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Extensions and Generalizations of Graphs: Directed Graphs, Hypergraphs, Signed Graph, Directed Acyclic Graph, Quantum Graph

Extensions and Generalizations of Graphs: Directed Graphs, Hypergraphs, Signed Graph, Directed Acyclic Graph, Quantum Graph


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About the Book

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Pages: 36. Chapters: Directed graphs, Hypergraphs, Signed graph, Directed acyclic graph, Quantum graph, Skew-symmetric graph, Packing in a hypergraph, Forbidden graph characterization, Topological sorting, Flow network, Table of vertex-symmetric digraphs, Tournament, Clique complex, Line graph of a hypergraph, Voltage graph, Quiver, De Bruijn graph, Multigraph, Dependency graph, Graph labeling, Kruskal-Katona theorem, Gain graph, Two-graph, Multitree, Ordered graph, BEST theorem, New digraph reconstruction conjecture, Kautz graph, St-connectivity, Why-Because analysis, Propositional directed acyclic graph, Strongly connected component, Rotation map, Cause-effect graph, Bidirected graph, Implication graph, Transpose graph, Wait-for graph, Hypertree, Dipole graph, Ancestral graph, Arborescence, Rooted graph. Excerpt: In mathematics, a hypergraph is a generalization of a graph, where 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 links. Therefore, is a subset of, where is the power set of . While graph edges are pairs of nodes, hyperedges are arbitrary sets of nodes, and can therefore contain an arbitrary number of nodes. However, it is often useful 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 triples, and so on. A hypergraph is also called a set system or a family of sets drawn from the universal set X. Hypergraphs can be viewed as incidence structures and vice versa. In particular, there is a Levi graph corresponding to every hypergraph, and vice versa. In comp...


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Product Details
  • ISBN-13: 9781156142745
  • Publisher: Books LLC, Wiki Series
  • Publisher Imprint: Books LLC, Wiki Series
  • Height: 246 mm
  • No of Pages: 38
  • Spine Width: 2 mm
  • Weight: 86 gr
  • ISBN-10: 1156142741
  • Publisher Date: 25 Jun 2011
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Sub Title: Directed Graphs, Hypergraphs, Signed Graph, Directed Acyclic Graph, Quantum Graph
  • Width: 189 mm


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