Page "Graphic matroid" Paragraph 3

The closure of a set of edges in is a flat consisting of the edges that are not independent of ( that is, the edges whose endpoints are connected to each other by a path in ).

This flat may be identified with the partition of the vertices of into the connected components of the subgraph formed by: Every set of edges having the same closure as gives rise to the same partition of the vertices, and may be recovered from the partition of the vertices, as it consists of the edges whose endpoints both belong to the same set in the partition.

In the lattice of flats of this matroid, there is an order relation whenever the partition corresponding to flat is a refinement of the partition corresponding to flat.