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lispracketgraph-theorydiscrete-mathematicss-expression
denis.shirshov
denis.shirshov

Reputation: 31

What is the name of mathematical object similar to a graph, but with different kind of edges?

While modeling biochemical networks in the cell using Racket, I recognized that I use a certain model for this task. This model resembles a directed graph, with edges pointed not only to vertices but sometimes to other edges.

I wonder is there any distinct name for this kind of model?

Here is an s-expression and a corresponding picture.

(example-object
  (vertices v1 v2 v3 v4)
  (v1 e1 v2)
  (v2 e2 v3)
  (v4 e3 e1)
  (e2 e4 e3))

enter image description here

Upvotes: 0

Views: 166

Answers (1)

sds
sds

Reputation: 60054

The paper linked from comments describes 3 types of components:

  1. Entities (represented by v nodes in your chart)
  2. Statements (e1 & e2)
  3. Influences (e3 & e4)

One way to represent this is to define a graph tower: level one graph $G_1$ is a graph with vertices $V_1$ and edges $E_1$. Level $n$ graph $G_n$ is a graph with vertices $V_n=V_{n-1}\cup E_{n-1}$ and edges $E_n$.

In your case the tower has just two levels:

  1. E/S graph with nodes=entities and edges=statements
  2. ES/I meta graph with nodes=elements of the E/S graph and edges=influences

PS. The reason to define the the graph tower in terms of traditional graphs is that those have been studied for long time, there are many theorems and algorithms about them, and they can be built upon in your study/manipulation of graph tower.

Upvotes: 4

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