Finding common elements from two columns in symmetric adjacency matrix

Question

I have a sparse symmetric matrix which represents authors of some book. Elements Ai,j and Aj,i are both equal to one if the people associated with indices i and j are coauthors and equal to zero otherwise. I'm trying to find a way in matrix representation such that given two columns (authors), I find their common co-authors. Preferably in Matlab or Julia code representation.

Answer 1

The binary & between the columns, applied elementwise, will return a vector with 1s only where both columns had 1s. You can do a findall over that to then return the indices where the result is 1, which indicates the common co-authors.

julia> A
5×5 SparseMatrixCSC{Bool, Int64} with 12 stored entries:
 ⋅  1  ⋅  1  1
 1  ⋅  ⋅  ⋅  1
 ⋅  ⋅  ⋅  ⋅  1
 1  ⋅  ⋅  ⋅  1
 1  1  1  1  ⋅

julia> common = A[:, 1] .& A[:, 5]
5-element SparseVector{Bool, Int64} with 2 stored entries:
  [2]  =  1
  [4]  =  1

julia> findall(common)
2-element Vector{Int64}:
 2
 4

This finds the common co-authors between authors 1 and 5, in Julia. The . before the & indicates that the operator should be applied elementwise. To generalize this, you can write it as a function like:

julia> function findcommoncoauths(adjmat, author1, author2)
         @views findall(adjmat[:, author1] .& adjmat[:, author2])
       end

(The @views is to avoid unnecessarily allocating new memory for the columns, which is a good practice for performant code.)