I now have a graph that includes many nodes and weighted edges. enter image description here

This graph is generated from a pandas data frame Here's the sample input dataframe

A B count
x y 3
x z 2
y x 5
y z 1
z x 1

The principle to sort the nodes is: when A goes to B (count) is bigger than B goes to A, then A is bigger than B. Otherwise, B is bigger than A. e.g. x to y is 3 and y to x is 5, so y is bigger than x.

Here's how I do it

I created a list to store the nodes that need to be rank. This is the output list. e.g. {X, Y, Z}

and create a dict to store all the relationships from the dataframe:

For example: ({'X': {'Y': 3, 'Z': 2}, {'Y': {'X': 5, 'Z': 1}, {'Z': {'X': 1, 'Y': 0}).

By looping through these relations in turn, high-level nodes are inserted into the previous space of low-level nodes, and the rest of the nodes are moved back one step.

The change of output list while the program running:

{X, Y, Z}
->{Y, X, Z}
->{Y, X, Z}
->{Y, X, Z}
->{Y, X, Z}
->{Y, X, Z}

Hence the output is {Y, X, Z}. This is the way I can imagine, but it is too heuristic. Is there any elegant method else? Can it identify a global order A>B>C from partial orders like A>B and B>C? Is this related to any famous problem?

IIUC, you can use pivot_table get what you expect:

out = (df.pivot_table(index='A', columns='B', values='count', fill_value=0)
         .agg(lambda s: s.drop(s.name).to_dict(), axis=1).to_dict())
print(out)

# Output
{'x': {'y': 3, 'z': 2},
 'y': {'x': 5, 'z': 1},
 'z': {'x': 1, 'y': 0}}
Can you provide a more detailed input dataframe and the expected output please?
Sorry for being unclear, I have edited my question. I just wanted to see if there was a more elegant way to rank these elements.
What you want is for each node, the list of connected nodes ordered by count, that's right?
Yes. I only need one list that shows the order of the node, and the order depends on the count (connected nodes)
Thanks for the reply. I already got a dictionary like this, and I used it to loop all the relationships to get the order of the output list. What I want is a more elegant solution to solve this problem. Maybe I don't need to loop them one by one and directly do something on the graph or the origin dataframe?
Really I don't understand what you want. If you have something functional update your post with your code. Maybe I can optimize what you have (or not)