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In graph theory, the mathematically simplest spatial network
In graph theory, a random geometric graph (RGG) is the mathematically simplest spatial network, namely an undirected graph constructed by randomly placing
Random_geometric_graph
probability). A HGG generalizes a random geometric graph (RGG) whose embedding space is Euclidean. Mathematically, a HGG is a graph G ( V , E ) {\displaystyle
Hyperbolic_geometric_graph
Graph generated by a random process
In mathematics, random graph is the general term to refer to probability distributions over graphs. Random graphs may be described simply by a probability
Random_graph
Network representing spatial objects
network is a lattice or a random geometric graph (see figure in the right), where nodes are distributed uniformly at random over a two-dimensional plane;
Spatial_network
Area of discrete mathematics
computer science, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A graph in this context
Graph_theory
Study of graphs defined by geometric means
Geometric graph theory in the broader sense is a large and amorphous subfield of graph theory, concerned with graphs defined by geometric means. In a
Geometric_graph_theory
Graph defined from a set of points in the Euclidean plane
graphs of infinite random point sets, the finite site percolation threshold gives the fraction of points needed to support connectivity: if a random subset
Gabriel_graph
Graph defined from a mathematical group
and geometric group theory. The structure and symmetry of Cayley graphs make them particularly good candidates for constructing expander graphs. Let
Cayley_graph
Intersection graph of unit disks in the plane
In geometric graph theory, a unit disk graph is the intersection graph of a family of unit disks in the Euclidean plane. That is, it is a graph with one
Unit_disk_graph
Topics referred to by the same term
RGG may refer to: Random geometric graph, a concept in mathematical graph theory Responsible Government Group (2009), a centre-right caucus in the City
RGG
American mathematician (1923–2013)
transmission, the Erdős–Rényi–Gilbert model for random graphs, the Gilbert disk model of random geometric graphs, the Gilbert–Shannon–Reeds model of card shuffling
Edgar_Gilbert
Decentralized type of wireless network
software originally developed by NRL. The traditional model is the random geometric graph. Early work included simulating ad hoc mobile networks on sparse
Wireless_ad_hoc_network
Two closely related models for generating random graphs
mathematical field of graph theory, the Erdős–Rényi models are two closely related models for generating random graphs and the evolution of a random network. These
Erdős–Rényi_model
Network whose degree distribution follows a power law
scale-free. Random graph – Graph generated by a random process Erdős–Rényi model – Two closely related models for generating random graphs Non-linear preferential
Scale-free_network
Branch of mathematics in probability theory
two types of percolation theory as well as the study of random graphs and random geometric graphs. Continuum percolation arose from an early mathematical
Continuum_percolation_theory
Structural analysis of a network
In network science, a biased random walk on a graph is a time path process in which an evolving variable jumps from its current state to one of various
Biased_random_walk_on_a_graph
Algorithm that employs a degree of randomness as part of its logic or procedure
S2CID 122784453. Seidel R. Backwards Analysis of Randomized Geometric Algorithms. Karger, David R. (1999). "Random Sampling in Cut, Flow, and Network Design
Randomized_algorithm
Python module
of random graphs, with arbitrary degree distribution and correlations. Support for well-established network models: Price, Barabási-Albert, Geometric Networks
Graph-tool
Linear algebra aspects of graph theory
In mathematics, spectral graph theory is the study of the properties of a graph in relationship to the characteristic polynomial, eigenvalues, and eigenvectors
Spectral_graph_theory
Degree of connectedness within a graph
In graph theory and network analysis, indicators of centrality assign numbers or rankings to nodes within a graph corresponding to their network position
Centrality
Process forming a path from many random steps
distances bounded. A random walk on a graph is a very special case of a Markov chain. Unlike a general Markov chain, random walk on a graph enjoys a property
Random_walk
Class of artificial neural networks
Geometric (PyTorch), TensorFlow GNN (TensorFlow), Deep Graph Library (framework agnostic), jraph (Google JAX), and GraphNeuralNetworks.jl/GeometricFlux
Graph_neural_network
Branch of geometry that studies combinatorial properties and constructive methods
polytope, unit disk graphs, and visibility graphs. Topics in this area include: Graph drawing Polyhedral graphs Random geometric graphs Voronoi diagrams
Discrete_geometry
Function type in graph theory
objects of exchangeable random graph models. Graphons are tied to dense graphs by the following pair of observations: the random graph models defined by graphons
Graphon
Area in mathematics devoted to the study of finitely generated groups
geometric group theory is to consider finitely generated groups themselves as geometric objects. This is usually done by studying the Cayley graphs of
Geometric_group_theory
phs (L:B) Percolation threshold / phs Random geometric graph Random regular graph Watts and Strogatz model Random matrix Circular ensemble Gaussian matrix
Catalog of articles in probability theory
Catalog_of_articles_in_probability_theory
Indian-American computer scientist and professor
showing that every monotone graph property has a sharp threshold in geometric random graphs; and showing that in a packet switch, output queuing (the gold
Ashish_Goel
Sparse graph with strong connectivity
In graph theory, an expander graph is a sparse graph that has strong connectivity properties, quantified using vertex, edge or spectral expansion. Expander
Expander_graph
Statistical models for network analysis
Exponential family random graph models (ERGMs) are a set of statistical models used to study the structure and patterns within networks, such as those
Exponential family random graph models
Exponential_family_random_graph_models
Periodic graphs are closely related to tessellations of space (or honeycombs) and the geometry of their symmetry groups, hence to geometric group theory
Periodic_graph_(geometry)
Maximum-entropy random graph models are random graph models used to study complex networks subject to the principle of maximum entropy under a set of structural
Maximum-entropy random graph model
Maximum-entropy_random_graph_model
Dimensionality reduction of graph-based semantic data objects [machine learning task]
algorithms for creating a knowledge graph embedding follow the same approach. First, the embedding vectors are initialized to random values. Then, they are iteratively
Knowledge_graph_embedding
Image segmentation algorithm
pixels. Therefore, the random walk occurs on the weighted graph (see Doyle and Snell for an introduction to random walks on graphs). Although the initial
Random_walker_algorithm
Scale-free network generation algorithm
that they have power-law (or scale-free) degree distributions, while random graph models such as the Erdős–Rényi (ER) model and the Watts–Strogatz (WS)
Barabási–Albert_model
Appendix:Glossary of graph theory in Wiktionary, the free dictionary. This is a glossary of graph theory. Graph theory is the study of graphs, systems of nodes
Glossary_of_graph_theory
Python library for graphs and networks
graph's topology and edge lengths, resulting in a layout that emphasizes geometric accuracy and readability. Random layout assigns each node a random
NetworkX
Collection of random variables
fields a stochastic (/stəˈkæstɪk/) or random process is a mathematical object usually defined as a family of random variables in a probability space, where
Stochastic_process
Mixing property of Markov chains and graphs
of a directed graph, in which case it can be used to analyze how quickly random walks in the graph converge. The conductance of a graph is closely related
Conductance_(graph_theory)
Computer science algorithm
computer science, graph traversal (also known as graph search) refers to the process of visiting (checking and/or updating) each vertex in a graph. Such traversals
Graph_traversal
Graph that can be embedded in the plane
In graph theory, a planar graph is a graph that can be embedded in the plane, i.e., it can be drawn on the plane in such a way that its edges intersect
Planar_graph
Directed graph with no directed cycles
In mathematics, particularly graph theory, and computer science, a directed acyclic graph (DAG) is a directed graph with no directed cycles. That is, it
Directed_acyclic_graph
Spectral graph theory concept
spectral graph theory, a Ramanujan graph is a regular graph whose spectral gap is almost as large as possible (see extremal graph theory). Such graphs are
Ramanujan_graph
Graph where most nodes are reachable in a small number of steps
networks were identified as a class of random graphs by Duncan Watts and Steven Strogatz in 1998. They noted that graphs could be classified according to two
Small-world_network
algorithm for constructing maximum-cardinality matching on graphs. Coloring algorithm: algorithms for graph (vertex or edge) coloring (subject to constraints,
List_of_algorithms
Concept in network science
stochastic block model is a generative model for random graphs. This model tends to produce graphs containing communities, subsets of nodes characterized
Stochastic_block_model
Swiss footballer
for FC Muri in the 1. Liga Classic. He has a side interest in random geometric graphs. He was loaned to FC Wohlen of the Challenge League on 19 October
Tobias Müller (footballer, born 1989)
Tobias_Müller_(footballer,_born_1989)
In computational geometry, a greedy geometric spanner is an undirected graph whose distances approximate the Euclidean distances among a finite set of
Greedy_geometric_spanner
Approximate nearest neighbor search algorithm
datasets. HNSW stores vectors in a graph. Each vector is a node, and links connect it to some nearby vectors. The graph has several layers: upper layers
Hierarchical navigable small world
Hierarchical_navigable_small_world
Tree which includes all vertices of a graph
of graph theory, a spanning tree T of an undirected graph G is a subgraph that is a tree which includes all of the vertices of G. In general, a graph may
Spanning_tree
Study of discrete mathematical structures
continuous functions). Objects studied in discrete mathematics include integers, graphs, and statements in logic. By contrast, discrete mathematics excludes topics
Discrete_mathematics
On short connecting nets with added points
programming relaxation and a technique called iterative, randomized rounding. The general graph Steiner tree problem is known to be fixed-parameter tractable
Steiner_tree_problem
Clustering and community detection algorithm
hypothetical randomized partition of communities). In the above image, our initial collection of unsorted nodes is represented by the graph on the left
Leiden_algorithm
Unrelated vertices in graphs
In graph theory, an independent set, stable set, coclique or anticlique is a set of vertices in a graph, no two of which are adjacent. That is, it is a
Independent set (graph theory)
Independent_set_(graph_theory)
Task of computing complete subgraphs
proteins. Listing the cliques in a dependency graph is an important step in the analysis of certain random processes. In mathematics, Keller's conjecture
Clique_problem
Network with non-trivial topological features
network is a graph (network) with non-trivial topological features—features that do not occur in simple networks such as lattices or random graphs but often
Complex_network
Graph related to another graph by a covering map
In the mathematical discipline of graph theory, a graph C is a covering graph of another graph G if there is a covering map from the vertex set of C to
Covering_graph
Branch of discrete mathematics
property for a random discrete object, such as a random graph? For instance, what is the average number of triangles in a random graph? Probabilistic
Combinatorics
Algorithm to search the nodes of a graph
limit is known due to the geometric growth of the number of nodes per level. DFS may also be used to collect a sample of graph nodes. However, incomplete
Depth-first_search
Academic field
offshoot of graph theory with Paul Erdős and Alfréd Rényi's eight famous papers on random graphs. For social networks the exponential random graph model or
Network_science
Geometric graph connecting nearby points
{\displaystyle O(n)} expected time, for random set of points distributed uniformly in the unit square. The relative neighborhood graph can be computed in linear time
Relative_neighborhood_graph
Conjecture in graph theory
the density of copies of H {\displaystyle H} in a graph is asymptotically minimized by a random graph, as one would expect a p | E ( H ) | {\displaystyle
Sidorenko's_conjecture
Graph with all vertices of degree 3
of graph theory, a cubic graph is a graph in which all vertices have degree three. In other words, a cubic graph is a 3-regular graph. Cubic graphs are
Cubic_graph
Random set of points on a space with random number and random position
processes such as Voronoi tessellations, random geometric graphs, and Boolean models. Empirical measure Random measure Point process notation Point process
Point_process
Graph representing edges of another graph
In the mathematical discipline of graph theory, the line graph of an undirected graph G is another graph L(G) that represents the adjacencies between edges
Line_graph
Problem in geometric probability
Sylvester's four point problem in geometric probability asks for the probability that four randomly chosen points in the Euclidean plane form a convex
Sylvester's four point problem
Sylvester's_four_point_problem
Intersection graph of unit intervals on the real line
In graph theory, a branch of mathematics, an indifference graph is an undirected graph constructed by assigning a real number to each vertex and connecting
Indifference_graph
Search algorithm
Therefore, geometric hashing should be able to find the object, too. There are two ways to detect mirrored objects. For the vector graph, make the left
Geometric_hashing
American mathematician
areas of spectral graph theory, extremal graph theory and random graphs, in particular in generalizing the Erdős–Rényi model for graphs with general degree
Fan_Chung
On tangency patterns of circles
intersection graphs of interior-disjoint geometric objects are called tangency graphs or contact graphs. As a special case, the coin graphs of packings
Circle_packing_theorem
Type of graph in mathematics
In graph theory, a branch of mathematics, a half graph is a special type of bipartite graph. These graphs are called the half graphs because they have
Half_graph
Decomposition of a graph into hamiltonion cycles
over a graph is its Cartesian product with the two-vertex complete graph. For instance, the prism over a cycle graph is the graph of a geometric prism
Hamiltonian_decomposition
Threshold of percolation theory models
1088/1742-5468/ac6519. ISSN 1742-5468. Dall, Jesper; Michael Christensen (2002). "Random geometric graphs". Physical Review E. 66 (1) 016121. arXiv:cond-mat/0203026. Bibcode:2002PhRvE
Percolation_threshold
Graph formed by touching unit circles
In geometric graph theory, a penny graph is a contact graph of unit circles. It is formed from a collection of unit circles that do not cross each other
Penny_graph
expected linear time MST algorithm is a randomized algorithm for computing the minimum spanning forest of a weighted graph with no isolated vertices. It was
Expected linear time MST algorithm
Expected_linear_time_MST_algorithm
Mathematical theory on behavior of connected clusters in a random graph
since then. In a slightly different mathematical model for obtaining a random graph, a site is "occupied" with probability p or "empty" (in which case its
Percolation_theory
averages and discrete analogs". In Pach, János (ed.). Towards a Theory of Geometric Graphs. Contemp. Math. Vol. 342. Amer. Math. Soc., Providence, RI. pp. 15–24
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
Shortest network connecting points
minimum spanning tree is a subgraph of other geometric graphs including the relative neighborhood graph and Delaunay triangulation. By constructing the
Euclidean minimum spanning tree
Euclidean_minimum_spanning_tree
Quantum algorithm
marked node in a graph. The concept of a quantum walk is inspired by classical random walks, in which a walker moves randomly through a graph or lattice. In
Quantum_walk_search
Variable representing a random phenomenon
word. A random sentence of given length N {\displaystyle N} may be represented as a vector of N {\displaystyle N} random words. A random graph on N {\displaystyle
Random_variable
Collection of statistical data sets
yet have very different distributions and appear very different when graphed. It was inspired by the smaller Anscombe's quartet that was created in
Datasaurus_dozen
Probability distribution
estimation, besides the geometric mean GX based on the random variable X, also another geometric mean appears naturally: the geometric mean based on the linear
Beta_distribution
Generalization of graph theory
hypergraph is a generalization of a graph in which an edge can join any number of vertices. In contrast, in an ordinary graph, an edge connects exactly two
Hypergraph
In computational geometry and geometric graph theory, a β-skeleton or beta skeleton is an undirected graph defined from a set of points in the Euclidean
Beta_skeleton
Real function with secant line between points above the graph itself
line segment between any two distinct points on the graph of the function lies above or on the graph of the function between the two points. Equivalently
Convex_function
Method of generating random small-world graphs
The Watts–Strogatz model is a random graph generation model that produces graphs with small-world properties, including short average path lengths and
Watts–Strogatz_model
Numeric quantity representing the center of a collection of numbers
the three classical Pythagorean means are the arithmetic mean (AM), the geometric mean (GM), and the harmonic mean (HM). These means were studied with proportions
Mean
Clustering and community detection algorithm
stochastic block model., it is prone to finding spurious communities in random graphs and has been shown to systematically overfit empirical data . The value
Louvain_method
scale-free networks; n-dimensional geometric random graphs (for all positive integers n); and stickiness model networks. GraphCrunch currently supports seven
GraphCrunch
Notion in combinatorics
"Topological hypergraphs", in Pach, János (ed.), Thirty Essays on Geometric Graph Theory, Springer, pp. 71–81, doi:10.1007/978-1-4614-0110-0_6, ISBN 978-1-4614-0109-4
Sauer–Shelah_lemma
Class of graphs
In graph theory, a forcing graph is one whose density determines whether a graph sequence is quasi-random. The term was first coined by Chung, Graham,
Forcing_graph
Assignment of colors to edges of a graph
In graph theory, a proper edge coloring of a graph is an assignment of "colors" to the edges of the graph so that no two incident edges have the same color
Edge_coloring
in geometric graphs. The planar separator theorem may be proven by using the circle packing theorem to represent a planar graph as the contact graph of
Geometric_separator
Probabilistic model
model is a probabilistic model for which a graph expresses the conditional dependence structure between random variables. Graphical models are commonly
Graphical_model
random graphs is a rapidly developing subject. It is based on the idea that if we take a graph randomly with a sufficiently small density, the graph would
Forbidden_subgraph_problem
Degree Preserving Randomization is a technique used in Network Science that aims to assess whether or not variations observed in a given graph could simply
Degree-preserving randomization
Degree-preserving_randomization
Graph without triples of adjacent vertices
area of graph theory, a triangle-free graph is an undirected graph in which no three vertices form a triangle of edges. Triangle-free graphs may be equivalently
Triangle-free_graph
Property of objects inherited by all their subobjects
Sanatan Rai; Bhaskar Krishnamachari (2003). "Monotone properties of random geometric graphs have sharp thresholds". Annals of Applied Probability. 15 (4):
Hereditary_property
Geometric algorithm
an extension of the graph Laplacian that describes the time evolution of vectors undergoing a random walk can be defined: the graph connection Laplacian:
Diffusion_map
Field of higher mathematics
Geometric analysis is a mathematical discipline where tools from differential equations, especially elliptic partial differential equations (PDEs), are
Geometric_analysis
Structure from which the geometry of the universe arises
composite geometric objects so it is not a pregeometric scheme in line with Wheeler's original conception of pregeometry. Pregeometric graph by Wilson
Pregeometry_(physics)
RANDOM GEOMETRIC-GRAPH
RANDOM GEOMETRIC-GRAPH
Male
Hungarian
 Variant spelling of Hungarian András, ANDOR means "man; warrior." Compare with another form of Andor.
Surname or Lastname
English
English : unexplained; perhaps a variant of Francom.
Surname or Lastname
English
English : variant of Brandon.
Surname or Lastname
English
English : patronymic from Rand 1.
Male
English
 Variant spelling of Middle English Randulf, RANDOLF means "shield-wolf." Compare with other forms of Randolf.
Male
German
Old German name, GOMERIC means "man-power."
Surname or Lastname
English (chiefly East Anglia)
English (chiefly East Anglia) : patronymic from the Middle English personal name Rand(e) (see Rand 1).
Boy/Male
English
Son of Rand.
Surname or Lastname
English
English : variant spelling of Randall.Americanized spelling of Randel.
Surname or Lastname
English
English : variant of Ransom.
Male
English
Pet form of English Randall and Randolph, both RANDY means "shield-wolf." Compare with feminine Randy.
Boy/Male
English American
Son of Rand.
Female
English
Pet form of English Miranda, RANDY means "worthy of admiration."Â Compare with masculine Randy.Â
Surname or Lastname
English
English : variant of Rand 1, from the Old French oblique case.
Surname or Lastname
English
English : probably a variant of Crandon, a habitational name from Crandon in Somerset or Crandean in Falmer, Sussex. Compare Grandin.
Male
Norwegian
 Norwegian form of Old Norse Arnþórr, ANDOR means "eagle of Thor." Compare with another form of Andor.
Male
English
Medieval form of English Randolf, RANDAL means "shield-wolf."
Male
Scandinavian
 Scandinavian form of Old Norse Randolfr, RANDOLF means "shield-wolf." Compare with another form of Randolf.
Female
English
Variant spelling of English Randy, RANDI means "worthy of admiration."
Female
English
Short form of English Miranda, RANDA means "worthy of admiration."Â
RANDOM GEOMETRIC-GRAPH
RANDOM GEOMETRIC-GRAPH
Surname or Lastname
English and Dutch
English and Dutch : variant spelling of Bay.
Boy/Male
African, American, Christian, Danish, French, German, Indian, Latin
Bald One
Boy/Male
Afghan, Australian, British, Chinese, Danish, English, French, German, Greek, Gujarati, Hindu, Indian, Parsi, Swedish
Lord; Abbreviation of Nicholas; Mythological; People's Victory; Champion; Good; Victorious People; Diminutive of Dominick
Boy/Male
Hindu
Rain
Girl/Female
Italian
Clear.
Girl/Female
Hindu
Lovable
Girl/Female
Indian
Another name for paan-ati
Boy/Male
Tamil
Sendhilnathan | ஸேஂதில நாதந
Lord Murugan
Girl/Female
Indian
Name of a fruit, Written in the Quran times
Boy/Male
Arabic
Ancient Idol in the Temple of Makkah
RANDOM GEOMETRIC-GRAPH
RANDOM GEOMETRIC-GRAPH
RANDOM GEOMETRIC-GRAPH
RANDOM GEOMETRIC-GRAPH
RANDOM GEOMETRIC-GRAPH
a.
Of or pertaining to aerometry; as, aerometric investigations.
n.
To redeem from captivity, servitude, punishment, or forfeit, by paying a price; to buy out of servitude or penalty; to rescue; to deliver; as, to ransom prisoners from an enemy.
n.
A roving motion; course without definite direction; want of direction, rule, or method; hazard; chance; -- commonly used in the phrase at random, that is, without a settled point of direction; at hazard.
n.
Distance to which a missile is cast; range; reach; as, the random of a rifle ball.
adv.
In a random manner.
n.
Ransom.
n.
To exact a ransom for, or a payment on.
a.
Alt. of Geometrical
a.
Going at random or by chance; done or made at hazard, or without settled direction, aim, or purpose; hazarded without previous calculation; left to chance; haphazard; as, a random guess.
a.
Pertaining to geometry.
n.
The larva of any geometrid moth. See Geometrid.
n.
Any species of geometrid moth; a geometrid.
v. i.
To go or stray at random.
n.
Anything driven at random.
n.
The release of a captive, or of captured property, by payment of a consideration; redemption; as, prisoners hopeless of ransom.
a.
Pertaining to, or according to the rules or principles of, geometry; determined by geometry; as, a geometrical solution of a problem.
n.
Random.
v. i.
To investigate or apprehend geometrical quantities or laws; to make geometrical constructions; to proceed in accordance with the principles of geometry.
pl.
of Geometry