99 questions/Solutions/88

import Data.List

type Node = Int
type Edge = (Node,Node)
type Graph = ([Node],[Edge])

depthfirst :: Graph -> Node -> [Node]
depthfirst (v,e) n
    | [x|x<-v,x==n] == [] = []
    | otherwise = dfrecursive (v,e) [n]
    
dfrecursive :: Graph -> [Node] -> [Node]
dfrecursive ([],_) _ = []
dfrecursive (_,_) [] = []
dfrecursive (v,e) (top:stack)
    | [x|x<-v,x==top] == [] = dfrecursive (newv, e) stack
    | otherwise = top : dfrecursive (newv, e) (adjacent ++ stack)
    where
        adjacent = [x | (x,y)<-e,y==top] ++ [x | (y,x)<-e,y==top]
        newv = [x|x<-v,x/=top]
        
connectedcomponents :: Graph -> [[Node]]
connectedcomponents ([],_) = []
connectedcomponents (top:v,e) 
    | remaining == [] = [connected]
    | otherwise = connected : connectedcomponents (remaining, e)
    where
        connected = depthfirst (top:v,e) top
        remaining = (top:v) \\ connected

You can call it:

connectedcomponents ([1,2,3,4,5],[(2,3),(3,4),(1,5)])