Pandas dataframe conditional inner join with itself

Question

I am searching for a way to inner join a column of a dataframe with itself, based on a condition. I have a large dataframe consisting of two colums, 'Group' and 'Person'. Now I would like to create a second dataframe, which has an entry for every person tuple, that has been in the same group. First dataframe:

    Group | Person
    a1    | p1
    a1    | p2
    a1    | p3
    a1    | p4
    a2    | p1

Output:

    Person1 | Person2 | Weight
    p1      | p2      | 1
    p1      | p3      | 1
    p1      | p4      | 1
    p2      | p3      | 1
    p2      | p4      | 1
    p3      | p4      | 1

The weight is increased, if a tuple of persons are part of multiple groups. So far, I was able to create a naive implementation, based on a sub dataframe and two for loops. Is there a more elegant and more importantly, a faster/builtin way to do so ?

My implentation so far:

    group = principals.iloc[i,0]

    sub = principals.loc[principals['Group'] == group]
    
    for j in range(len(sub)-1):
        for k in range (j+1,len(sub)):
            #check if tuple exists -> update or create new entry

I was thinking, whether there is a functionality similar to SQL inner join, based on the condition of the group being the same and then joining person against person. I could take care of the double p1|p1 entry in that case...

Many thanks in advance