Mathematics and statistics

Graph spectrum

The graph spectrum is the set of eigenvalues of a graph's adjacency matrix, real because the matrix is symmetric, and the subject of spectral graph theory.

Graph structure theorem

The graph structure theorem, proved by Neil Robertson and Paul Seymour, describes every graph with no fixed graph H as a minor as built from pieces embeddable in a surface.

Graph theoretical analysis

Graph theoretical analysis models systems as graphs of nodes and edges and computes summary measures, an interdisciplinary toolset applied to brain networks, power grids, and social networks.

Graph theory is the branch of mathematics that studies graphs, structures of vertices and edges modeling pairwise relationships, originating in Euler's 1735 analysis of the Königsberg bridges problem.

Graph Theory with Applications

Graph Theory with Applications is a graduate-level graph theory textbook by J. A. Bondy and U. S. R. Murty, published in 1976 and praised by reviewers as outstanding.

GraphBLAS

GraphBLAS (Graph Basic Linear Algebra Subprograms) is a specification for an API that expresses graph algorithms as sparse matrix operations over semirings, developed by the open GraphBLAS Forum and modeled on the BLAS standard.

Graphic matroid

The graphic matroid, also called the cycle matroid, is the matroid on a graph's edges whose independent sets are forests and whose bases are spanning trees.

Graphical lasso

The graphical lasso (glasso) is an algorithm that estimates a sparse inverse covariance matrix using an l1 penalty, introduced by Friedman, Hastie, and Tibshirani in 2008.

Graphical model

A graphical model represents a joint probability distribution as a graph, with nodes for variables and edges for direct interactions; missing arcs encode conditional independence.

Graphoid

A graphoid is an abstract relation capturing the behavior of conditional independence, defined by five axioms introduced by Judea Pearl and Azaria Paz in 1985.

Graphon

A graphon is a symmetric measurable function on the unit square serving as the limit object for convergent sequences of dense graphs, introduced by Lovász and Szegedy in 2004.

Graphviz

Graphviz is open source graph visualization software that turns textual descriptions of abstract graphs into automatically arranged diagrams; it originated at AT&T Bell Laboratories and is used in software engineering, bioinformatics, and machine learning.

Grassmannian

The Grassmannian, also called the Grassmann manifold, is the space of k-dimensional linear subspaces of a vector space, fundamental to algebraic geometry and named for Hermann Grassmann.

Gray code

Gray code, also known as reflected binary code, is an ordering of binary numbers in which successive values differ in exactly one bit, useful in rotary encoders.

Great circle

A great circle, or orthodrome, is the largest circle on a sphere, formed by a plane through its center; its shorter arc is the shortest path between two points.

Great Internet Mersenne Prime Search

The Great Internet Mersenne Prime Search (GIMPS) is a volunteer computing project founded by George Woltman in 1996 that has discovered the last 18 Mersenne primes, including the largest known prime.

Greater-than sign

The greater-than sign (>) is a mathematical symbol indicating the value on its left exceeds the value on its right, first printed in Thomas Harriot's 1631 algebra book.

Greatest common divisor

The greatest common divisor, also known as the highest common factor, is the largest positive integer that divides two integers, found by the Euclidean algorithm from Euclid's Elements.

Greedy coloring

Greedy coloring, also called the first-fit algorithm, is a simple graph coloring method that processes vertices in a chosen order, giving each the smallest color its already-colored neighbors lack.

Green–Tao theorem

The Green–Tao theorem is a result in number theory proved by Ben Green and Terence Tao in 2004, stating that the prime numbers contain arbitrarily long arithmetic progressions.

Green's function

Green's function is the response of a linear differential equation with its boundary conditions to a point source, named for George Green, who introduced it in 1828.

Green's identities

Green's identities, also known as Green's formulas, are two integral formulas relating smooth functions inside a region to their values and normal derivatives on the boundary.

Green's relations

Green's relations are five equivalence relations defined on a semigroup from its principal ideals, introduced by J. A. Green in 1951 and central to semigroup theory.

Green's theorem

Green's theorem relates a line integral around a closed plane curve to a double integral over the region it encloses, generalizing the Fundamental Theorem of Calculus.

Grey prediction model

The gray prediction model is a small-sample forecasting method from gray system theory, whose standard form GM(1,1) fits a differential equation to as few as four observations.

Grey relational analysis

Grey relational analysis, also called gray correlation analysis, is a method from gray system theory, proposed by Deng Ju-Long in 1982, that measures the similarity of data sequences.

Grey wolf optimizer

The gray wolf optimizer (GWO) is a swarm intelligence metaheuristic introduced by Seyedali Mirjalili and colleagues in 2014, mimicking wolf pack hierarchy and cooperative hunting to optimize numerical functions.

Griffiths group

The Griffiths group, named for Phillip A. Griffiths, is the group of homologically trivial codimension-r algebraic cycles on a smooth projective variety modulo algebraically trivial ones.

Gröbner basis

A Gröbner basis (Groebner bases) is a generating set for an ideal in a polynomial ring, introduced by Bruno Buchberger in 1965 and named after his advisor Wolfgang Gröbner.