Haskell

The solution for part two could now be used for part one as well but then I would have to rewrite part 1 .-.

import Control.Arrow

import Data.Ord (comparing)

import qualified Data.List as List
import qualified Data.Map as Map
import qualified Data.Set as Set

parse = Map.fromListWith Set.union . List.map (second Set.singleton) . uncurry (++) . (id &&& List.map (uncurry (flip (,)))) . map (break (== '-') >>> second (drop 1)) . takeWhile (/= "") . lines

depthSearch connections ps
        | length ps == 4 && head ps == last ps = [ps]
        | length ps == 4 = []
        | otherwise  = head
                >>> (connections Map.!)
                >>> Set.toList
                >>> List.map (:ps)
                >>> List.concatMap (depthSearch connections)
                $ ps

interconnections (computer, connections) = depthSearch connections [computer]

part1 = (Map.assocs &&& repeat)
        >>> first (List.map (uncurry Set.insert))
        >>> first (Set.toList . Set.unions)
        >>> uncurry zip
        >>> List.concatMap interconnections
        >>> List.map (Set.fromList . take 3)
        >>> List.filter (Set.fold (List.head >>> (== 't') >>> (||)) False)
        >>> Set.fromList
        >>> Set.size

getLANParty computer connections = (connections Map.!)
        >>> findLanPartyComponent connections [computer]
        $ computer

filterCandidates connections participants candidates = List.map (connections Map.!)
        >>> List.foldl Set.intersection candidates
        >>> Set.filter ((connections Map.!) >>> \ s -> List.all (flip Set.member s) participants)
        $ participants

findLanPartyComponent connections participants candidates
        | Set.null validParticipants = participants
        | otherwise = findLanPartyComponent connections (nextParticipant : participants) (Set.delete nextParticipant candidates)
        where
                nextParticipant = Set.findMin validParticipants
                validParticipants = filterCandidates connections participants candidates

part2 = (Map.keys &&& repeat)
        >>> uncurry zip
        >>> List.map ((uncurry getLANParty) >>> List.sort)
        >>> List.nub
        >>> List.maximumBy (comparing List.length)
        >>> List.intercalate ","

main = getContents
        >>= print
        . (part1 &&& part2)
        . parse