python list of lists common elements iteration

Question

list= [[5, 4, 6], [6, 4, 5], [7, 1, 2]]

I have the above list, I want to compare every list index like [5,4,6] with [6,4,5] and [7,1,2] ie with every other list index

and for output: if there exist any common elements between 2 indexes in comparision then I want to output in a format "the first element of each index" along with any common elements in the index.

answer for this iteration would be [5,4,6] as 5 is the first element of the index in comparison, 6 is the first element of the index in comparison, 4 is the common element.

next compare [6, 4, 5] with [5,4,6 ] and [7,1,2] and the answer would be [6,5,4]

next compare [7,1,2] with [5,4,6] and [6, 4, 5] and the answer would be [7]

Please help, I have been trying for really long.

basically I want every list index to check for common elements with every other list index and if 2 list indexes have anything in common I want to get a new output list with the first element of both list indexes and common elements

final output= [[5,6,4],[6,5,4],[7]]

Answer 1

myL = [[5, 4, 6], [6, 4, 5], [7, 1, 2]]
newLi = []

for i in range(len(myL)):  
  tmpLi = []
  firstList = myL[i]
  for a in range(len(myL)):
    if a != i:
      secondList = myL[a]
      inCommon = set(firstList).intersection(secondList)
      if len(inCommon) != 0:
        tmpLi.append(firstList[0])
        tmpLi.append(secondList[0])
        for b in inCommon:
          if b not in tmpLi:
            tmpLi.append(b)
  if len(tmpLi) == 0:
    tmpLi.append(firstList[0])
  newLi.append(tmpLi)
print(newLi)