Graph Centrality measure

Question

[Saeed Rahmani]

I had read a paper of "Characterization of protein-interaction networks in tumors", In table of graph parameters, It has a parameter of Graph Centrality and said:

GCi = 1/ max(d(i,j)

and describe:

max(d(i,j)) is the length of the shortest path between vertices i and j for a given vertices i. This is a define to d(i,j).

I think this is wrong and :

max(d(i,j)) is the longest length of the shortest path between vertices i and j for a given vertices i.

This parameter what is say? and I think right?

Answer 1

[Girolamo]

The length of the shortest path between a pair of nodes is the number of nodes you have to traverse from node i to node j. You can have many shortest paths between the node i and node j but they have always the same length. So, I think that the definition of the paper is right.

[LLTommy]

Your definition of shortest path might be correct, but the title of post asks about 'Centrality', which is something else. I don't know the paper nor do I understand the question, so I can not really say anything else about it - but maybe provide a link to wikipedia talking about Graph Centrality. There are many different centrality measurements.

[russhh]

Yes, there are many dfferent centrality measurements, but OP only asked about a specific vertex centrality

[Saeed Rahmani]

Hi, Thanks. No it is Graph Centrality, different of Closeness, Betweenness, Degree, Vertex Centralizes.