The CV link connnects subordinating conjunctions to the main verbs of clauses. The goal of CV is to make the correspondance between link-grammar and traditional dependency grammars more concrete. CV always makes a cycle with the C link, which identifies the subject of a clause.

        +-------CV------+        
        +----Ce---+     |        
        |         +--SX-+        
        |         |     |        
    I told   him  I    was angry   

CV attaches to the head, rather than to any auxiliary verbs:

            +-------CV------+
            +-Cs+--Sp-+--Ix-+
            |   |     |     |
   call me when you  will   be ready


            +-------CV------+-----IV----+      
            +-Cs+-Spx+-Pgfb-+--TOf-+-Ix-+
            |   |    |      |      |    |
  call me when you  are   going   to   be ready

See also the WV link, for connecting to head-verbs to the left wall, the IV link for connecting to the head-verb of infinitive clauses and the AF link for connecting to adjectival complements. Sometimes, the B link can play a similar role for relative clauses.

See also the CP link, which connects to quotation and paraphrasing verbs, as does Eq link and COq link.