About: Graph (topology)

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In topology, a branch of mathematics, a graph is a topological space which arises from a usual graph by replacing vertices by points and each edge by a copy of the unit interval , where is identified with the point associated to and with the point associated to . That is, as topological spaces, graphs are exactly the simplicial 1-complexes and also exactly the one-dimensional CW complexes. Thus, in particular, it bears the quotient topology of the set The topology on this space is called the graph topology.

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  • In topology, a branch of mathematics, a graph is a topological space which arises from a usual graph by replacing vertices by points and each edge by a copy of the unit interval , where is identified with the point associated to and with the point associated to . That is, as topological spaces, graphs are exactly the simplicial 1-complexes and also exactly the one-dimensional CW complexes. Thus, in particular, it bears the quotient topology of the set under the quotient map used for gluing. Here is the 0-skeleton (consisting of one point for each vertex ), are the intervals ("closed one-dimensional unit balls") glued to it, one for each edge , and is the disjoint union. The topology on this space is called the graph topology. (en)
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  • In topology, a branch of mathematics, a graph is a topological space which arises from a usual graph by replacing vertices by points and each edge by a copy of the unit interval , where is identified with the point associated to and with the point associated to . That is, as topological spaces, graphs are exactly the simplicial 1-complexes and also exactly the one-dimensional CW complexes. Thus, in particular, it bears the quotient topology of the set The topology on this space is called the graph topology. (en)
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  • Graph (topology) (en)
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