Extension of a partial order to a total of partitions of a weak alternating automaton
If I understand you correctly, you are asking for a linear extension of the partial order induced by the partitioning of the weak alternating automaton into its maximal strictly connected components and the transitions between the states. 

Note that the "extension of the partial order" to a total order is not unique. The process of obtaining any such total order is called topologic sorting.

See the following wikipedia page for details and a link to an algorithm: http://en.wikipedia.org/wiki/Partially_ordered_set