Graph-tool, a free and efficient Python module for manipulation and statistical analysis of graphs.
Chris Godsil and Gordon Royle (2001), Algebraic Graph Theory. Graduate Texts in Mathematics, Vol.
Graph of a function | graph | Bipartite graph | planar graph | graph theory | directed graph | Under Graph | random graph | Planar graph | Graph traversal | Graph theory | Graph (mathematics) | Gabriel graph | visibility graph | Unit distance graph | rook's graph | Rado graph | minor (graph theory) | Lattice graph | interval graph | Graph-tool | Graph (data structure) | Graph coloring | graph coloring | Graph | Factor graph | Exponential random graph models | Directed graph | Directed acyclic graph | De Bruijn graph |
A Simple Algorithm for Constructing Szemerédi's Regularity Partition is a paper by Alan M. Frieze and Ravi Kannan giving an algorithmic version of the Szemerédi regularity lemma to find an ε-regular partition of a given graph.
An important case is when the curve is the graph of a real function (a function of one real variable and returning real values).
Speedup calculations and graph display were added in May 2013.
It can be used to prove that the Erdős–Rényi model of random graphs, when applied to countably infinite graphs, always produces a unique graph, the Rado graph.
A Gaussian function, a specific kind of function whose graph is a bell-shaped curve
On a sparse graph, Johnson's algorithm may be more efficient, taking Bipartite
Bipartite graph, a graph in which the vertices are partitioned into two sets and every edge has an endpoint in each set
Simon Plouffe gives an infinite collection of identities between the trigamma function, π2 and Catalan's constant; these are expressible as paths on a graph.
The Bethe lattice or Cayley tree, is the Cayley graph of the free group on n generators.
Colin de Verdière's invariant is a graph parameter for any graph G, introduced by Yves Colin de Verdière in 1990.
More precisely, the problem is polynomial-time if the graph is 2-colorable, that is, it is bipartite, and is NP-complete otherwise.
In January 2012, the music collective, New Party Systems, an ensemble containing First, released a song First wrote (C2011 Silent Graph Music ASCAP), "We Are" –– an anthem for the 99%, with a video by director, Toni Comas.
De Bruijn graph, a graph representing overlaps between sequences of symbols
Taran Adarsh praised the performances of the main actors and the music by Anu Malik such as 'Humnasheen' and 'Mujhse Kyon Roothe Ho?' but said "the sluggish pace of its narrative and classy treatment act as barricades. And the pre-climax portions, involving the child and the conclusion to the triangle, take the graph of the film downhill."
In the mathematical field of Lie theory, a Dynkin diagram, named for Eugene Dynkin, is a type of graph with some edges doubled or tripled (drawn as a double or triple line) and, within certain constraints, directed multiple edges.
Similar coloring techniques may also be used to schedule other sports pairings that are not all-play-all; for instance, in the National Football League, the pairs of teams that will play each other in a given year are determined, based on the teams' records from the previous year, and then an edge coloring algorithm is applied to the graph formed by the set of pairings in order to assign games to the weekends on which they are played.
During its roll-out stage, bloggers showed how Facebook Graph Search could be used to uncover potentially embarrassing information (e.g., companies employing people who like racism) or illegal interests (e.g., Chinese residents who like the banned group Falun Gong).
Heiko Harborth raised the question of whether every planar graph has a straight line representation in which all edge lengths are integers.
The FKT algorithm, named after Fisher, Kasteleyn, and Temperley, counts the number of perfect matchings in a planar graph in polynomial time.
Typically, spring-like attractive forces based on Hooke's law are used to attract pairs of endpoints of the graph's edges towards each other, while simultaneously repulsive forces like those of electrically charged particles based on Coulomb's law are used to separate all pairs of nodes.
Chromatic number of a graph, sometimes (Chi) is used, which is also used for the Euler characteristic
He moved to Montreal in 1963, and was instrumental in bringing to Canada a number of combinatorialists and graph theorists, including Anton Kotzig, and Jaroslav Nešetřil who wrote a thesis under Sabidussi.
Royle is the co-author (with Chris Godsil) of the book Algebraic Graph Theory (Springer Verlag, 2001, ISBN 0-387-95220-9).
GReAT, Graph Rewriting and Transformation, a Model Transformation Language
As with the hypercube graphs, and their isometric (distance-preserving) subgraphs the partial cubes, a halved cube graph may be embedded isometrically into a real vector space with the Manhattan metric (L1 distance function).
The graph representing the result of this transformation is bipartite, as all constraints are between a new and an old variable.
Resource Management Feature : Collects CPU、Memory、Disk、Network resource informations and visualises in graph format.
For instance, in searching for a solution to a puzzle such as Rubik's Cube, one may define an implicit graph in which each vertex represents one of the possible states of the cube, and each edge represents a move from one state to another.
We can compare this with the Mandelbrot set, a mathematical set generated by a simple equation, but whose graph is so complex that it will probably never be completely explored.
Cayley's formula follows from Kirchhoff's theorem as a special case, since every vector with 1 in one place, −1 in another place, and 0 elsewhere is an eigenvector of the Laplacian matrix of the complete graph, with the corresponding eigenvalue being n.
Kosaraju's algorithm, an algorithm to find the strongly connected component of a directed graph.
Tournaments, K. B. Reid, L. W. Beineke - Selected topics in graph theory, 1978
The number of domino tilings of a graph can be calculated using the determinant of special matrices, which allow to connect it to the discrete Green function which is approximately conformally invariant.
A formula proved by Crispin Nash-Williams characterizes the arboricity exactly: it is the maximum, over all subgraphs of the given graph , of the quantity .
They also show that this median of a set S of vertices in a median graph satisfies the Condorcet criterion for the winner of an election: compared to any other vertex, it is closer to a majority of the vertices in S.
Each entry contains the leading terms of the sequence, keywords, mathematical motivations, literature links, and more, including the option to generate a graph or play a musical representation of the sequence.
Unlike the other tools, in Compendium the composite hierarchy does not form a DAG, but rather an arbitrary graph: view A can appear on view B, and B can in turn appear on A. The user's intuitive notion of "inside" must be adapted somewhat in this case.
Applications of PQ trees include creating a contig map from DNA fragments, testing a matrix for the consecutive ones property, recognizing interval graphs and determining whether a graph is planar.
For example, while a general quasisymmetric map in the complex plane could map the real line to a set of Hausdorff dimension strictly greater than one, a δ-monotone will always map the real line to a rotated graph of a Lipschitz function L:ℝ → ℝ.
Then, for any sets U and V, by the Chinese remainder theorem, the numbers that are quadratic resides modulo every prime in U and nonresidues modulo every prime in V form a periodic sequence, so by Dirichlet's theorem on primes in arithmetic progressions this number-theoretic graph has the extension property.
Siddani Bhaskara Rao a Graph theorist was a professor and director of the Indian Statistical Institute (ISI), Calcutta
Planar separator theorem (graph theory) states that any planar graph can be split into smaller pieces by removing a small number of vertices.
This pattern is best visualized in the form of the so-called butterfly diagram, first constructed by the husband-wife team of E. Walter and Annie Maunder in the early twentieth century (see graph below).
Support curve is a statistical term, coined by A. W. F. Edwards, to describe the graph of the natural logarithm of the likelihood function.
However, it was pointed out by Ikuhiko Hata that the photograph was originally published in the Asahi Graph on 10 November 1937 and actually said it was “a group of girls of the ‘Rising Sun’ village who are returning to the village from farm work with the assistance of our troops”.
The prototype of such results is Turán's theorem, where there is one forbidden subgraph: a complete graph with k vertices (k is fixed).
Unit distance graph: a graph whose lines connect points that must be a distance apart that is equal to one
The graph of the computer worm Conficker is particularly clearcut and shows great interest throughout the week, dropping sharply over weekends.
One plan involves taping money to a donkey in a graph paper pouch that reads "HERE I AM ROCK YOU LIKE A HURRICANE", and another creating a treasure map for Estonian children.