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UNDER GRAPH

  • Under Graph
  • Japanese rock music group

    Under Graph is a Japanese band that was formed in 1997. Vocals/Guitar: Naoto Matohara (真戸原 直人, Matohara Naoto) Birthdate: July 27, 1977 Equipment: Gibson

    Under Graph

    Under_Graph

  • Diameter (graph theory)
  • Longest distance between two vertices

    In graph theory, the diameter of a connected undirected graph is the farthest distance between any two of its vertices. That is, it is the diameter of

    Diameter (graph theory)

    Diameter (graph theory)

    Diameter_(graph_theory)

  • Graph minor
  • Subgraph with contracted edges

    In graph theory, an undirected graph H is called a minor of the undirected graph G if H can be formed from G by deleting edges and vertices and by contracting

    Graph minor

    Graph_minor

  • Graph (discrete mathematics)
  • Vertices connected in pairs by edges

    In discrete mathematics, particularly in graph theory, a graph is a structure consisting of a set of objects where some pairs of the objects are in some

    Graph (discrete mathematics)

    Graph (discrete mathematics)

    Graph_(discrete_mathematics)

  • Diamond graph
  • Planar graph with 4 nodes and 5 edges

    in the graph shares at most one vertex. The family of graphs in which each connected component is a cactus graph is downwardly closed under graph minor

    Diamond graph

    Diamond graph

    Diamond_graph

  • Random 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

    Random graph

    Random_graph

  • Petersen graph
  • Cubic graph with 10 vertices and 15 edges

    mathematical field of graph theory, the Petersen graph is an undirected graph with 10 vertices and 15 edges. It is a small graph that serves as a useful

    Petersen graph

    Petersen graph

    Petersen_graph

  • Graph theory
  • 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

    Graph theory

    Graph_theory

  • Graph database
  • Database using graph structures for queries

    A graph database (GDB) is a database that uses graph structures for semantic queries with nodes, edges, and properties to represent and store data. A key

    Graph database

    Graph_database

  • Glossary of graph theory
  • 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

    Glossary_of_graph_theory

  • Bipartite graph
  • Graph divided into two independent sets

    In the mathematical field of graph theory, a bipartite graph (or bigraph) is a graph whose vertices can be divided into two disjoint and independent sets

    Bipartite graph

    Bipartite graph

    Bipartite_graph

  • Directed acyclic 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

    Directed acyclic graph

    Directed_acyclic_graph

  • Graph isomorphism
  • Bijection between the vertex set of two graphs

    In graph theory, an isomorphism of graphs G and H is a bijection between the vertex sets of G and H f:V(G)→V(H) such that any two vertices u and v of G

    Graph isomorphism

    Graph isomorphism

    Graph_isomorphism

  • Cayley graph
  • Graph defined from a mathematical group

    In mathematics, a Cayley graph, also known as a Cayley color graph, Cayley diagram, group diagram, or color group, is a graph that encodes the abstract

    Cayley graph

    Cayley graph

    Cayley_graph

  • DOT (graph description language)
  • File format

    DOT is a graph description language, developed as a part of the Graphviz project. DOT graphs are typically stored as files with the .gv or .dot filename

    DOT (graph description language)

    DOT_(graph_description_language)

  • Graph coloring
  • Methodic assignment of colors to elements of a graph

    In graph theory, graph coloring is a methodic assignment of labels traditionally called "colors" to elements of a graph. The assignment is subject to certain

    Graph coloring

    Graph coloring

    Graph_coloring

  • Split graph
  • Graph which partitions into a clique and independent set

    In graph theory, a branch of mathematics, a split graph is a graph in which the vertices can be partitioned into a clique and an independent set. Split

    Split graph

    Split graph

    Split_graph

  • Cograph
  • Graph formed by complementation and disjoint union

    In graph theory, a cograph, or complement-reducible graph, or P4-free graph, is a graph that can be generated from the single-vertex graph K1 by complementation

    Cograph

    Cograph

    Cograph

  • JanusGraph
  • Graph database

    JanusGraph is an open source, distributed graph database under The Linux Foundation. JanusGraph is available under the Apache License 2.0. The project

    JanusGraph

    JanusGraph

    JanusGraph

  • Lattice graph
  • Graph whose embedding in a Euclidean space forms a regular tiling

    In graph theory, a lattice graph, mesh graph, or grid graph is a graph whose drawing, embedded in some Euclidean space ⁠ R n {\displaystyle \mathbb {R}

    Lattice graph

    Lattice graph

    Lattice_graph

  • Cactus graph
  • Mathematical tree of cycles

    single edge. The family of graphs in which each component is a cactus is downwardly closed under graph minor operations. This graph family may be characterized

    Cactus graph

    Cactus graph

    Cactus_graph

  • Graph partition
  • Subdivision of vertices into disjoint sets

    In mathematics, a graph partition is the reduction of a graph to a smaller graph by partitioning its set of nodes into mutually exclusive groups. Edges

    Graph partition

    Graph_partition

  • Apex graph
  • Graph which can be made planar by removing a single node

    In graph theory, a branch of mathematics, an apex graph is a graph that can be made planar by the removal of a single vertex. The deleted vertex is called

    Apex graph

    Apex graph

    Apex_graph

  • Graph embedding
  • Embedding a graph in a topological space, often Euclidean

    In topological graph theory, an embedding (also spelled imbedding) of a graph G {\displaystyle G} on a surface Σ {\displaystyle \Sigma } is a representation

    Graph embedding

    Graph embedding

    Graph_embedding

  • Property graph
  • Mathematical model used by graph-oriented databases

    A property graph, labeled property graph, or attributed graph is a data model of various graph-oriented databases, where pairs of entities are associated

    Property graph

    Property graph

    Property_graph

  • Voltage graph
  • Directed graph whose edges are labelled invertibly by elements of a group

    graph, but it is generally used in topological graph theory as a concise way to specify another graph called the derived graph of the voltage graph.

    Voltage graph

    Voltage_graph

  • TigerGraph
  • American software company

    Mingxi, Like and Yu under the name GraphSQL. In September 2017, the company came out of stealth mode under the name TigerGraph with $33 million in funding

    TigerGraph

    TigerGraph

  • Graph automorphism
  • Mapping a graph onto itself without changing edge-vertex connectivity

    In the mathematical field of graph theory, an automorphism of a graph is a form of symmetry in which the graph is mapped onto itself while preserving

    Graph automorphism

    Graph_automorphism

  • Graph labeling
  • Assignment of labels to elements of a graph

    discipline of graph theory, a graph labeling is the assignment of labels, traditionally represented by integers, to edges and/or vertices of a graph. Formally

    Graph labeling

    Graph_labeling

  • Force-directed graph drawing
  • Physical simulation to visualize graphs

    Force-directed graph drawing algorithms are a class of algorithms for drawing graphs in an aesthetically-pleasing way. Their purpose is to position the

    Force-directed graph drawing

    Force-directed graph drawing

    Force-directed_graph_drawing

  • Component (graph theory)
  • Maximal subgraph whose vertices can reach each other

    In graph theory, a component of an undirected graph is a connected subgraph that is not part of any larger connected subgraph. The components of any graph

    Component (graph theory)

    Component (graph theory)

    Component_(graph_theory)

  • Graph drawing
  • Visualization of node-link graphs

    Graph drawing is an area of mathematics and computer science combining methods from geometric graph theory and information visualization to derive two-dimensional

    Graph drawing

    Graph drawing

    Graph_drawing

  • Linkless embedding
  • Embedding a graph in 3D space with no cycles interlinked

    In topological graph theory, a mathematical discipline, a linkless embedding of an undirected graph is an embedding of the graph into three-dimensional

    Linkless embedding

    Linkless_embedding

  • Skew-symmetric graph
  • Directed graph isomorphic to its own transpose graph

    In graph theory, a branch of mathematics, a skew-symmetric graph is a directed graph that is isomorphic to its own transpose graph, the graph formed by

    Skew-symmetric graph

    Skew-symmetric_graph

  • Rado graph
  • Infinite graph containing all countable graphs

    In the mathematical field of graph theory, the Rado graph, Erdős–Rényi graph, or random graph is a countably infinite graph that can be constructed (with

    Rado graph

    Rado graph

    Rado_graph

  • Paley graph
  • Graph of numbers differing by a square

    Paley graphs form an infinite family of conference graphs, which yield an infinite family of symmetric conference matrices. Paley graphs allow graph-theoretic

    Paley graph

    Paley graph

    Paley_graph

  • Graph homomorphism
  • Structure-preserving correspondence between node-link graphs

    In the mathematical field of graph theory, a graph homomorphism is a mapping between two graphs that respects their structure. More concretely, it is a

    Graph homomorphism

    Graph homomorphism

    Graph_homomorphism

  • Call graph
  • Representation of subroutine calls in a computer program

    A call graph (also known as a call multigraph) is a directed graph that represents calling relationships between subroutines in a computer program. Each

    Call graph

    Call graph

    Call_graph

  • Pathwidth
  • Representation of a graph as a path graph "thickened" by some amount

    decompositions. They play a key role in the theory of graph minors: the families of graphs that are closed under graph minors and do not include all forests may be

    Pathwidth

    Pathwidth

  • Neo4j
  • Graph database implemented in Java

    Foundation, an open-source initiative under the Linux Foundation. Graph database management systems, such as the Neo4j Graph Database, are used in artificial

    Neo4j

    Neo4j

    Neo4j

  • Generalized Petersen graph
  • Family of cubic graphs formed from regular and star polygons

    In graph theory, the generalized Petersen graphs are a family of cubic graphs formed by connecting the vertices of a regular polygon to the corresponding

    Generalized Petersen graph

    Generalized Petersen graph

    Generalized_Petersen_graph

  • Symmetric graph
  • Graph in which all ordered pairs of linked nodes are automorphic

    In the mathematical field of graph theory, a graph G is symmetric or arc-transitive if, given any two ordered pairs of adjacent vertices (u1,v1) and (u2

    Symmetric graph

    Symmetric graph

    Symmetric_graph

  • Tree-depth
  • Numerical invariant of graphs

    In graph theory, the tree-depth of a connected undirected graph G {\displaystyle G} is a numerical invariant of G {\displaystyle G} , the minimum height

    Tree-depth

    Tree-depth

  • Graph of a polytope
  • In polytope theory, the edge graph (also known as vertex-edge graph or just graph) of a polytope is a combinatorial graph whose vertices and edges correspond

    Graph of a polytope

    Graph of a polytope

    Graph_of_a_polytope

  • Median graph
  • Graph with a median for each three vertices

    In graph theory, a division of mathematics, a median graph is an undirected graph in which every three vertices a, b, and c have a unique median: a vertex

    Median graph

    Median graph

    Median_graph

  • Threshold graph
  • Graph formed by adding isolated or universal vertices

    In graph theory, a threshold graph is a graph that can be constructed from a one-vertex graph by repeated applications of the following two operations:

    Threshold graph

    Threshold graph

    Threshold_graph

  • Signed graph
  • Graph with sign-labeled edges

    In the area of graph theory in mathematics, a signed graph is a graph in which each edge has a positive or negative sign. A signed graph is balanced if

    Signed graph

    Signed graph

    Signed_graph

  • Medial graph
  • Edge-face adjacencies in another graph

    graph theory, the medial graph of plane graph G is another graph M(G) that represents the adjacencies between edges in the faces of G. Medial graphs were

    Medial graph

    Medial graph

    Medial_graph

  • Kuratowski's theorem
  • On forbidden subgraphs in planar graphs

    In graph theory, Kuratowski's theorem is a mathematical forbidden graph characterization of planar graphs, named after Kazimierz Kuratowski. It states

    Kuratowski's theorem

    Kuratowski's theorem

    Kuratowski's_theorem

  • Treewidth
  • Number denoting a graph's closeness to a tree

    In graph theory, the treewidth of an undirected graph is an integer number which specifies, informally, how far the graph is from being a tree. The smallest

    Treewidth

    Treewidth

  • Snark (graph theory)
  • 3-regular graph with no 3-edge-coloring

    In the mathematical field of graph theory, a snark is an undirected graph with exactly three edges per vertex whose edges cannot be colored with only three

    Snark (graph theory)

    Snark (graph theory)

    Snark_(graph_theory)

  • Maximum cut
  • Problem in graph theory

    graphs closed under graph minors and having the structure of clique-sums of planar graphs and graphs of bounded size. A minor-closed family of graphs

    Maximum cut

    Maximum cut

    Maximum_cut

  • Periodic graph
  • Topics referred to by the same term

    crystal Periodic graph (geometry), a Euclidean graph preserved under a lattice of translations Periodic graph (graph theory), a graph that is periodic

    Periodic graph

    Periodic_graph

  • Two-graph
  • Set of unordered triples from a vertex set

    the two-graph. A regular two-graph has the property that every pair of vertices lies in the same number of triples of the two-graph. Two-graphs have been

    Two-graph

    Two-graph

  • Graph property
  • Property of graphs that depends only on abstract structure

    In graph theory, a graph property or graph invariant is a property of graphs that depends only on the abstract structure, not on graph representations

    Graph property

    Graph property

    Graph_property

  • Robertson–Seymour theorem
  • Finiteness of sets of forbidden graph minors

    graph theory, the Robertson–Seymour theorem (also called the graph minors theorem) states that the undirected graphs, partially ordered by the graph minor

    Robertson–Seymour theorem

    Robertson–Seymour_theorem

  • Degeneracy (graph theory)
  • Measurement of graph sparsity

    In graph theory, a k-degenerate graph is an undirected graph in which every non-empty subgraph has at least one vertex of degree at most k. That is, some

    Degeneracy (graph theory)

    Degeneracy (graph theory)

    Degeneracy_(graph_theory)

  • Quotient graph
  • In graph theory, a quotient graph Q of a graph G is a graph whose vertices are blocks of a partition of the vertices of G and where block B is adjacent

    Quotient graph

    Quotient_graph

  • Forbidden graph characterization
  • Describing a family of graphs by excluding certain (sub)graphs

    In graph theory, a branch of mathematics, many important families of graphs can be described by a finite set of individual graphs that do not belong to

    Forbidden graph characterization

    Forbidden graph characterization

    Forbidden_graph_characterization

  • Logic of graphs
  • Logical formulation of graph properties

    the mathematical fields of graph theory and finite model theory, the logic of graphs deals with formal specifications of graph properties using sentences

    Logic of graphs

    Logic_of_graphs

  • E-graph
  • Graph data structure

    In computer science, an e-graph is a data structure that stores an equivalence relation over terms of some language. Let Σ be a set of uninterpreted functions

    E-graph

    E-graph

  • YΔ- and ΔY-transformation
  • Operation on graphs

    In graph theory, ΔY- and YΔ-transformations (also written delta-wye and wye-delta) are a pair of operations on graphs. A ΔY-transformation replaces a triangle

    YΔ- and ΔY-transformation

    YΔ- and ΔY-transformation

    YΔ-_and_ΔY-transformation

  • Asymmetric graph
  • Undirected graph with no non-trivial symmetries

    In graph theory, a branch of mathematics, an undirected graph is called an asymmetric graph if it has no nontrivial symmetries. Formally, an automorphism

    Asymmetric graph

    Asymmetric graph

    Asymmetric_graph

  • Independence complex
  • complex of a graph is a mathematical object describing the independent sets of the graph. Formally, the independence complex of an undirected graph G, denoted

    Independence complex

    Independence complex

    Independence_complex

  • Flip graph
  • Graph that encodes local operations in mathematics

    In mathematics, a flip graph is a graph whose vertices are combinatorial or geometric objects, and whose edges link two of these objects when they can

    Flip graph

    Flip graph

    Flip_graph

  • Laves graph
  • Periodic spatial graph

    Laves graph is an infinite and highly symmetric system of points and line segments in three-dimensional Euclidean space, forming a periodic graph. Three

    Laves graph

    Laves graph

    Laves_graph

  • GNRS conjecture
  • have greater stretch factor. The graphs that have an embedding with at most a given distortion are closed under graph minor operations, operations that

    GNRS conjecture

    GNRS conjecture

    GNRS_conjecture

  • Control-flow graph
  • Graphical representation of a computer program or algorithm

    In computer science, a control-flow graph (CFG) is a representation, using graph notation, of all paths that might be traversed through a function during

    Control-flow graph

    Control-flow graph

    Control-flow_graph

  • Schreier coset graph
  • Construction in combinatorial group theory

    theory, the Schreier coset graph is a graph associated with a group G, a generating set of G, and a subgroup of G. The Schreier graph encodes the abstract structure

    Schreier coset graph

    Schreier_coset_graph

  • Graphviz
  • Software package for graph visualization

    Graphviz is free software licensed under the Eclipse Public License. dot a command-line tool to produce layered graph drawings in a variety of output formats

    Graphviz

    Graphviz

    Graphviz

  • Graph Query Language
  • Query language for property graphs

    GQL (Graph Query Language) is a standardized query language for property graphs first described in ISO/IEC 39075, released in April 2024 by ISO/IEC. The

    Graph Query Language

    Graph_Query_Language

  • Indifference graph
  • 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

    Indifference graph

    Indifference_graph

  • Turán graph
  • Balanced complete multipartite graph

    The Turán graph, denoted by T ( n , r ) {\displaystyle T(n,r)} , is a complete multipartite graph; it is formed by partitioning a set of n {\displaystyle

    Turán graph

    Turán graph

    Turán_graph

  • Feedback arc set
  • Edges that hit all cycles in a graph

    In graph theory and graph algorithms, a feedback arc set or feedback edge set in a directed graph is a subset of the edges of the graph that contains at

    Feedback arc set

    Feedback arc set

    Feedback_arc_set

  • Matching (graph theory)
  • Set of edges without common vertices

    In the mathematical discipline of graph theory, a matching or independent edge set in an undirected graph is a set of edges without common vertices. In

    Matching (graph theory)

    Matching_(graph_theory)

  • String graph
  • Intersection graph for curves in the plane

    graph theory, a string graph is an intersection graph of curves in the plane; each curve is called a "string". Given a graph G, G is a string graph if

    String graph

    String_graph

  • Implicit function theorem
  • On converting relations to functions of several real variables

    that provides sufficient conditions under which a planar curve specified by F(x,y)=0 can also be specified as the graph of a function f, so that for each

    Implicit function theorem

    Implicit_function_theorem

  • Misleading graph
  • Graph that misrepresents data

    In statistics, a misleading graph, also known as a distorted graph, is a graph that misrepresents data, constituting a misuse of statistics and with the

    Misleading graph

    Misleading graph

    Misleading_graph

  • Graphon
  • Function type in graph theory

    In graph theory and statistics, a graphon (also known as a graph limit) is a symmetric measurable function W : [ 0 , 1 ] 2 → [ 0 , 1 ] {\displaystyle

    Graphon

    Graphon

    Graphon

  • Circle packing theorem
  • On tangency patterns of circles

    whose interiors are disjoint. The intersection graph of a circle packing, called a coin graph, is the graph having a vertex for each circle, and an edge

    Circle packing theorem

    Circle packing theorem

    Circle_packing_theorem

  • Graph paper
  • Writing paper with a grid

    Graph paper, coordinate paper, grid paper, or squared paper is writing paper that is printed with fine lines making up a regular grid. It is available

    Graph paper

    Graph paper

    Graph_paper

  • Cubic function
  • Polynomial function of degree 3

    function is monotonic. The graph of a cubic function is symmetric with respect to its inflection point; that is, it is invariant under a rotation of a half

    Cubic function

    Cubic function

    Cubic_function

  • Independent set (graph theory)
  • 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)

    Independent_set_(graph_theory)

  • Homeomorphism (graph theory)
  • Graphs that differ only by edge subdivision

    In graph theory, two graphs G {\displaystyle G} and G ′ {\displaystyle G'} are homeomorphic if there is a graph isomorphism from some subdivision of G

    Homeomorphism (graph theory)

    Homeomorphism_(graph_theory)

  • XDI
  • protocol under development by the OASIS XDI Technical Committee. The name comes from the addressable graph model XDI uses: every node in the XDI graph is its

    XDI

    XDI

  • Perfect graph
  • Graph with tight clique-coloring relation

    In graph theory, a perfect graph is a graph in which the chromatic number equals the size of the maximum clique, both in the graph itself and in every

    Perfect graph

    Perfect graph

    Perfect_graph

  • Shortest path problem
  • Computational problem of graph theory

    In graph theory, the shortest path problem is the problem of finding a path between two vertices (or nodes) in a graph such that the sum of the weights

    Shortest path problem

    Shortest path problem

    Shortest_path_problem

  • Double graph
  • Graph operation in graph theory

    In the mathematical field of graph theory, the double graph of a simple graph G is a graph derived from G by a specific construction. The concept and

    Double graph

    Double graph

    Double_graph

  • Graph (topology)
  • Topological space arising from a usual graph

    In topology, a branch of mathematics, a graph is a topological space which arises from a usual graph G = ( E , V ) {\displaystyle G=(E,V)} by replacing

    Graph (topology)

    Graph_(topology)

  • Cycle double cover
  • Cycles in a graph that cover each edge twice

    In graph-theoretic mathematics, a cycle double cover is a collection of cycles in an undirected graph that together include each edge of the graph exactly

    Cycle double cover

    Cycle double cover

    Cycle_double_cover

  • Wagner's theorem
  • On forbidden minors in planar graphs

    In graph theory, Wagner's theorem is a mathematical forbidden graph characterization of planar graphs, named after Klaus Wagner, stating that a finite

    Wagner's theorem

    Wagner's theorem

    Wagner's_theorem

  • Turán's theorem
  • Extremal graph theory bound on clique-free graph edges

    In graph theory, Turán's theorem bounds the number of edges that can be included in an undirected graph that does not have a complete subgraph of a given

    Turán's theorem

    Turán's_theorem

  • Ancestral graph
  • In statistics and Markov modeling, an ancestral graph is a type of mixed graph used to provide a graphical representation for the result of marginalizing

    Ancestral graph

    Ancestral graph

    Ancestral_graph

  • Closed graph theorem (functional analysis)
  • Theorems connecting continuity to closure of graphs

    analysis, the closed graph theorem is a result connecting the continuity of a linear operator to a topological property of their graph. Precisely, the theorem

    Closed graph theorem (functional analysis)

    Closed_graph_theorem_(functional_analysis)

  • Microsoft Automatic Graph Layout
  • Software library

    Microsoft Automatic Graph Layout (MSAGL) is a .NET library for automatic graph layout. It was created by Lev Nachmanson at Microsoft Research. Earlier

    Microsoft Automatic Graph Layout

    Microsoft_Automatic_Graph_Layout

  • Kautz graph
  • The Kautz graph K M N + 1 {\displaystyle K_{M}^{N+1}} is a directed graph of degree M {\displaystyle M} and dimension N + 1 {\displaystyle N+1} , which

    Kautz graph

    Kautz graph

    Kautz_graph

  • Friedman's SSCG function
  • Fast-growing function

    graphs SCG ( k ) {\displaystyle {\text{SCG}}(k)} . In mathematics, especially graph theory, a simple subcubic graph (SSCG) is a finite simple graph in

    Friedman's SSCG function

    Friedman's_SSCG_function

  • NP-intermediate
  • Complexity class of problems

    being NP-intermediate are the graph isomorphism problem, and decision versions of factoring and the discrete logarithm. Under the exponential time hypothesis

    NP-intermediate

    NP-intermediate

  • Fibrations of graphs
  • spectral graph theory, distributed computing, symbolic dynamics, graph neural networks, and category theory, under different names such as graph divisor

    Fibrations of graphs

    Fibrations_of_graphs

  • Biclique-free graph
  • Property in graph theory

    In graph theory, a branch of mathematics, a t-biclique-free graph is a graph that has no Kt,t (complete bipartite graph with 2t vertices) as a subgraph

    Biclique-free graph

    Biclique-free_graph

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