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Abstract mathematical system of two types of objects and a relation between them
In mathematics, an incidence structure is an abstract system consisting of two types of objects and a single relationship between these types of objects
Incidence_structure
Field of mathematics which studies incidence structures
In mathematics, incidence geometry is the study of incidence structures. A geometric structure such as the Euclidean plane is a complicated object that
Incidence_geometry
Matrix that shows the relationship between two classes of objects
mathematics, an incidence matrix is a logical matrix that shows the relationship between two classes of objects, usually called an incidence relation. If
Incidence_matrix
Concept in graph theory
u} and v {\displaystyle v} . A graph can also be specified as an incidence structure S = ( P , B , I ) {\displaystyle S=(P,B,I)} , where P {\displaystyle
Incidence_(graph)
Topics referred to by the same term
Incidence list, a concept in graph theory Incidence matrix, a matrix that shows the relationship between two classes of objects Incidence structure,
Incidence
Graph representing incident points and lines
graph or incidence graph is a bipartite graph associated with an incidence structure. From a collection of points and lines in an incidence geometry or
Levi_graph
Axiomatically defined geometrical space
parallel class structure of an affine plane of order n may be used to construct a set of n − 1 mutually orthogonal latin squares. Only the incidence relations
Affine plane (incidence geometry)
Affine_plane_(incidence_geometry)
Hopcroft's problem of finding point–line incidences Incidence algebra Incidence geometry Incidence matrix Incidence structure Levi graph Menelaus theorem Joel
Incidence_(geometry)
Branch of geometry that studies combinatorial properties and constructive methods
polyhedra Incidence structures generalize planes (such as affine, projective, and Möbius planes) as can be seen from their axiomatic definitions. Incidence structures
Discrete_geometry
Paper-and-pencil game for two players
by playing on an arbitrary incidence structure, where rows are lines and cells are points. Tic-tac-toe's incidence structure consists of nine points, three
Tic-tac-toe
projective geometry, an intersection theorem or incidence theorem is a statement concerning an incidence structure – consisting of points, lines, and possibly
Intersection_theorem
Structure in combinatorial mathematics
In combinatorial mathematics, a block design is an incidence structure consisting of a set together with a family of subsets known as blocks, chosen such
Block_design
Generalization of graph theory
hypergraph. Hypergraphs can be viewed as incidence structures. In particular, there is a bipartite "incidence graph" or "Levi graph" corresponding to every
Hypergraph
Any collection of sets, or subsets of a set
simplicial complex. An incidence structure consists of a set of points, a set of lines, and an (arbitrary) binary relation, called the incidence relation, specifying
Family_of_sets
Points and lines with equal incidences
but with some additional restrictions: every two points of the incidence structure can be associated with at most one line, and every two lines can
Configuration_(geometry)
Type of incidence structure
In geometry, a generalized quadrangle is an incidence structure whose main feature is the lack of any (non-degenerate) triangles yet containing many quadrangles
Generalized_quadrangle
Generalised concept of incidence structure of polygons
In mathematics, a generalized polygon is an incidence structure introduced by Jacques Tits in 1959. Generalized n-gons encompass as special cases projective
Generalized_polygon
Geometry with 7 points and 7 lines
finite incidence structure, so many of its properties can be established using combinatorial techniques and other tools used in the study of incidence geometries
Fano_plane
In projective geometry, a bijection between projective spaces that preserves collinearity
space defined axiomatically in terms of an incidence structure (a set of points P, lines L, and an incidence relation I specifying which points lie on
Collineation
Area of discrete mathematics
plane. The Levi graph is a bipartite graph that associates to the incidence structure and projective configuration. By applying to information visualization
Graph_theory
Type of incidence structure
An incidence structure C = ( P , L , I ) {\displaystyle C=(P,L,I)} consists of a set P {\displaystyle P} of points, a set L {\displaystyle L}
Partial_geometry
Type of incidence structure
near-linear space) is a basic incidence structure in the field of incidence geometry, that carries slightly less structure than a linear space. The notion
Partial_linear_space
Geometric concept of a 2D space with "points at infinity" adjoined
shared by all projective planes. A projective plane is a rank 2 incidence structure ( P , L , I ) {\displaystyle ({\mathcal {P}},{\mathcal {L}},I)} consisting
Projective_plane
Measure of the economic effect of a tax
In economics, the tax incidence measures who actually pays for a tax. Economists distinguish between the entities who ultimately bear the burden of a
Tax_incidence
Topics referred to by the same term
arrangement of polygons that can be folded up to form a polyhedron An incidence structure consisting of points and parallel classes of lines An operator algebra
Net
Smallest 3D projective space
counting points, lines, and planes on the diagonal. The incidences are expressed off diagonal. The structure is self dual, swapping points and planes, expressed
PG(3,2)
Poset representing certain properties of a polytope
combinatorial structures now known as abstract polytopes was first described by Egon Schulte in his 1980 PhD dissertation. In it he defined "regular incidence complexes"
Abstract_polytope
Type of incidence structure
A linear space is a basic structure in incidence geometry. A linear space consists of a set of elements called points, and a set of elements called lines
Linear_space_(geometry)
Relationship between elements of two sets
elements lies in just one block. These incidence structures have been generalized with block designs. The incidence matrix used in these geometrical contexts
Binary_relation
Euclidean reflection. More generally, a Möbius plane is an incidence structure with the same incidence relationships as the classical Möbius plane. It is one
Möbius_plane
Type of Benz planes
c\right)\right\}\mid a,b,c\in \mathbb {R} ,a\neq 0\right\}.\end{aligned}}} The incidence structure ( P , Z , ∈ ) {\displaystyle ({\mathcal {P}},{\mathcal {Z}},\in )}
Minkowski_plane
Type of geometry
that facts are independent of any metric structure. Under the projective transformations, the incidence structure and the relation of projective harmonic
Projective_geometry
Aspect of geometry
maximal flag has exactly r elements. An incidence geometry of rank 2 is commonly called an incidence structure with elements of type 1 called points and
Flag_(geometry)
maximal arcs: Let K be a maximal arc with degree d. Consider the incidence structure S ( K ) = ( P , B , I ) {\displaystyle S(K)=(P,B,I)} , where P contains
Maximal_arc
Associative algebra used in combinatorics
In order theory, a field of mathematics, an incidence algebra is an associative algebra, defined for every locally finite partially ordered set and commutative
Incidence_algebra
Concept in incidence geometry
act as automorphism groups of near polygons. A near 2d-gon is an incidence structure ( P , L , I {\displaystyle P,L,I} ), where P {\displaystyle P} is
Near_polygon
(1974, 10.13), is a Tits building of type F4 (a specific generalized incidence structure). The four types of vertices are called points, lines, planes, and
Metasymplectic_space
Nicolas Laguerre. The classical Laguerre plane is an incidence structure that describes the incidence behaviour of the curves y = a x 2 + b x + c {\displaystyle
Laguerre_plane
Standard hostname for a networked device's loopback interface
Features Clique Component Cut Cycle Data structure Edge Loop Neighborhood Path Vertex Adjacency list / matrix Incidence list / matrix Types Bipartite Complete
Localhost
slope doubles when they pass the y-axis. The Moulton plane is an incidence structure M = ⟨ P , G , I ⟩ {\displaystyle {\mathfrak {M}}=\langle P,G,{\textrm
Moulton_plane
Diffraction using small incidence angles
Grazing incidence diffraction (GID) is a technique for interrogating a material using small incidence angles for an incoming wave, often leading to the
Grazing_incidence_diffraction
Matrix of binary truth values
find necessary and sufficient conditions for the existence of an incidence structure with given point degrees and block degrees; or in matrix language
Logical_matrix
Line which touches a circle at exactly one point
In technical language, these transformations do not change the incidence structure of the tangent line and circle, even though the line and circle may
Tangent_lines_to_circles
Topics referred to by the same term
alpha subunit, a class of proteins Generalized quadrangle, a type of incidence structure in mathematics Generalized quantifier, a type of expression in linguistic
Gq_(disambiguation)
Mathematical theory on behavior of connected clusters in a random graph
to discriminate the gases. She also discovered that the size of these structures depends on the temperature of carbonation during the coal production.
Percolation_theory
Polygon with 2 sides and 2 vertices
used in constructing and analyzing various topological structures, such as incidence structures. Monogon Polygon Demihypercube "ResearchGate". The Symmetries
Digon
Geometrical structure
set of circles to form a set of blocks results in an inhomogeneous incidence structure: three distinct points determine one block, but lines are distinguishable
Benz_plane
Construction in group theory
projective space axiomatically in terms of an incidence structure (a set of points P, lines L, and an incidence relation I specifying which points lie on
Projective_linear_group
Research program on the symmetries of geometry
with respect to the Euclidean group of symmetries, while only the incidence structure and the cross-ratio are preserved under the most general projective
Erlangen_program
Approximate nearest neighbor search algorithm
The algorithm repeatedly chooses locally better nodes, using the graph structure to approach the query point. The HNSW graph is built incrementally. When
Hierarchical navigable small world
Hierarchical_navigable_small_world
Study of angle-preserving transformations
mathematical structure of inversive geometry has been interpreted as an incidence structure where the generalized circles are called "blocks": In incidence geometry
Inversive_geometry
Special type of projective plane
a hyperplane Σ {\displaystyle \Sigma } of PG(2n+2, K). Define an incidence structure A(S) with "points," the points of PG(2n+2, K) not on Σ {\displaystyle
Translation_plane
Topological geometry deals with incidence structures consisting of a point set P {\displaystyle P} and a family L {\displaystyle {\mathfrak {L}}} of subsets
Topological_geometry
Decision tracking and managing method
dependency structure method, dependency source matrix, problem solving matrix, incidence matrix, N2 matrix, interaction matrix, dependency map or design precedence
Design_structure_matrix
Electronic communication subsystem on an integrated circuit
Features Clique Component Cut Cycle Data structure Edge Loop Neighborhood Path Vertex Adjacency list / matrix Incidence list / matrix Types Bipartite Complete
Network_on_a_chip
Video work by artist Gary Hill
Incidence of Catastrophe (1987–88, 43:51 min.) is a single-channel video by American new-media artist Gary Hill. It is one of several works by Hill inspired
Incidence_of_Catastrophe
Mathematical problem
existence of k-2 MOLS(n). A transversal design T[k,1;n] is the dual incidence structure of an (k,n)-net. That is, it has nk points and n2 blocks. Each point
Mutually orthogonal Latin squares
Mutually_orthogonal_Latin_squares
Study of graphs as a representation of relations between discrete objects
transmission line impedances). Most of these studies focus only on the abstract structure of the power grid using node degree distribution and betweenness distribution
Network_theory
Expenditure incidence is the effect of government expenditure upon the distribution of private incomes. This is commonly contrasted with benefit incidence as an
Expenditure_incidence
Network whose degree distribution follows a power law
are needed to be immunized. However, in many realistic cases the global structure is not available and the largest degree nodes are not known. Properties
Scale-free_network
Relationship between two sets, defined by a set of ordered pairs
functions with distinct domains and ranges, such as sqrt : N → R+. Incidence structure, a heterogeneous relation between set of points and lines Order theory
Relation_(mathematics)
3-regular graph with 30 vertices and 45 edges
edge or a perfect matching, and connected vertices represent the incidence structure between edges and matchings. Based on this construction, Coxeter
Tutte–Coxeter_graph
Eric (2017), Projective Planes of Small Order explicitly lists the incidence structure of these planes. Veblen, Oswald; Wedderburn, Joseph H.M. (1907),
Hall_plane
Geometric system with a finite number of points
it can be defined as an incidence structure (P, L, I) consisting of a set P of points, a set L of lines, and an incidence relation I stating which points
Finite_geometry
Completion of the usual space with "points at infinity"
it can be defined as an incidence structure (P, L, I) consisting of a set P of points, a set L of lines, and an incidence relation I that states which
Projective_space
Journal publisher
Mathematics and Computational Science Geometry & Topology Innovations in Incidence Geometry—Algebraic, Topological and Combinatorial Involve: A Journal of
Mathematical Sciences Publishers
Mathematical_Sciences_Publishers
Arrangement of a communication network
fieldbusses and computer networks. Network topology is the topological structure of a network and may be depicted physically or logically. It is an application
Network_topology
Social structure made up of a set of social actors
A social network is a social structure consisting of a set of social actors (such as individuals or organizations), networks of dyadic ties, and other
Social_network
Concept in graph theory
In the study of complex networks, a network is said to have community structure if the nodes of the network can be easily grouped into (potentially overlapping)
Community_structure
Property that assigns truth values to k-tuples of individuals
thus anticipating the development of database management systems. Incidence structure Hypergraph Logic of relatives Logical matrix Partial order Predicate
Finitary_relation
Stochastic process formalizing cumulative advantage
Features Clique Component Cut Cycle Data structure Edge Loop Neighborhood Path Vertex Adjacency list / matrix Incidence list / matrix Types Bipartite Complete
Preferential_attachment
Computer system for solving algebra problems
invariants, and compute with the module structure. Lie theory Algebraic geometry Arithmetic geometry Finite incidence structures Cryptography Coding theory Optimization
Magma (computer algebra system)
Magma_(computer_algebra_system)
Geometrical property
with respect to the Euclidean group of symmetries, while only the incidence structure and the cross-ratio are preserved under the most general projective
Symmetry_(geometry)
Degree of connectedness within a graph
applicable, rendering the comparison moot. The characterization by walk structure shows that almost all centralities in wide use are radial-volume measures
Centrality
Fetal blood vessel bypassing the lungs
The ductus arteriosus, also called the ductus Botalli, named after the Italian physiologist Leonardo Botallo, is a blood vessel in the developing fetus
Ductus_arteriosus
Clustering and community detection algorithm
and Newman, M. E. J. and Moore, Cristopher (2004). "Finding community structure in very large networks". Phys. Rev. E. 70 (6) 066111. arXiv:cond-mat/0408187
Leiden_algorithm
Knowledge base that represents semantic relations between concepts in a network
who in 1960 had published descriptions of algorithms for using a phrase structure grammar to generate syntactically well-formed nonsense sentences. Sheldon
Semantic_network
Concept in projective geometry
be defined axiomatically as an incidence structure, in terms of a set P of points, a set L of lines, and an incidence relation I that determines which
Duality_(projective_geometry)
Process by which people befriend similar people
individuals (and likewise for unvaccinated individuals). Homophilic network structure matters because it can change how processes spread on networks: in epidemic
Homophily
Scale-free network generation algorithm
indicating that growth alone is not sufficient to produce a scale-free structure. Model B retains preferential attachment but eliminates growth. The model
Barabási–Albert_model
Diverse collection of blood-related cancers
the true incidence due to underdiagnosed or underreported patients. MDS is more common in males than females, with a male-to-female incidence ratio around
Myelodysplastic_syndrome
Data structure representing a graph
for each of the two endpoints of the edge). The object oriented incidence list structure suggested by Goodrich and Tamassia has special classes of vertex
Adjacency_list
Special labeling in graph theory
vertices, edges or faces in a graph. The incidence coloring is a special graph labeling where each incidence of an edge with a vertex is assigned a color
Incidence_coloring
Abstract data type in computer science
Only the cost for one edge can be stored between each pair of vertices. Incidence matrix A two-dimensional matrix, in which the rows represent the vertices
Graph_(abstract_data_type)
Hypergeometric function identities Hypergeometric series Hypergraph Incidence structure Induction puzzles Integer partition Ferrers graph Kakeya needle problem
Index of combinatorics articles
Index_of_combinatorics_articles
Graph where most nodes are reachable in a small number of steps
small-world topology of short path length and high clustering. The network structure has been found in the mammalian cortex across species as well as in large
Small-world_network
Void between celestial bodies
that varies from 250 to 500 kilometres (160 to 310 mi), depending on the incidence of solar radiation. Beyond this altitude, collisions between molecules
Outer_space
Grazing-incidence small-angle scattering (GISAS) is a diffraction technique used to study nanostructured surfaces and thin films. The scattered probe
Grazing-incidence small-angle scattering
Grazing-incidence_small-angle_scattering
Form of non-monogamy
define open marriage by agreement alone will tend to report a higher incidence than studies that define open marriage by agreement and behavior. Spaniel
Open_marriage
Two closely related models for generating random graphs
generalization of the Erdős–Rényi model for graphs with latent community structure Watts–Strogatz model – Method of generating random small-world graphs
Erdős–Rényi_model
How trading mechanisms and market design shape prices, liquidity, and transaction costs
expansion into the study of the impact of market microstructure on the incidence of market abuse, such as insider trading, market manipulation and broker-client
Market_microstructure
Medical condition
vessels), microvascular arteriolar remodeling (changes in the vessel structure) such as intimal thickening, smooth muscle cell proliferation, perivascular
Microvascular_angina
Network that allows computers to share resources and communicate with each other
assumption that network addresses are structured and that similar addresses imply proximity within the network. Structured addresses allow a single routing
Computer_network
Transposable elements in the genomes of some organisms
Mammalian-wide interspersed repeats (MIRs) are transposable elements in the genomes of some organisms and belong to the group of short interspersed nuclear
Mammalian-wide interspersed repeat
Mammalian-wide_interspersed_repeat
Network with non-trivial topological features
assortativity or disassortativity among vertices, community structure, and hierarchical structure. In the case of directed networks these features also include
Complex_network
Network whose links change over time
of evolution of the network and the process are similar, the temporal structure of time-varying networks has a dramatic impact on the spread of the process
Temporal_network
Country primarily in North America
labelled as a centre party (Armingeon et al., 2018), contributes to the incidence of this group of parties." Chinoy, Sahil (June 26, 2019). "What Happened
United_States
University, San Bernardino. Sarli, through his research, described an incidence structure for twisted groups 𝐺, where points are elementary abelian root subgroups
John_Sarli
Points with no line through exactly two points
defined as abstract incidence structures of points and lines, satisfying the properties that, for every pair of points, the structure includes exactly one
Sylvester–Gallai configuration
Sylvester–Gallai_configuration
Infectious disease
support structures for people with TB. However, the evidence base for such interventions—particularly among underserved groups in low-incidence countries—remains
Tuberculosis
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