How to calculate maximum possible edges Only between two different labels (or groups of nodes) in a network?

Question

[eswaripj]

Dear Experts,

I have a network with two types of nodes: bacteria and fungi. I.e., some of the nodes (10,000 nodes) represent proteins derived from bacterial genome and all other nodes (900 nodes) represent proteins derived from fungal genome.

How do I calculate the maximum possible number of edges between these two groups? I.e., calculate the maximum number of potential edges only between B-F (Bacteria-Fungi), excluding all the edges between B-B and F-F.

Specific example: IF I have a network with 10,000 Bacterial nodes, and Fungal 900 nodes, what is the maximum number of B-F edges only (excluding all B-B and F-F? (Is it 900x10,000 for undirected network? and 2x900x10,000 for directed?) where x between the numbers represent multiplication.

I searched the forum, tutorial and all in the search option, to see if the question is already answered. To the best of my knowledge I could not find it - probably due to my lack of knowledge in the field - so if you find this a duplicate question, kindly apologize and provide me with the link to the answer.

Thank you in advance for your reply, Eswari

[GenoMax]

Please leave the classification as a question.

Forum posts are used for issues where there is topic of general interest that many can weigh in.

[eswaripj]

Genomax, Thank you for changing the classification and explaining.

Answer 1

[Jean-Karim Heriche]

You already have the answer. At most, each bacterial protein will be linked to all fungal ones and conversely each fungal protein will be linked to all bacterial ones so that there are at most N(bacterial) x N(fungal) edges in an undirected graph. In a directed graph there would be N(bacterial) x N(fungal) edges in each direction so 2 x N(bacterial) x N(fungal) edges.

[eswaripj]

Thank you Jean-Karim.