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- Nearest_neighbor_graph abstract "The nearest neighbor graph (NNG) for a set of n objects P in a metric space (e.g., for a set of points in the plane with Euclidean distance) is a directed graph with P being its vertex set and with a directed edge from p to q whenever q is a nearest neighbor of p (i.e., the distance from p to q is no larger than from p to any other object from P).In many discussions the directions of the edges are ignored and the NNG is defined as an ordinary (undirected) graph. However, the nearest neighbor relation is not a symmetric one, i.e., p from the definition is not necessarily a nearest neighbor for q.In some discussions, in order to make the nearest neighbor for each object unique, the set P is indexed and in the case of a tie the object with, e.g., the largest index is taken for the nearest neighbor.The k-nearest neighbor graph (k-NNG) is a graph in which two vertices p and q are connected by an edge, if the distance between p and q is among the k-th smallest distances from p to other objects from P. The NNG is a special case of the k-NNG, namely it is the 1-NNG. k-NNGs obey a separator theorem: they can be partitioned into two subgraphs of at most n(d + 1)/(d + 2) vertices each by the removal of O(k1/dn1 − 1/d) points.Another special case is the (n − 1)-NNG. This graph is called the farthest neighbor graph (FNG).In theoretical discussions of algorithms a kind of general position is often assumed, namely, the nearest (k-nearest) neighbor is unique for each object. In implementations of the algorithms it is necessary to bear in mind that this is not always the case.NNGs for points in the plane as well as in multidimensional spaces find applications, e.g., in data compression, motion planning, and facilities location. In statistical analysis, the nearest-neighbor chain algorithm based on following paths in this graph can be used to find hierarchical clusterings quickly. Nearest neighbor graphs are also a subject of computational geometry.".
- Nearest_neighbor_graph thumbnail Nearest_neighbor_graph.svg?width=300.
- Nearest_neighbor_graph wikiPageExternalLink www.kgraph.org.
- Nearest_neighbor_graph wikiPageID "12061759".
- Nearest_neighbor_graph wikiPageLength "6016".
- Nearest_neighbor_graph wikiPageOutDegree "36".
- Nearest_neighbor_graph wikiPageRevisionID "646296653".
- Nearest_neighbor_graph wikiPageWikiLink Asymptotically_optimal.
- Nearest_neighbor_graph wikiPageWikiLink Asymptotically_optimal_algorithm.
- Nearest_neighbor_graph wikiPageWikiLink Big_O_notation.
- Nearest_neighbor_graph wikiPageWikiLink Category:Articles_with_inconsistent_citation_formats.
- Nearest_neighbor_graph wikiPageWikiLink Category:Geometric_graphs.
- Nearest_neighbor_graph wikiPageWikiLink Computational_geometry.
- Nearest_neighbor_graph wikiPageWikiLink Data_compression.
- Nearest_neighbor_graph wikiPageWikiLink Degree_(graph_theory).
- Nearest_neighbor_graph wikiPageWikiLink Delaunay_triangulation.
- Nearest_neighbor_graph wikiPageWikiLink Directed_edge.
- Nearest_neighbor_graph wikiPageWikiLink Directed_graph.
- Nearest_neighbor_graph wikiPageWikiLink Element_distinctness_problem.
- Nearest_neighbor_graph wikiPageWikiLink Element_uniqueness_problem.
- Nearest_neighbor_graph wikiPageWikiLink Euclidean_distance.
- Nearest_neighbor_graph wikiPageWikiLink Euclidean_minimum_spanning_tree.
- Nearest_neighbor_graph wikiPageWikiLink Facilities_location.
- Nearest_neighbor_graph wikiPageWikiLink Facility_location_problem.
- Nearest_neighbor_graph wikiPageWikiLink Farthest_neighbor_graph.
- Nearest_neighbor_graph wikiPageWikiLink Forest_(graph_theory).
- Nearest_neighbor_graph wikiPageWikiLink Gabriel_graph.
- Nearest_neighbor_graph wikiPageWikiLink General_position.
- Nearest_neighbor_graph wikiPageWikiLink Graph_(mathematics).
- Nearest_neighbor_graph wikiPageWikiLink Hierarchical_clustering.
- Nearest_neighbor_graph wikiPageWikiLink Metric_space.
- Nearest_neighbor_graph wikiPageWikiLink Model_of_computation.
- Nearest_neighbor_graph wikiPageWikiLink Models_of_computation.
- Nearest_neighbor_graph wikiPageWikiLink Motion_planning.
- Nearest_neighbor_graph wikiPageWikiLink Nearest-neighbor_chain_algorithm.
- Nearest_neighbor_graph wikiPageWikiLink Nearest_neighbor_graph.
- Nearest_neighbor_graph wikiPageWikiLink Path_(graph_theory).
- Nearest_neighbor_graph wikiPageWikiLink Planar_graph.
- Nearest_neighbor_graph wikiPageWikiLink Planar_separator_theorem.
- Nearest_neighbor_graph wikiPageWikiLink Plane_(geometry).
- Nearest_neighbor_graph wikiPageWikiLink Semi-Yao_graph.
- Nearest_neighbor_graph wikiPageWikiLink Sorting.
- Nearest_neighbor_graph wikiPageWikiLink Statistical_analysis.
- Nearest_neighbor_graph wikiPageWikiLink Statistics.
- Nearest_neighbor_graph wikiPageWikiLink Symmetric_relation.
- Nearest_neighbor_graph wikiPageWikiLink The_plane.
- Nearest_neighbor_graph wikiPageWikiLink Tree_(graph_theory).
- Nearest_neighbor_graph wikiPageWikiLink Vertex_degree.
- Nearest_neighbor_graph wikiPageWikiLink Weakly_connected_component.
- Nearest_neighbor_graph wikiPageWikiLink File:Nearest_neighbor_graph.svg.
- Nearest_neighbor_graph wikiPageWikiLinkText "''k''-nearest neighbor graph".
- Nearest_neighbor_graph wikiPageWikiLinkText "Nearest neighbor graph".
- Nearest_neighbor_graph wikiPageWikiLinkText "all the nearest neighbors".
- Nearest_neighbor_graph wikiPageWikiLinkText "nearest neighbor graph".
- Nearest_neighbor_graph wikiPageWikiLinkText "nearest neighbor".
- Nearest_neighbor_graph hasPhotoCollection Nearest_neighbor_graph.
- Nearest_neighbor_graph wikiPageUsesTemplate Template:Reflist.
- Nearest_neighbor_graph subject Category:Articles_with_inconsistent_citation_formats.
- Nearest_neighbor_graph subject Category:Geometric_graphs.
- Nearest_neighbor_graph hypernym Graph.
- Nearest_neighbor_graph type Software.
- Nearest_neighbor_graph comment "The nearest neighbor graph (NNG) for a set of n objects P in a metric space (e.g., for a set of points in the plane with Euclidean distance) is a directed graph with P being its vertex set and with a directed edge from p to q whenever q is a nearest neighbor of p (i.e., the distance from p to q is no larger than from p to any other object from P).In many discussions the directions of the edges are ignored and the NNG is defined as an ordinary (undirected) graph.".
- Nearest_neighbor_graph label "Nearest neighbor graph".
- Nearest_neighbor_graph sameAs Graf_nejbližšího_souseda.
- Nearest_neighbor_graph sameAs Nearest_neighbor_graph.
- Nearest_neighbor_graph sameAs Grafo_do_vizinho_mais_próximo.
- Nearest_neighbor_graph sameAs m.02vnjny.
- Nearest_neighbor_graph sameAs Q2855103.
- Nearest_neighbor_graph sameAs Q2855103.
- Nearest_neighbor_graph wasDerivedFrom Nearest_neighbor_graph?oldid=646296653.
- Nearest_neighbor_graph depiction Nearest_neighbor_graph.svg.
- Nearest_neighbor_graph isPrimaryTopicOf Nearest_neighbor_graph.