Editing Connectedness (section)

==Connectivity==
{{Main article|Connectivity (graph theory)}}
Properties and parameters based on the idea of connectedness often involve the word ''connectivity''. For example, in [[graph theory]], a [[connected graph]] is one from which we must remove at least one vertex to create a disconnected graph.<ref>{{Cite book|title=Graph Theory and Applications|last=Bondy|first=J.A.|last2=Murty|first2=U.S.R.|publisher=Elsevier Science Publishing Co.|year=1976|isbn=0444194517|location=New York, NY|pages=[https://archive.org/details/graphtheorywitha0000bond/page/42 42]|url=https://archive.org/details/graphtheorywitha0000bond/page/42}}</ref> In recognition of this, such graphs are also said to be ''1-connected''. Similarly, a graph is ''2-connected'' if we must remove at least two vertices from it, to create a disconnected graph. A ''3-connected'' graph requires the removal of at least three vertices, and so on. The ''[[connectivity (graph theory)|connectivity]]'' of a graph is the minimum number of vertices that must be removed to disconnect it. Equivalently, the connectivity of a graph is the greatest integer ''k'' for which the graph is ''k''-connected.

While terminology varies, [[noun]] forms of connectedness-related properties often include the term ''connectivity''. Thus, when discussing simply connected topological spaces, it is far more common to speak of ''simple connectivity'' than ''simple connectedness''. On the other hand, in fields without a formally defined notion of ''connectivity'', the word may be used as a synonym for ''connectedness''.

Another example of connectivity can be found in regular tilings. Here, the connectivity describes the number of neighbors accessible from a single [[tile]]:
<gallery>
Image:Triangular_3_connectivity.svg|3-connectivity in a [[triangular tiling]],&nbsp;
Image:Square_4_connectivity.svg|[[4-connected graph|4-connectivity]] in a [[square tiling]],&nbsp;
Image:Hexagonal_connectivity.svg|6-connectivity in a [[hexagonal tiling]],&nbsp;
Image:Square_8_connectivity.svg|[[8-connectivity]] in a [[square tiling]] (note that distance equality is not kept)
</gallery>