A graph is identified by its vertices and its edges . A graph also admits a natural topology, called the graph topology, by identifying every edge with the unit interval and gluing them together at coincident vertices.
This construction can be easily realized in the framework of simplicial complexes. We can form a simplicial complex . And the desired topological realization of the graph is just the geometric realization of .
Viewing a graph as a topological space has several advantages:
A connected graph is a tree if and only if its fundamental group is trivial.
Remark: A graph is/can be regarded as a one-dimensional -complex.
|Date of creation||2013-03-22 13:37:03|
|Last modified on||2013-03-22 13:37:03|
|Last modified by||mps (409)|
|Synonym||one-dimensional CW complex|