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Graph made from disjoint union of complete graphs
In graph theory, a branch of mathematics, a cluster graph is a graph formed from the disjoint union of complete graphs. Equivalently, a graph is a cluster
Cluster_graph
Binary operation combining the vertex and edge sets of two graphs
cluster graphs are the disjoint unions of complete graphs. The 2-regular graphs are the disjoint unions of cycle graphs. More generally, every graph is
Disjoint_union_of_graphs
Clustering methods
corresponding to the smallest eigenvalues of the graph Laplacian can be used for meaningful clustering of the masses. For example, assuming that all the
Spectral_clustering
Topics referred to by the same term
of complete graphs Clusterable graph, in balance theory Cluster algebra, a class of commutative rings used in representation theory Cluster expansion,
Cluster
Adjacent subset of an undirected graph
cluster graph is a graph whose connected components are cliques. A block graph is a graph whose biconnected components are cliques. A chordal graph is
Clique_(graph_theory)
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
Physical simulation to visualize graphs
versatile class of graph drawing algorithms. Examples of existing extensions include the ones for directed graphs, 3D graph drawing, cluster graph drawing, constrained
Force-directed_graph_drawing
Maximal subgraph whose vertices can reach each other
in any graph. In a connected graph, there is exactly one component: the whole graph. In a forest, every component is a tree. In a cluster graph, every
Component_(graph_theory)
Type of random graph
statistical mechanics, probability theory, graph theory, etc. the random cluster model is a random graph that generalizes and unifies the Ising model
Random_cluster_model
Measure of how connected and clustered a node is in its graph
In graph theory, a clustering coefficient is a measure of the degree to which nodes in a graph tend to cluster together. Evidence suggests that in most
Clustering_coefficient
In graph drawing, a clustered planar graph is a graph together with a hierarchical clustering on its vertices, such that the graph can be drawn together
Clustered_planarity
Graph whose biconnected components are all cliques
subclasses of the perfect graphs, block graphs are perfect. Every tree, cluster graph, or windmill graph is a block graph. Every block graph has boxicity at most
Block_graph
Game engine
detail clusters with a low-detail equivalent. The set of active clusters is tracked on the GPU by performing a per-frame traversal of the cluster graph using
Unreal_Engine_5
Mathematical theory on behavior of connected clusters in a random graph
probability one a unique infinite closed cluster (a closed cluster is a maximal connected set of "closed" edges of the graph). Thus the subcritical phase may
Percolation_theory
Grouping a set of objects by similarity
known as quasi-cliques, as in the HCS clustering algorithm. Signed graph models: Every path in a signed graph has a sign from the product of the signs
Cluster_analysis
Graph able to be partitioned into multiple independent sets
one vertex. Complete k-partite graphs, complete multipartite graphs, and their complement graphs, the cluster graphs, are special cases of cographs,
Multipartite_graph
Open-source data analytics cluster computing framework
Malak, Michael (14 June 2016). "Finding Graph Isomorphisms In GraphX And GraphFrames: Graph Processing vs. Graph Database". slideshare.net. sparksummit
Apache_Spark
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
Planar graph with 4 nodes and 5 edges
diamond-free graphs are locally clustered: that is, they are the graphs in which every neighborhood is a cluster graph. Alternatively, a graph is diamond-free
Diamond_graph
Class of artificial neural networks
Graph neural networks (GNNs) are artificial neural networks designed for tasks whose inputs are graphs. Because graphs usually do not have a canonical
Graph_neural_network
Type of chart
compared, and the other axis represents a measured value. Some bar graphs present bars clustered or stacked in groups of more than one, showing the values of
Bar_chart
Statistical method in data analysis
hierarchical clustering (also called hierarchical cluster analysis or HCA) is a method of cluster analysis that seeks to build a hierarchy of clusters. Strategies
Hierarchical_clustering
Graph where most nodes are reachable in a small number of steps
network is a graph characterized by a high clustering coefficient and low distances. In an example of a social network, high clustering implies the high
Small-world_network
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
Entangled state of qubits
the case of cluster states. Another way of thinking of cluster states is as a particular instance of graph states, where the underlying graph is a connected
Cluster_state
Method of partitioning data points into groups based on their similarity
graph is a signed graph), indicating whether the corresponding endpoints are similar or dissimilar. The goal is to find a clustering (that is, a partition
Correlation_clustering
Plotting by a computer application
runtime, it plans an abstract path through the cluster graph, then refines that path within each cluster. This significantly reduces the search space and allows
Pathfinding
Matrix representation of a graph
directed graph is by definition generally non-symmetric, while, e.g., traditional spectral clustering is primarily developed for undirected graphs with symmetric
Laplacian_matrix
Subdivision of vertices into disjoint sets
computers, among others. Recently, the graph partition problem has gained importance due to its application for clustering and detection of cliques in social
Graph_partition
Concept in quantum computing
computing, a graph state is a special type of multi-qubit state that can be represented by a graph. Each qubit is represented by a vertex of the graph, and there
Graph_state
Class of commutative rings
all the clusters of all the seeds in this graph. The cluster algebra also comes with the extra structure of the seeds of this graph. A cluster algebra
Cluster_algebra
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
an algorithm based on graph connectivity for cluster analysis. It works by representing the similarity data in a similarity graph, and then finding all
HCS_clustering_algorithm
Topics referred to by the same term
vertices that represent cliques that differ by exactly one vertex Cluster graph, a graph in which each component is a clique This disambiguation page lists
Clique_graph_(disambiguation)
Graph formed by complementation and disjoint union
more general graph classes. Special types of cograph include complete graphs, complete bipartite graphs, cluster graphs, and threshold graphs. Cographs are
Cograph
Object diagram, and the Package diagram. Cluster graph Illustration called City of London Skyscraper Cluster Diagram at skyscrapernews.com. Retrieved
Cluster_diagram
Theory of attitude change
triangle of three mutual enemies makes a clusterable graph but not a balanced one. Therefore, in a clusterable network one cannot conclude that "the enemy
Balance_theory
Method of generating random small-world graphs
a random graph generation model that produces graphs with small-world properties, including short average path lengths and high clustering. It was proposed
Watts–Strogatz_model
Least-weight tree connecting graph vertices
Taxonomy. Cluster analysis: clustering points in the plane, single-linkage clustering (a method of hierarchical clustering), graph-theoretic clustering, and
Minimum_spanning_tree
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
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
Method of result aggregation from multiple clustering algorithms
the graph to be partitioned. In sHBGF, the graph has n + t vertices, where t is the total number of underlying clusters. Bayesian consensus clustering (BCC):
Consensus_clustering
Two closely related models for generating random graphs
the mathematical field of graph theory, the Erdős–Rényi models are two closely related models for generating random graphs and the evolution of a random
Erdős–Rényi_model
Multi-model database
a single cluster" Commercial self-managed: ArangoDB Enterprise is a paid subscription that includes graph-aware sharding (called “SmartGraphs”) and collection
ArangoDB
Canadian computing company
Plotly provides online graphing, analytics, and statistics tools for individuals and collaboration, as well as scientific graphing libraries for Python
Plotly
Smallest transitive relation containing a given binary relation
acyclic graph (DAG) is the reachability relation of the DAG and a strict partial order. The transitive closure of an undirected graph produces a cluster graph
Transitive_closure
Dimensionality reduction of graph-based semantic data objects [machine learning task]
prediction, triple classification, entity recognition, clustering, and relation extraction. A knowledge graph G = { E , R , F } {\displaystyle {\mathcal {G}}=\{E
Knowledge_graph_embedding
Clustering method used in network science
can belong to only one cluster at a given moment. The original algorithm applies to undirected, weighted, and unweighted graphs. Chinese whispers runs
Chinese whispers (clustering method)
Chinese_whispers_(clustering_method)
Trail in which only the first and last vertices are equal
In graph theory, a cycle in a graph is a non-empty trail in which only the first and last vertices are equal. A directed cycle in a directed graph is
Cycle_(graph_theory)
problems on massive graphs into smaller, more manageable ones. The coarsening process involves merging nodes of a graph into clusters called supernodes
Graph_Coarsening_Algorithm
Network whose degree distribution follows a power law
free graphs with low degree correlation and clustering coefficient, one can generate new graphs with much higher degree correlations and clustering coefficients
Scale-free_network
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
Clustering algorithm minimizing the sum of distances to k representatives
one-dimensional graph.[citation needed] The above image shows an example of a Jaccard Dissimilarity graph. Step 1 Medoid-based clustering is used to find clusters within
K-medoids
cliques. That is, each color class should form a cluster graph. The subchromatic number χS(G) of a graph G is the fewest colors needed in any subcoloring
Subcoloring
Abstract data type in computer science
science, a graph is an abstract data type that is meant to implement the undirected graph and directed graph concepts from the field of graph theory within
Graph_(abstract_data_type)
Mixing property of Markov chains and graphs
a cluster (which can be seen as a set of vertices in a graph) should be low. Apart from this, the conductance of the subgraph induced by a cluster (called
Conductance_(graph_theory)
homogeneous graph is also ultrahomogeneous. It is a special case of a homogenous model. The only finite homogeneous graphs are the cluster graphs mKn formed
Homogeneous_graph
Topics referred to by the same term
way of clustering nodes in a signed graph Cluster (disambiguation) This disambiguation page lists articles associated with the title Clustering. If an
Clustering
Mathematical concept for comparing objects
natural number n. Borel equivalence relation Cluster graph – Graph made from disjoint union of complete graphs Conjugacy class – In group theory, equivalence
Equivalence_relation
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
Cubic graph with 8 vertices and 12 edges
mathematical field of graph theory, the Wagner graph is a 3-regular graph with 8 vertices and 12 edges. It is the 8-vertex Möbius ladder graph. As a Möbius ladder
Wagner_graph
Graph with equal-size maximal independent sets
graph is well-covered: every maximal independent set consists of a single vertex. Similarly, every cluster graph (a disjoint union of complete graphs)
Well-covered_graph
Clustering and community detection algorithm
function aggregateGraph returns a new graph whose vertices are the partition of the old graph, and whose edges are calculated using the old graph. This function
Louvain_method
Density-based data clustering algorithm
core points on the neighbor graph, ignoring all non-core points. Assign each non-core point to a nearby cluster if the cluster is an ε (eps) neighbor, otherwise
DBSCAN
Convex polyhedron with 14 triangle faces
triaugmented triangular prism form a maximal planar graph with 9 vertices and 21 edges, called the Fritsch graph. It was used by Rudolf and Gerda Fritsch to show
Triaugmented_triangular_prism
Informally, a family of graphs has few cliques if the graphs do not have a large number of large clusters. A clique of a graph is a complete subgraph,
Graphs_with_few_cliques
Diagram with a treelike structure
representing a tree graph. This diagrammatic representation is frequently used in different contexts: in hierarchical clustering, it illustrates the arrangement
Dendrogram
Graph representing faces of another graph
mathematical discipline of graph theory, the dual graph of a planar graph G is a graph that has a vertex for each face of G. The dual graph has an edge for each
Dual_graph
Problem in natural language processing and information retrieval
particular cluster. A simple, cost-effective way of overcoming the above limitation is to embed the centroid terms with the highest weight in a graph structure
Cluster_labeling
Python library for graphs and networks
structure of the graph, making it useful for identifying clusters and communities. Source: Construct the Laplacian matrix of the graph. A Laplacian matrix
NetworkX
applications like LDA, which can be used to cluster documents and extract topical representations. Graph analytics - contains applications like pagerank
GraphLab
Spherical collection of stars
diagrams) of globular clusters allow astronomers to determine many of the properties of their populations of stars. A H–R diagram is a graph of a large sample
Globular_cluster
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
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
In graph theory, the mathematically simplest spatial network
geometric graphs resemble real human social networks in a number of ways. For instance, they spontaneously demonstrate community structure - clusters of nodes
Random_geometric_graph
Mathematical concept
t.} Among these graphs are the graphs of equivalence relations. These graphs, called cluster graphs, are characterized as the graphs such that the connected
Equivalence_class
Vector quantization algorithm minimizing the sum of squared deviations
clusters in which each observation belongs to the cluster with the nearest mean (cluster centers or cluster centroid). This results in a partitioning of the
K-means_clustering
Heuristic used in computer science
Assuming this happens, there will be a sharp elbow in the graph of explained variation versus clusters: increasing rapidly up to k (under-fitting region), and
Elbow_method_(clustering)
Chemical graph theory concerns the graph-theoretic structure of molecules and other clusters of atoms. Both the Errera graph itself and its dual graph are
Errera_graph
Chordal graph where all cycles of even length have odd chords
chordal graphs, which in turn includes the cluster graphs as the 2-leaf powers. Another important subclass of strongly chordal graphs are interval graphs. In
Strongly_chordal_graph
Subgraph induced by all nodes linked to a given node of a graph
represent graphs in computer algorithms, via the adjacency list and adjacency matrix representations. Neighbourhoods are also used in the clustering coefficient
Neighbourhood_(graph_theory)
Pictorial representation of the behavior of subatomic particles
device of covariant perturbation theory, the graphs were called Feynman–Dyson diagrams or Dyson graphs, because the path integral was unfamiliar when
Feynman_diagram
Square matrix containing the distances between elements in a set
In mathematics, computer science and especially graph theory, a distance matrix is a square matrix (two-dimensional array) containing the distances, taken
Distance_matrix
Type of disease cluster
News. Pub Med - latest standards for evaluating cancer clusters Cancer Mortality Maps & Graphs: U.S., 1950-94 National Institute of Environmental Health
Cancer_cluster
Cluster analysis problem
some point the marginal gain will drop, giving an angle in the graph. The number of clusters is chosen at this point, hence the "elbow criterion". In most
Determining the number of clusters in a data set
Determining_the_number_of_clusters_in_a_data_set
Directed graph describing citations in documents
A citation graph (or citation network), in information science and bibliometrics, is a directed graph that describes the citations within a collection
Citation_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
Graph layout on multiple half-planes
In graph theory, a book embedding is a generalization of planar embedding of a graph to embeddings in a book, a collection of half-planes all having the
Book_embedding
Generalization of graph theory
hypergraph learning techniques include hypergraph spectral clustering that extends the spectral graph theory with hypergraph Laplacian, and hypergraph semi-supervised
Hypergraph
accuracy Clustering: a class of unsupervised learning algorithms for grouping and bucketing related input vector Computer Vision Grabcut based on Graph cuts
List_of_algorithms
Python module
Support for clustering coefficients, as well as network motif statistics and community structure detection. Generation of random graphs, with arbitrary
Graph-tool
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
Type of discrete calculus
mathematics, calculus on finite weighted graphs is a discrete calculus for functions whose domain is the vertex set of a graph with a finite number of vertices
Calculus on finite weighted graphs
Calculus_on_finite_weighted_graphs
Measure of network community structure
structure of networks or graphs which measures the strength of division of a network into modules (also called groups, clusters or communities). Networks
Modularity_(networks)
Type of directed graph
based on following paths in this graph can be used to find hierarchical clusterings quickly. Nearest neighbor graphs are also a subject of computational
Nearest_neighbor_graph
Concept in graph theory
Such insight can be useful in improving some algorithms on graphs such as spectral clustering. Importantly, communities often have very different properties
Community_structure
combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, mathematical logic, number theory, set theory, Ramsey
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
such as natural language processing, sentiment analysis, translation, and cluster analysis. These datasets consist of sounds and sound features used for
List of datasets for machine-learning research
List_of_datasets_for_machine-learning_research
Analog of the continuous Laplace operator
learning for clustering and semi-supervised learning on neighborhood graphs. There are various definitions of the discrete Laplacian for graphs, differing
Discrete_Laplace_operator
Academic field
unsupervised clustering methods. Network models serve as a foundation to understanding interactions within empirical complex networks. Various random graph generation
Network_science
CLUSTER GRAPH
CLUSTER GRAPH
Surname or Lastname
English and North German
English and North German : metonymic occupational name for a plasterer, from Middle English, Middle Low German plaster (from Latin emplastrum ‘(wound) plaster’ (originally a paste), from Greek emplastron, a derivative of emplassein ‘to shape or form’; the term was carried over into building terminology to mean ‘bonding agent’).English : habitational name from any of various places called Plaistow (in East London, Derbyshire, Sussex, and elsewhere), from Old English plegestÅw ‘place where people gather for sport or play’. This can also be a variant of Plaisted (through interchangeable use of the Old English elements stÅw and stede, both meaning ‘place’, in earlier times).German and Ashkenazic Jewish (Pflaster) : from Middle High German pflaster (German Pflaster, from Latin plastrum) ‘street pavement’, ‘pavement’, cognate with 1.
Male
English
 English surname transferred to forename use, derived from the city name Chester, from an Old English form of Latin castra, CHESTER means "legionary camp."Â
Surname or Lastname
English
English : metonymic occupational name for a grower or seller of costards (Anglo-Norman French, from coste ‘rib’), a variety of large apples, so called for their prominent ribs. In some cases, it may have been a nickname (from the same word) for a person with an apple-shaped (i.e. round) head.Dutch : status name for a churchwarden, from Late Latin custor ‘guard’, ‘warden’.Variant spelling of German Koster.This name is recorded in Beverwijck in New Netherland (Albany, NY) in the mid 17th century.
Surname or Lastname
English
English : habitational name from Leicester, named in Old English from the tribal name Ligore (itself adapted from a British river name) + Old English ceaster ‘Roman fort or walled city’ (Latin castra ‘legionary camp’).English (of Norman origin) : habitational name from Lestre in Normandy.English and Scottish : variant of Lister.
Girl/Female
Assamese, Celebrity, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Punjabi, Sikh, Tamil, Traditional
Flame; Lustre; Glow; Shine; Luster; Nice
Male
Gaelic
Gaelic form of Latin Alexandrus, ALASTER means "defender of mankind."
Male
Gaelic
Gaelic form of Latin Alexandrus, ALISTER means "defender of mankind."
Surname or Lastname
Americanized spelling of German Köster or Küster ‘sexton’ (see Kuster).English
Americanized spelling of German Köster or Küster ‘sexton’ (see Kuster).English : variant of Coster.The American military officer George Custer (1839–76) was a descendant of a German officer from Hesse by the name of Küster.
Surname or Lastname
English
English : habitational name from Chester, the county seat of Cheshire, or from any of various smaller places named with this word (as for example Little Chester in Derbyshire or Chester le Street in County Durham), which is from Old English ceaster ‘Roman fort or walled city’ (Latin castra ‘legionary camp’).
Male
English
English slang term for someone who breaks things transferred to forename use, originally derived from the verb bust, BUSTER means "to break, smash," hence "breaker, destroyer, smasher."
Surname or Lastname
English
English : possibly from Middle English cloutere, clutere, an occupational name for a cobbler or patcher, from an agent derivative of cloute, clut(e) ‘patch’.Possibly an altered form of German Klutterer, an occupational name for a traveling entertainer, Middle High German kluterære, or a shortened form of Klüttermann ‘clodhopper’, a nickname for a peasant.
Girl/Female
Australian, Finnish
Bunch; Cluster
Male
English
Anglicized form of Gaelic Alaster, ALYSTER means "defender of mankind."
Surname or Lastname
English and Scottish
English and Scottish : variant of Lister.
Male
English
English surname transferred to forename use, from the city name Leicester which was recorded in the 10th century as Ligora caester "Ligora's fort." Ligora is related to Liguria, a very old place name of obscure origin, dating back to pre-Roman times. There has been some speculation concerning a possible connection between Ligora/Liguria and Celtic Lug, LESTER means "oath."
Male
Gaelic
Gaelic form of Latin Alexandrus, ALESTER means "defender of mankind."
Boy/Male
Hebrew, Hindu, Indian, Marathi
Grape Cluster
Surname or Lastname
English
English : habitational name from the city of Gloucester. The place originally bore the British name Glēvum (apparently from a cognate of Welsh gloyw ‘bright’), to which was added the Old English element ceaster ‘Roman fort or walled city’ (Latin castra ‘legionary camp’).
Girl/Female
British, English, Finnish
Bunch; Cluster
Surname or Lastname
English (Devon)
English (Devon) : occupational name for a treasurer or accountant, from Middle English counter (from Old French conteor).
CLUSTER GRAPH
CLUSTER GRAPH
Boy/Male
Hindu, Indian
Lord Sai; Offering; Light
Boy/Male
Muslim
Aspect
Girl/Female
Hindu, Indian, Marathi
Purity
Girl/Female
Tamil
Shritama | à®·à¯à®°à¯€à®¤à®¾à®®à®¾à®‚
This name means like the Goddess Lakshmi
Boy/Male
Tamil
Irenpreet | ஈரேநà¯à®ªà¯à®°à®¿à®¤
Loving
Boy/Male
Hindu, Indian, Marathi
A Mountain
Girl/Female
Australian, French, Hawaiian, Hebrew
Light; Enlightens; Glowing; Encourages
Boy/Male
Hindu, Indian
Kind-hearted Person; Sat means Good and Chit means Mind or Heart
Surname or Lastname
English
English : variant spelling of Whitaker.
Boy/Male
Tamil
A companion of the prophet (Saw)
CLUSTER GRAPH
CLUSTER GRAPH
CLUSTER GRAPH
CLUSTER GRAPH
CLUSTER GRAPH
n.
A confused collection; hence, confusion; disorder; as, the room is in a clutter.
v. t.
To raise a blister or blisters upon.
v. t.
Alt. of Lustre
n.
Growing in, or full of, clusters; like clusters.
n.
Same as Luster.
n.
One who casts; as, caster of stones, etc. ; a caster of cannon; a caster of accounts.
n.
Same as Clyster.
n.
Clatter; confused noise.
v. t.
To crowd together in disorder; to fill or cover with things in disorder; to throw into disorder; to disarrange; as, to clutter a room.
v. t.
To collect into a cluster or clusters; to gather into a bunch or close body.
n.
A number of similar things collected together or lying contiguous; a group; as, a cluster of islands.
n.
Alt. of Lustre
n.
Glitter; luster.
v. i.
To grow in clusters or assemble in groups; to gather or unite in a cluster or clusters.
imp. & p. p.
of Cluster
a.
Contrary; opposite; contrasted; opposed; adverse; antagonistic; as, a counter current; a counter revolution; a counter poison; a counter agent; counter fugue.
v. i.
To be affected with a blister or blisters; to have a blister form on.
n.
One who cuts; as, a stone cutter; a die cutter; esp., one who cuts out garments.
n.
A vesicatory; a plaster of Spanish flies, or other matter, applied to raise a blister.
a.
Having the form of a cluster of grapes; clustered like grapes.