20bits - Latest Comments in Graph Theory: Part III (Facebook)

Re: Graph Theory: Part III (Facebook)

Dharmalingam Ganesan — Sat, 09 Jul 2011 14:30:42 -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.

Re: Graph Theory: Part III (Facebook)

Dharmalingam Ganesan — Sat, 09 Jul 2011 13:42:43 -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 squeezes the size of v). The eigenvalue just denotes the scale (lambda).

Re: Graph Theory: Part III (Facebook)

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Re: Graph Theory: Part III (Facebook)

Guest — Sat, 23 Apr 2011 22:19:16 -0000

Whoa, that's a lot of math there, math boy! That's what I'm going to call you from now on! Math boy!

Re: Graph Theory: Part III (Facebook)

Scott Biggs — Wed, 27 Oct 2010 06:49:02 -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.

Re: Graph Theory: Part III (Facebook)

leocel — Mon, 12 Jul 2010 22:28:21 -0000

can i have some example of influence graph please?

Re: Graph Theory: Part III (Facebook)

data recovery — Wed, 26 May 2010 09:14:58 -0000

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

Re: Graph Theory: Part III (Facebook)

Jesse — Tue, 25 Dec 2007 03:00:28 -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.

Re: Graph Theory: Part III (Facebook)

Coder — Thu, 20 Dec 2007 17:50:33 -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.

Re: Graph Theory: Part III (Facebook)

Microphone — Tue, 27 Nov 2007 14:19:28 -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.

Re: Graph Theory: Part III (Facebook)

Jawad Shuaib — Fri, 09 Nov 2007 11:42:35 -0000

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

- Jawad Shuaib

Re: Graph Theory: Part III (Facebook)

Michael Bierbauer — Tue, 06 Nov 2007 10:39:45 -0000

I was looking for a concise description of, and applications for graph theory for, a Discrete Mathematics course that I am teaching in the spring. The students are advanced high school students.

Your blog is a great place for them to start to get an overview and begin to appreciate what they are about to learn.

Thanks.