Like in English, you can use "genug" with or without a noun, i.e. you can use it as an adjective or as an indefinite pronoun. I guess that's what you mean by "the valence is optional".
Use as an adjective (with reference to a noun)
You can use genug to nearer determine a noun like you would use any adjective. Genug is not what you would call a normal adjective though.
It isn't declined, which you can justifiably call strange. The reasons lie probably both in its etymology and special meaning. In singular, it behaves more similar to words like "ein bisschen" or "wenig". In plural, its grammar resembles numerals like "zwei" or "hundert". It's just genug in all cases, and both in singular and plural. It can't be increased (no "genüger" or "am genügsten"), there's also no "sehr genug" or "wenig genug".
Ist noch genug kaltes Bier da? (nominative singular) (Is there still enough cold beer?)
Sind alle mit genug kaltem Bier versorgt? (dative singular) (Is everyone supplied with enough cold beer?)
Wir haben nicht mehr genug Eier für Pfannkuchen. (accusative plural) (We don't have enough eggs left to make pancakes.)
Use as an indefinite pronoun
You can use "genug" as an indefinite pronoun. In that case, genug replaces a noun.
Genug ist schiefgegangen. Wir müssen etwas ändern. (Enough has gone wrong. We'll have to change something.)
Genug is the subject in this sentence. The answer to the question "enough of what?" is only implied. Note that it is only written with a capital letter because it's the beginning of the sentence here. Like all pronouns, it is written in lowercase in the middle of a sentence.
"Genug" as a pronoun is almost always used as a singular. That's why the singular verb form ist is used. You could say that something uncountable (think "stuff") is implied. Other words that can be used in a similar way are "etwas", "viel", "wenig" etc.
There are instances where "genug" is clearly refering to something countable, for example persons. In that case you might see a sentence like:
Ich glaube, es sind genug da, wir können mit der Besprechung anfangen. (I guess enough are here, we can start the meeting.)
Unless the implied noun has been mentionend before, this is quite colloquial/sloppy though in German. More correctly, you would always say "genug Leute", "genug Kollegen" or something like that.
If the implied noun has been mentionend before, it's just adjective use with an omission to avoid repetition, which is more common:
Kann ich mir noch eine Wurst nehmen? - Natürlich, es sind mehr als genug [omitted: Würste] da. (May I help myself to another sausage? - Of course, there are more than enough available.)
Other uses
There are other uses of "genug", for example as an adverb. For more discussion on that, see the answers to this question:
Welche Wortart ist »genug«?