making a data.frame igraph compatible by creating edgelist from location data

Question

I am currently working on a project visualizing a network of think tank board members and their respective boards. The data I have is in the following format:

     name edge
1    A    1
2    A    2
3    A    3
4    B    4
5    B    5
6    C    6

However, to make it compatible for igraphs graph_from_data_frame() function, I would need the following format:

   name from to
1    A    1  2
2    A    1  3
3    A    2  3
4    B    4  5
5    C    6  0

I have already tried

 df1 <- setDT(df1)[, list(edge = toString(edge)), name]
 df1 <- separate(df1, "edge", c("X", "Y", "Z"))

yielding

  name X    Y    Z
1:    A 1    2    3
2:    B 4    5 <NA>
3:    C 6 <NA> <NA>

However, I do not know how to get from this (or the initial format) to the required format to use graph_from_data_frame() I hope you can help me. Thanks in advance