Comments on: Graph Theory: Part III (Facebook)

By: Dharmalingam Ganesan

Dharmalingam Ganesan — Sat, 09 Jul 2011 18:30:00 +0000

This is a lot of fun. One suggestion: Think the article did not explain what is the meaning of “small” and “large” here: If λ is small then the CEO has a lot of influence, if it is large then he has little.
Also, after computing the principal eigenvector, how to interpret it in terms of influence is not elaborated yet.

By: Dharmalingam Ganesan

Dharmalingam Ganesan — Sat, 09 Jul 2011 17:42:00 +0000

Geometric interpretation of Eigenvalues: When we multiple a matrix with a vector (i.e., A.v), we are transforming the vector v into a new position. If the transformation preserves the original direction of v, then the vector v is an eigenvector. It is possible that the transformation could have scaled the vector v (either extends or squeeze the size of v). The eigenvalue just denotes the scale (lambda).

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By: Scott Biggs

Scott Biggs — Wed, 27 Oct 2010 08:49:02 +0000

Very interesting, thank you! But I have always had difficulty with the Eigenvalues. The main problem is the lambda value. Because some people share more influence than others, thus each person has their own lambda value.

Making your first lambda formula:

Ie(CEO) = 1/lambda(CEO) * [Ie(VP1) + Ie(VP2) + Ie(VP3) + Ie(VP4)]

Since the lambda value is not constant, it makes vectorization very difficult, but that's not the hard part: we're once again trying to ascertain information about an individual, but this time it's the lambda value instead of the influence. We've just moved things down the tube just to be stuck again.

By: leocel

leocel — Tue, 13 Jul 2010 00:28:21 +0000

can i have some example of influence graph please?

By: data recovery

data recovery — Wed, 26 May 2010 11:14:58 +0000

A great and compact presentation of graph theory fundamentals. Keep up the good work

By: Jesse

Jesse — Tue, 25 Dec 2007 08:00:28 +0000

Coder,

I didn’t mean connectivity in any technical sense, but yes, the vertex connectivity of that graph is 1.

I meant “connectivity” only as shorthand to talk about that nodes potential to transmit messages through the graph.

By: Coder

Coder — Thu, 20 Dec 2007 22:50:33 +0000

On your second graph, “single person low degree but high connectivity” doesn’t the graph have a vertex connectivity = edge connectivity = 1? I’m not sure if you meant high eccentricity. Maybe I’m missing something.

Anyways, I thoroughly enjoy your mathematically approach to facebook’s problems. I try to find ways that I can apply graph theory to the world around me.

By: Microphone

Microphone — Tue, 27 Nov 2007 19:19:28 +0000

This is awesome. I had a linear algebra for in my computer science class. I never find it interesting not was it useful. But now, I am happy that I took that class because I can understand what you are talking about and how we can use this to apply programming.

By: Jawad Shuaib

Jawad Shuaib — Fri, 09 Nov 2007 16:42:35 +0000

This is awesome material I can read during my spare time and apply at workplace. Thank you for the entire series!

- Jawad Shuaib