Graph (topology)
Topological space arising from a usual graph / From Wikipedia, the free encyclopedia
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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.[1]
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 closed intervals glued to it, one for each edge
, and
is the disjoint union.[1]
The topology on this space is called the graph topology.