Are there mappings from vectors/matrices of reals (or vectors/matrices of real-valued functions) to the graph? Motivating example: network of synapses and neurons as the domain and knowledge graph as the codomain. Is there mathematics that researches such objects?
I have received quite fraudulent answer, that is correct (this is big failure of the contemporary math education that focuses not on the ideas and reasoning but on the search for tricky, fraudulent, most easy answers that are eligible to miss the essence of the problem), but that misses the essence of my question.
The essence of my question is this: from the one side there is category of real-valued tensors (simply n-dimensional vectors or vector-valued functions, nothing more fancy from differential geometry) and from the other side there is category of graphs. Functor is mapping between those categories and in essence my question is two questions:
- What mathematical constructions can realize the functor from the category of n-dimensional vecotrs to the category of graphs;
- What metrics can be assigned to the realization of those functors and how we can find the optimal realization according to some metric.
Is there math that tries to find answers on any of those two questions?
Of course, there are plenty of them.
For example, you can assignt to every graph an adjacency matrix, that is a square matrix wit entires 0 and 1: https://en.wikipedia.org/wiki/Adjacency_matrix
or incidence matrix https://en.wikipedia.org/wiki/Incidence_matrix
Of course you can go vice versa also. Having such a matrix you can make a graph.