Let´s suppose their weight is 1.0. Look at vertex 0 and vertex 1:
Without averaging: closeness(0) = 1 / 15 = 0.0666 and closeness(1) = 1 / 2 = 0.5
With averaging: closeness(0) = 9 / 15 = 0.6 and closeness(1) = 2 / 2 = 1.0
In both cases vertex 1 gets a better score.
That doesn´t make much sense because vertex 1 can only get to vertex 4 and 5.
On the other hand we have vertex 0 with a lower closeness, but from it we can get to every other vertex ( 1 - 9 ).
If it was an undirected graph, this problem wouldn´t come up.
Can someone give me some hints on how to deal with this?
Thank You.
Cheers
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Hello Everyone,
Is there a way to properly normalize a vertex score on directed graphs?
Let me explain with an example: A simple hierarchy
Vertices: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
Edges:
(0, 1)
(0, 2)
(0, 3)
(1, 4)
(1, 5)
(2, 6)
(2, 7)
(3, 8)
(3, 9)
Let´s suppose their weight is 1.0. Look at vertex 0 and vertex 1:
Without averaging: closeness(0) = 1 / 15 = 0.0666 and closeness(1) = 1 / 2 = 0.5
With averaging: closeness(0) = 9 / 15 = 0.6 and closeness(1) = 2 / 2 = 1.0
In both cases vertex 1 gets a better score.
That doesn´t make much sense because vertex 1 can only get to vertex 4 and 5.
On the other hand we have vertex 0 with a lower closeness, but from it we can get to every other vertex ( 1 - 9 ).
If it was an undirected graph, this problem wouldn´t come up.
Can someone give me some hints on how to deal with this?
Thank You.
Cheers