Simple data-manipulation in R

Question

@Aniko points out that one way to view my problem is that I need to find the connected components of a graph, where the vertices are called groups and, variables group and nominated_group indicate an edges between those two groups. My goal is to create a variable parent_Group which indexes the connected components. Or as I put it before:

I have a dataframe with four variables: ID, group, and nominated_ID, and nominated_Group.

Consider sister-groups: Groups A and B are sister-groups if there is at least one case in the data where group==A and nominated_group==B, or vice versa.

I would like to create a variable parent_group which takes on a unique value for each set of sister-groups. In other words, no nominations should occur between cases in different parent_groups. Making the parent_group sequential numbers seems like a good idea.

Many thanks for the help I already received here! I can't really contribute here but note that I try to pay it forward at stats.exchange and on wikipedia.

In my fake data, A and B are sister-groups. Either case ID=4 or ID=5 are sufficient to make this true. Each group is also their own sister-group. The goal, the creation of parent_group, should result in one parent_group for all cases in A or B, and another parent_group for group C

df <- data.frame(ID = c(9, 5, 2, 4, 3, 7), 
  group = c("A", "A", "B", "B", "A", "C"),
  nominated_ID = c(9, 8, 4, 9, 2, 7)     )

df$nominated_group <- with(df, group[match(nominated_ID, ID)])

df

  ID group nominated_ID nominated_group
1  9     A            9               A
2  5     A            8            <NA>
3  2     B            4               B
4  4     B            9               A
5  3     A            2               B
6  7     C            7               C