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After reading a bunch of articles about graph theory, I think that the problem I am working on involves incidence matrices. There are three classes B, P and L. I know the relationship of every instance of class B with every instance of class P and so on for instances of Class L and P as well.

I mapped them in two matrices X and Y. My goal is to find out which instances of Class B are related to instances of Class L. I did a matrix multiplication of few examples of X and Y, and it seems to provide me with correct answer every time, but I want to theoretically understand why is this working. I tried looking up what does a product of two incidence matrices mean, but cannot find something which would explain this in layman's terms.

$$ X_{Class B \times Class P}= \begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 1 \\ \end{bmatrix} \qquad Y_{Class P \times Class L}= \begin{bmatrix} 1 & 0 \\ 0 & 1 \\ 1 & 1 \\ \end{bmatrix}. $$

Chirag Agrawal
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  • https://en.wikipedia.org/wiki/Composition_of_relations – saulspatz Oct 09 '20 at 04:20
  • Thanks for reference. I read that and the one on Heterogenous relation. However, both of them only speak of relationship between a matrix and its transpose which is almost similar to what I asked, but still is less intuitive. – Chirag Agrawal Oct 09 '20 at 04:33
  • The part under the heading "composition in terms of matrices" is what you want. Notice that the product has to be defined a bit differently from the ordinary matrix product, though. – saulspatz Oct 09 '20 at 04:42

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