Creating Adjacency Matrix and Social Network Graph

Question

I have to build a directed graph of a social network based on interactions with a business. My starting element is a two column table [user_id, [Friends]]. The entries for user_id come from subsetting a larger set on the basis of interaction with a specified business(if an interaction is detected, the user_id is included in this table). The entries for user_id are factors, and the entries for Friends are a list of factors, pulled directly from the database and include all friends per user_id.

example:

| user_id | Friends                |
|--------:|------------------------|
| Jake    | ['Laura','Bob','Mary'] |
| Laura   | ['Bob','John','Peter'] |
| Bob     | ['Jane','Fred','Mary'] | 

In order to determine my edges, I would like to cross reference each user_id with the friends of every other user_id. From the example: is Bob in Jake's or Laura's friends list? is Jake in Bob's or Laura's friends list? is Laura in Bob's or Jake's friends list?

Every time the question is answered positively, add an edge between users. This I am hoping to represent in an adjacency matrix. Our example would return something like this:

|       | Bob | Jake | Laura | Jane | Fred | Mary | John | Peter |
|------:|-----|------|-------|------|------|------|------|-------|
| Bob   |     |      |       |      |      |      |      |       |
| Jake  | 1   |      | 1     |      |      |      |      |       |
| Laura | 1   |      |       |      |      |      |      |       |
| Jane  |     |      |       |      |      |      |      |       |
| Fred  |     |      |       |      |      |      |      |       |
| Mary  |     |      |       |      |      |      |      |       |
| John  |     |      |       |      |      |      |      |       |
| Peter |     |      |       |      |      |      |      |       |

Finally I would like to build a graph based on this matrix

Thanks!

Edit for clarity and added example

Answer 1

I'm not sure I completely understand the question, but maybe you could get your graph from an edge list created by merging your user id and friend tables. For example:

set.seed(1)                                                                                        
n <- 10                                                                                            
uid <- ceiling(runif(10, max=5))                                                                   
fid <- letters[ceiling(runif(10, max=5))]                                                          
tab <- data.frame(user_id=uid, Friends=fid)                                                        
tab3 <- tab2 <- tab                                                                                
names(tab2) <- c('ego_id', 'Friends')                                                              
names(tab3) <- c('alter_id', 'Friends')                                                            
mg <- merge(tab2, tab3)                                                                            
test <- mg$ego_id == mg$alter_id                                                                   
mg <- mg[!test, ]                                                                                  
g <- igraph::graph.data.frame(mg[, c('ego_id', 'alter_id')], directed=TRUE)

Which turns this fake table, tab

    user_id Friends
 1        2       b
 2        2       a
 3        3       d
 4        5       b
 5        2       d
 6        5       c
 7        5       d
 8        4       e
 9        4       b
 10       1       d

into this igraph graph, g

 IGRAPH DN-- 5 18 --
 + attr: name (v/c)
 + edges (vertex names):
  [1] 2->5 2->4 5->2 5->4 4->2 4->5 3->1 3->5 3->2 1->3 1->5 1->2 5->3 5->1 5->2
 [16] 2->3 2->1 2->5

Now from the comments, it has become clear that question is how to get a graph from a factor and a list of factors using an adjacency matrix as an intermediate step. Here's one way to do that

!> user_id <- factor(c('Jake', 'Laura', 'Bob'))                                                       
 > Friends <- list(factor(c('Laura', 'Bob', 'Mary')),                                                 
 +                 factor(c('Bob', 'John', 'Peter')),                                                 
 +                 factor(c('Jane', 'Fred', 'Mary')))                                                 
 > all_nodes <- unique(c(levels(unlist(Friends)), levels(user_id)))                                   
 > A1 <- sapply(Friends, function(x) all_nodes %in% x)                                                
 > colnames(A1) <- as.character(user_id)                                                              
 > rownames(A1) <- as.character(all_nodes)                                                            
 > test <- !as.character(all_nodes) %in% as.character(user_id)                                        
 > extra_cols <- as.character(all_nodes[test])                                                        
 > A2 <- matrix(FALSE, nrow=nrow(A1), ncol=length(extra_cols))                                        
 > colnames(A2) <- extra_cols                                                                         
 > A <- cbind(A1, A2)                                                                                 
 > A <- A[rownames(A), rownames(A)]                                                                   
 > A <- t(A)                                                                                          
 > g <- igraph::graph_from_adjacency_matrix(A)                                                        
 > g                                                                                                  
 IGRAPH DN-- 8 9 --
 + attr: name (v/c)
 + edges (vertex names):
 [1] Bob  ->Mary  Bob  ->Fred  Bob  ->Jane  Laura->Bob   Laura->John
 [6] Laura->Peter Jake ->Bob   Jake ->Laura Jake ->Mary