Editing Almost all (section)

===Meaning in graph theory===
In [[graph theory]], if <var>A</var> is a set of (finite [[graph labeling|labelled]]) [[graph (discrete mathematics)|graph]]s, it can be said to contain almost all graphs, if the proportion of graphs with <var>n</var> vertices that are in <var>A</var> tends to 1 as <var>n</var> tends to infinity.{{r|Babai}} However, it is sometimes easier to work with probabilities,{{r|Spencer}} so the definition is reformulated as follows. The proportion of graphs with <var>n</var> vertices that are in <var>A</var> equals the probability that a random graph with <var>n</var> vertices (chosen with the [[discrete uniform distribution|uniform distribution]]) is in <var>A</var>, and choosing a graph in this way has the same outcome as generating a graph by flipping a coin for each pair of vertices to decide whether to connect them.{{r|Bollobas}} Therefore, equivalently to the preceding definition, the set <var>''A''</var> contains almost all graphs if the probability that a coin-flip–generated graph with <var>n</var> vertices is in <var>A</var> tends to 1 as <var>n</var> tends to infinity.{{r|Spencer|Gradel}} Sometimes, the latter definition is modified so that the graph is chosen randomly in some [[random graph#Models|other way]], where not all graphs with <var>n</var> vertices have the same probability,{{r|Bollobas}} and those modified definitions are not always equivalent to the main one.

The use of the term "almost all" in graph theory is not standard; the term "[[asymptotically almost surely]]" is more commonly used for this concept.{{r|Spencer}}

Example:
* Almost all graphs are [[asymmetric graph|asymmetric]].{{r|Babai}}
* Almost all graphs have [[diameter (graph theory)|diameter]] 2.{{r|Buckley}}