How to apply netting in Adjacency matrix

I have a weighted Adjacency matrix 138 x 138 representing interbank exposure. A link ij in the matrix represents loans originating from bank i to bank j. I would like to have a netted bilateral exposure such that if two banks lend to one another, for instance, a bank A(i) lends to bank B(j) and B(i) has also lent to A(j). I intend to compare the two loans and subtract the loans and assign the difference to a bank that had the highest value while deleting the link for a bank with the lowest values(assign zero) in the matrix. Any help on how to represent this in a Matlab code will be appreciated.

Answer 1

[Steven Lord]

This sounds like it might be a homework assignment, so I'm only going to give a hint. The transpose operator .' may be of interest to you.

Once you have your modified adjacency matrix, if you want to perform further analysis on it you may want to use it to create a digraph as that will let you easily visualize the network (calling plot on the digraph) and determine node successors, shortest paths, etc.

[FoxK]

Hi Steve, Thank you for the hint. This is part of a research I am working on (not homework) the Adjancency matrix I have mentioned is just part of a sample of 1 year. I am farmiliar with most network operations, I tried to solve my challenge using tOut and sOut, tril and triu,successors and predecessors. my challenge I guess is a logical representation of the idea.

[Steven Lord]

Let's look at a small example. In this example bank 1 owes bank 2 $8 and bank 2 owes bank 1 $3 (where $ would probably represent a million dollars, but I just wanted to work with small numbers.)

>> rng default
>> A = reshape(randperm(9), [3 3])
>> A = A - diag(diag(A))
A =
     0     8     2
     3     0     4
     7     1     0

Would this be your desired result?

>> M = max(A-A.', 0)
M =

     0     5     0
     0     0     3
     5     0     0

Let's plot the digraph of bank relationships, with the amount owed as the edge labels.

plot(digraph(M), 'EdgeLabelMode', 'auto')

[FoxK]

Thanks Steve Works Perfectly