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mickymouse1995

can anyone help me with getting my head around eigenvector centrality?

What is the formula I need to use to work it out and then how do i use this formula to work it out?

Thank You

Reply 1

Slowbro93

Original post by mickymouse1995

can anyone help me with getting my head around eigenvector centrality?

What is the formula I need to use to work it out and then how do i use this formula to work it out?

Thank You

Before I give you the formula, do you know what an eigenvector is? This will then make the formula make sense :smile:

Reply 2

mickymouse1995

Original post by Slowbro93

Before I give you the formula, do you know what an eigenvector is? This will then make the formula make sense :smile:

yeah i know what an eigenvector is :smile:

Reply 3

Slowbro93

Original post by mickymouse1995

yeah i know what an eigenvector is :smile:

Okay

In that case, suppose I have some vector

\mathbf{v}

Then my vector is an eigenvector if for some square matrix A:

A\mathbf{v}=\alpha \mathbf{v}

where

\alpha

is some real or complex number.

Now if you look at my equation you can see that I can rearrange it such that:

(A-\alpha \mathbf{I})\mathbf{v} =0

Do you know what you can do to find the corresponding values of alpha? :smile:

Reply 4

mickymouse1995

yeah im just confused how i go from a network to a matrix...

Reply 5

Slowbro93

Original post by mickymouse1995

yeah im just confused how i go from a network to a matrix...

I would recommend this link. This may be able to clear some stuff for you :smile:

https://www.khanacademy.org/math/linear-algebra/alternate_bases/eigen_everything/v/linear-algebra-introduction-to-eigenvalues-and-eigenvectors

Reply 6

mickymouse1995

sooooo confused....

I have been asked to define eigenvector centrality in as much detail as necessary to calculate it in practical examples...

i have no idea what this means.....

Reply 7

Slowbro93

Original post by mickymouse1995

sooooo confused....

I have been asked to define eigenvector centrality in as much detail as necessary to calculate it in practical examples...

i have no idea what this means.....

Found this page: http://en.wikipedia.org/wiki/Centrality

Didn't do any networks in my undergrad so can't help with the application. Sorry :frown:

Reply 8

ghostwalker

Original post by mickymouse1995

sooooo confused....

I have been asked to define eigenvector centrality in as much detail as necessary to calculate it in practical examples...

i have no idea what this means.....

Not something I've studied, but in case it's of any use:

There is an algorithm for eigenvector centrality (google), which is basically choose a starting vector, e.g. (1,1,...,1), apply adjacency matrix, scale the result, repeat until there is no change.