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Here is a DF which I take as a representation of my future vertices:

Id   Name
01   Alpha
02   Beta
03   Delta
04   Epsilon

I want to get an igraph representation of a full graph with these nodes in R. As far as I know igraph's graph.full function cannot take DF as input and I cannot really want to create an intermediary DF with all possible conection combination. Any clever idea?

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All full graphs of the same order and direction are the same, so just make a full graph of the right size and then put your vertex data on the vertices:

> d = data.frame(Id=c("01","02","03","04"),Name=c("Alpha","Beta","Delta","Epsilon"),stringsAsFactors=FALSE)
> d
  Id    Name
1 01   Alpha
2 02    Beta
3 03   Delta
4 04 Epsilon
> g = graph.full(nrow(d))
> V(g)$Name = d$Name
> V(g)$Id = d$Id
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