I need some references that go beyond the classical and graphical representation of a graph with vertices and edges; I'm trying to dive into the math world and see if I can get an alternative representation for this data structure . My research includes just everything, from graphical representations, text representations, to more abstract representation with matrices ( ?, if this option exists at all ) or other math objects .
My question is literally open for any valid representation you can think of .
to clarify further my intentions I will say this:
- my research is intentionally generic and it focuses on the best way to think about graphs given a particular problem, sometimes a matrix is better than a graphical representation, sometimes a picture is the best option, other times there is probably an even better choice including things I don't know yet .
- currently I have 2 major scenarios that need the perfect solution :
- a representation of multiple links between a widget and an $n$ number of properties, a problem about data structures and their representation, where I have a set $W$ composed of multiple instances of different widgets $w_n$ that need a connection to another set $P$ of multiple instances of different properties $p_n$ ( basically something like the CSS in the web world, it's an exemplification, but it's basically what I need )
- how to retrieve the informations about the connections, from said data structure algorithmically without incurring is incredibly large magnitudes and big scaling factors .
For now I can tell that a data structure that scales quadratically is not practical, I also need multiple links from-to each vertex, so a "plain" graph is not enough anyway and I need an hypergraph .