Which punctuation for definition

Throwing in yet another alternative, how about a comma followed by an "i.e."?

To this end, I first devised a novel algorithm to enumerate all possible partitions, i.e. ways of dividing a network into meaningful parts.

(Yes, I do realize that id est is not a punctuation mark.)

If "ways of dividing a network into meaningful parts" is an explanation of the preceding section, I would use either a dash or parentheses.

To this end, I first devised a novel algorithm to enumerate all possible partitions -- ways of dividing a network into meaningful parts.

Or

To this end, I first devised a novel algorithm to enumerate all possible partitions (ways of dividing a network into meaningful parts).