Correlation between degree of two vertices in a n-vertices graph

In summary, the correlation between the degree of two vertices in a n-vertices graph is a measure of the relationship between the number of edges connected to each vertex. It is calculated using a mathematical formula called the correlation coefficient, which takes into account the degrees of all the vertices in the graph. A positive correlation between the degree of two vertices indicates a strong relationship, while a negative correlation indicates a weak relationship. The correlation can also be used to determine the type of graph, with a complete graph having a perfect positive correlation and a random graph having little to no correlation between the degrees of any two vertices.
  • #1
ppftw
2
0
Hi! I'm a bit stumped on this computer-science-related statistics (I think that's what it would fall under) problem. It's over here:

http://math.stackexchange.com/questions/796517/correlation-between-the-degree-of-two-vertices-in-an-undirected-graph/796526?noredirect=1#796526

It would be awesome if someone could modify the answer, confirm it, or suggest an alternative approach...
 
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  • #2
What is Var of Bin(n-1,p)?
The rest looks ok.
 
  • #3
Oh, it should be (n-1)p(1-p). Thanks for catching that and your response.
 

FAQ: Correlation between degree of two vertices in a n-vertices graph

What is the correlation between the degree of two vertices in a n-vertices graph?

The correlation between the degree of two vertices in a n-vertices graph refers to the relationship between the number of edges connected to each vertex. It measures how closely related the degrees of the two vertices are.

How is the correlation between the degree of two vertices calculated?

The correlation between the degree of two vertices is calculated using a mathematical formula called the correlation coefficient. This formula takes into account the degrees of all the vertices in the graph and calculates a value between -1 and 1, where 1 indicates a perfect positive correlation and -1 indicates a perfect negative correlation.

What does a positive correlation between the degree of two vertices indicate?

A positive correlation between the degree of two vertices means that as one vertex's degree increases, the other vertex's degree also tends to increase. This suggests that the two vertices are well-connected and have a strong relationship in the graph.

What does a negative correlation between the degree of two vertices indicate?

A negative correlation between the degree of two vertices means that as one vertex's degree increases, the other vertex's degree tends to decrease. This suggests that the two vertices are not well-connected and have a weak relationship in the graph.

Can the correlation between the degree of two vertices be used to determine the type of graph?

Yes, the correlation between the degree of two vertices can be used to determine the type of graph. For example, in a complete graph where every vertex is connected to every other vertex, there will be a perfect positive correlation between the degrees of any two vertices. However, in a random graph where the edges are randomly distributed, there will be little to no correlation between the degrees of any two vertices.

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