorem states that for any pair of positive integers ( r, s ), there exists a least positive integer R ( r, s ) such that for any complete graph on R ( r, s ) vertices, whose edges are coloured red or blue, there exists either a complete subgraph on r vertices which is entirely blue, or a complete subgraph on s vertices which is entirely red.

order R ( n < sub > 1 </ sub >, ..., n < sub > c </ sub >) are coloured with c different colours, then for some i between 1 and c, it must contain a complete subgraph of order n < sub > i </ sub > whose edges are all colour i. The special case above has c

Input: A connected graph G whose edges have distinct weights

However, if a graph contains a " negative cycle ", i. e., a cycle whose edges sum to a negative value, then walks of arbitrarily low weight can be constructed by repeatedly following the cycle, so there may not be a shortest path.

Jonathan Miller points out that apart from " adding suggestive gleams at the bevelled edges, the most important way the mirror betrays its identity is by disclosing imagery whose brightness is so inconsistent with the dimness of the surrounding wall that it can only have been borrowed, by reflection, from the strongly illuminated figures of the King and Queen ".