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A hypergraph is also called a set system or a family of sets drawn from the universal set X.
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hypergraph and is
In the UNL approach, information conveyed by natural language is represented, sentence by sentence, as a hypergraph composed of a set of directed binary labeled links ( referred to as relations ) between nodes or hypernodes ( the Universal Words, or simply UW ), which stand for concepts.
In mathematics, a hypergraph is a generalization of a graph in which an edge can connect any number of vertices.
Formally, a hypergraph is a pair where is a set of elements called nodes or vertices, and is a set of non-empty subsets of called hyperedges or edges.
However, it is often desirable to study hypergraphs where all hyperedges have the same cardinality ; a k-uniform hypergraph is a hypergraph such that all its hyperedges have size k. ( In other words, it is a collection of sets of size k .) So a 2-uniform hypergraph is a graph, a 3-uniform hypergraph is a collection of unordered triples, and so on.
hypergraph and also
The primal graph is sometimes also known as the Gaifman graph of the hypergraph.
When the vertices of a hypergraph are explicitly labeled, one has the notions of equivalence, and also of equality.
Equivalently, a Sperner family is an antichain in the inclusion lattice over the power set of E. A Sperner family is also sometimes called an independent system or, if viewed from the hypergraph perspective, a clutter.
hypergraph and called
In computational geometry, a hypergraph may sometimes be called a range space and then the hyperedges are called ranges.
Because hypergraph links can have any cardinality, there are several notions of the concept of a subgraph, called subhypergraphs, partial hypergraphs and section hypergraphs.
The set of automorphisms of a hypergraph H (= ( X, E )) is a group under composition, called the automorphism group of the hypergraph and written Aut ( H ).
If all edges have the same cardinality k, the hypergraph is said to be uniform or k-uniform, or is called a k-hypergraph.
The transpose of the incidence matrix defines a hypergraph called the dual of, where is an m-element set and is an n-element set of subsets of.
( Since a family of sets may be called a hypergraph, and since every set in has size r, is a uniform hypergraph of rank r .)
hypergraph and set
Most classes of CSPs that are known to be tractable are those where the hypergraph of constraints has bounded treewidth ( and there are no restrictions on the set of constraint relations ), or where the constraints have arbitrary form but there exist essentially non-unary polymorphisms of the set of constraint relations.
The difference between a set system and a hypergraph ( which is not well defined ) is in the questions being asked.
Given a subset of the index set, the partial hypergraph generated by is the hypergraph
A connected graph G with the same vertex set as a connected hypergraph H is a host graph for H if every hyperedge of H induces a connected subgraph in G. For a disconnected hypergraph H, G is a host graph if there is a bijection between the connected components of G and of H, such that each connected component G < nowiki >'</ nowiki > of G is a host of the corresponding H < nowiki >'</ nowiki >.
A hypergraph homomorphism is a map from the vertex set of one hypergraph to another such that each edge maps to one other edge.
A hypergraph automorphism is an isomorphism from a vertex set into itself, that is a relabeling of vertices.
A transversal ( or " hitting set ") of a hypergraph H = ( X, E ) is a set that has nonempty intersection with every edge.
The transversal hypergraph of H is the hypergraph ( X, F ) whose edge set F consists of all minimal transversals of H.
Consider, for example, the generalized hypergraph whose vertex set is and whose edges are and.
However, the transitive closure of set membership for such hypergraphs does induce a partial order, and " flattens " the hypergraph into a partially ordered set.
hypergraph and system
Each hypergraph or set system can be regarded as an incidence
hypergraph and family
The edges of a hypergraph may form an arbitrary family of sets, so the line graph of a hypergraph is the same as the intersection graph of the sets from the family.
The intersection number of a graph is the minimum number of elements in a family of sets whose intersection graph is, or equivalently the minimum number of vertices in a hypergraph whose line graph is.
hypergraph and sets
A hypergraph H may be represented by a bipartite graph BG as follows: the sets X and E are the partitions of BG, and ( x < sub > 1 </ sub >, e < sub > 1 </ sub >) are connected with an edge if and only if vertex x < sub > 1 </ sub > is contained in edge e < sub > 1 </ sub > in H. Conversely, any bipartite graph with fixed parts and no unconnected nodes in the second part represents some hypergraph in the manner described above.
A hypergraph is a combinatorial structure that, like an undirected graph, has vertices and edges, but in which the edges may be arbitrary sets of vertices rather than having to have exactly two endpoints.
As a special case of this correspondence between bipartite graphs and hypergraphs, any multigraph ( a graph in which there may be two or more edges between the same two vertices ) may be interpreted as a hypergraph in which some hyperedges have equal sets of endpoints, and represented by a bipartite graph that does not have multiple adjacencies and in which the vertices on one side of the bipartition all have degree two.
hypergraph and drawn
This circuit diagram can be interpreted as a drawing of a hypergraph in which four vertices ( depicted as white rectangles and disks ) are connected by three hyperedges drawn as trees.
hypergraph and from
A hypergraph is bipartite if and only if its vertices can be partitioned into two classes U and V in such a way that each hyperedge contains at least one vertex from both classes.
A bipartite graph may be used to model a hypergraph in which is the set of vertices of the hypergraph, is the set of hyperedges, and contains an edge from a hypergraph vertex to a hypergraph edge exactly when is one of the endpoints of.
In computer science, a graph is an abstract data type that is meant to implement the graph and hypergraph concepts from mathematics.
In the framework of edge coloring simple hypergraphs, defines a number from a simple hypergraph as the number of hypergraph vertices that belong to a hyperedge of three or more vertices.
hypergraph and .
An example of a hypergraph, with and.
In particular, there is a bipartite " incidence graph " or " Levi graph " corresponding to every hypergraph, and conversely, most, but not all, bipartite graphs can be regarded as incidence graphs of hypergraphs.
The collection of hypergraphs is a category with hypergraph homomorphisms as morphisms.
A subhypergraph is a hypergraph with some vertices removed.
The partial hypergraph is a hypergraph with some edges removed.
When a notion of equality is properly defined, as done below, the operation of taking the dual of a hypergraph is an involution, i. e.,
is and also
It is also possible, but equally doubtful, that he actually shot down the hundreds of men with which his legend credits him.
Recognizing that the Rule of Law is `` a dynamic concept which should be employed not only to safeguard the civil and political rights of the individual in a free society '', the Congress asserted that it also included the responsibility `` to establish social, economic, educational and cultural conditions under which his legitimate aspirations and dignity may be realized ''.
At General Power's seat in the balcony there is also a gold phone.
In addition to the authentication and acknowledgment procedures which precede and follow the sending of the go messages, again in special codes, each message also contains an `` internal authenticator '', another specific signal to convince the recipient that he is getting the real thing.
He added that he also stresses the works of these favorite masters on tour, especially Mahler's First and Fourth symphonies, and Das Lied Von der Erde, and Bruckner's Sixth -- which is rarely played -- and Seventh.
The test of form is fidelity to the experience, a gauge also accepted by the abstract expressionist painters.
Though he is also concerned with freeing dance from pedestrian modes of activity, Merce Cunningham has selected a very different method for achieving his aim.
The answers derived by these means may determine not only the temporal organization of the dance but also its spatial design, special slips designating the location on the stage where the movement is to be performed.
It is because there is not only darkness but also light that our situation becomes inexplicable.
but there is also compassion.
also he is a drunk, and has lost his job on that account.
And if I have gone into so much detail about so small a work, that is because it is also so typical a work, representing the germinal form of a conflict which remains essential in Mann's writing: the crude sketch of Piepsam contains, in its critical, destructive and self-destructive tendencies, much that is enlarged and illuminated in the figures of, for instance, Naphta and Leverkuhn.
By `` image '' is meant not only a visual presentation, but also remembered sensations of any of the five senses plus the feelings which are immediately conjoined therewith.
he is questioning, also, every epistemology which stems from Hume's presupposition that experience is merely sense data in abstraction from causal efficacy, and that causal efficacy is something intellectually imputed to the world, not directly perceived.
it is true that they are also extremely dull.
Now the detective must save his own skin by informing on the girl he loves, who is also the real murderer.
But it is also the climax to one of the absorbing chapters in our current political history.
Since a civilizational crisis involves also a crisis in private interests and in the ruling class, reaction is normally found among those who feel themselves to be among the ruling class.
`` The Rocking Horse Winner '' is also a story about a boy's love for his mother.
Evidence is plentiful that early and later also he has been indebted to the Gothic romancers, who deal in extravagant horror, to the symbolists writing at the end of the preceding century, and in particular to the stream-of-consciousness novelists, Henry James and James Joyce among them.
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