问题
Background: I am a newbie to graph theory, specially in "graph cut". Please don't be too technical and fast. Thank you.
Suppose I have a weighted undirected connected graph G=(V,E). I have a variable A that holds an integer value and I want to remove/cut all edges from the graph G whose weight are below the value of A.
Question 1: If this already exist in graph theory (I saw max-cut, min-cut, s-t cut, etc) how is it called?
Question 2: How can I formally express/define this approach using mathematical symbols.
Thank you for your suggestions.
回答1:
You have:
- a Graph
G - composed of a set of vertices
V - and a edges
Ewhich is a set of pairs of vertices (i.e.E = {{x,y} : x ∈ V, y ∈ V}). - each edge has a weight (assumed to be a natural number) which you can specify using a function (i.e.
∀ e ∈ E : weight(e) ∈ ℕ).
Then the graph G' with removed edges with weight not less than a (note: singular elements/values are usually denoted using lower-case whereas sets/lists/etc are usually denoted using upper-case) is given by:
G' = (V, { e ∈ E : weight(e) ≥ a })- or
G' = (V,E') : E' = { e ∈ E : weight(e) ≥ a }
or, to make it more explicit that you are removing elements from E, you could be long-winded and define it as:
G' = (V, E \ { e ∈ E : weight(e) < a })- or
G' = (V,E') : E' = E \ { e ∈ E : weight(e) < a }
回答2:
From what I understand, you want to remove the edges whose weight are less than A.
This has nothing to do with cuts in graphs.
I think the mathematical expression of what you want is:
G'(V', E') = G(V, Q) : Q = {x: x <= A and x belongs to E}
来源：https://stackoverflow.com/questions/31671697/cut-in-a-weighted-undirected-connected-graph