of the surface ( see Euler characteristic ). The size of a graph is E, its number of edges. For example, Angelina Jolie, Catherine Zeta-Jones, Drew Barrymore, Dennis Hopper, Eddie Murphy, Kevin Bacon, Kevin Spacey, Madonna, Mel Gibson and Shirley Maclaine form an independent set in the Kevin Bacon graph. A vertex whose deletion increases the number of components is called a cutvertex, whilst an edge with the same property is called a bridge. The degree or valency of a vertex is the number of edges that connect to it, where an edge that connects a vertex to itself (a loop ) is counted twice. It is called the empty graph on ndisplaystyle n vertices. Note that this is still the same graph - the location of the vertices and edges in the diagram makes no difference to the graph. Cliques can also arise in other ways. That is to say that V(Kn)1,ndisplaystyle V(K_n)1,ldots,n and E(Kn)ij:1ijndisplaystyle E(K_n)ij:1leq ileq jleq. Under the umbrella of social networks are many different types of graphs. Some of this work is found in Harary and Palmer (1973).

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Graph -theoretic methods, in various forms, have proven particularly useful in linguistics, since natural language often lends itself well to discrete structure.

Traditionally, syntax and compositional semantics follow tree-based structures, whose expressive power lies in the principle of compositionality.

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30, isbn, retrieved Gardner, Martin (1992 Fractal Music, Hypercards, and moreMathematical Recreations from Scientific American,. These are graphs that can be drawn as dot-and-line diagrams on a plane (or, equivalently, on a sphere) without any edges crossing except at the vertices where they meet. Other senses of graph stem from different conceptions of the edge set. The circumference is a much harder question, but probably will consist of most of the vertices on the graph of degree at least. Complete Graph on 5 vertices Paths edit The path graph Pndisplaystyle P_n has V(Pn)1,ndisplaystyle V(P_n)1,ldots,n and E(P_n)12,23,34,ldots n-1)n. V and E are usually taken to be finite, and many of the well-known results are not true (or are rather different) for infinite graphs because many of the arguments fail in the infinite case. In mathematics, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects.

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