tag:blogger.com,1999:blog-6314876008291942531.post8194826145704649220..comments2024-01-14T00:36:43.430-08:00Comments on Antonio Gulli's coding playground: Six degree of separation and Facebook studyUnknownnoreply@blogger.comBlogger5125tag:blogger.com,1999:blog-6314876008291942531.post-37794447920671766462011-12-01T01:13:17.916-08:002011-12-01T01:13:17.916-08:00This smells like a mix of random walk with restart...This smells like a mix of random walk with restart (reset probability), plus a non uniform jump distribution modelling how close I estimate are my target and the men in the middle (P). The probability of fwd the message can be probably described by using a sigmoid function like in neural networks (the activation intuition is probably the same). Just my 2cents. Btw, Max is the guy for estimating P. I know, I see a ranking problem everywherecodingplaygroundhttps://www.blogger.com/profile/08478993186814330588noreply@blogger.comtag:blogger.com,1999:blog-6314876008291942531.post-24761306938946118622011-12-01T01:13:04.960-08:002011-12-01T01:13:04.960-08:00Paolo: Yes, actually this is a realistic model of ...Paolo: Yes, actually this is a realistic model of what probably happens in reality; it would be cool to find some way to experiment how close it is to what actually takes placcodingplaygroundhttps://www.blogger.com/profile/08478993186814330588noreply@blogger.comtag:blogger.com,1999:blog-6314876008291942531.post-24258661711149912392011-11-30T22:57:30.606-08:002011-11-30T22:57:30.606-08:00Paolo, thanks a lot for your detailed explanation....Paolo, thanks a lot for your detailed explanation. I agree that your measure is the shortest path distance in the acquaintance graph, and this can be also seen as the 'routing distance' in this graph (btw similar to OSPF routing protocol).<br /><br />Probably my understanding of Milgram's work is just uneducated or driven by the empirical intuition that there is a non zero cost c of carrying the message, or a non zero probability p to drop it. Sometime you don't know who can be a potential target, or a good man in the middle for routing the message, sometime you are too lazy to go to the post office to send the letter, sometime you don't have a stamp, sometime you don't want to disturb your near-friends. In these cases, I would model a reset probability that in case of drop would restart and inject a new message in the system. In other words, there is some measure of Uncertancy that would make the model closer to the intuition.<br /><br />Think about routing a message in LinkedIn and asking to one of your friend to forward the message to someone you want to contact and they know directly. They may drop the message and you need to start again.<br /> <br />In any case, I understand that this would give a different measure and your measure is actually a lower bound of it.codingplaygroundhttps://www.blogger.com/profile/08478993186814330588noreply@blogger.comtag:blogger.com,1999:blog-6314876008291942531.post-26978969606501669332011-11-30T00:04:18.966-08:002011-11-30T00:04:18.966-08:00I can! Actually, Milgram's experiment was for ...I can! Actually, Milgram's experiment was for us only a source of inspiration, but clearly what we did and what Milgram did are quite different things (we try to make this clear straight from the introduction).<br />If you read carefully Milgram's work, it seems evident (at least, to me) that what he WANTED to do was actually measuring shortest-path distances in an acquaintance graph: let me (at least for the time being) assume that we all agree on what "acquaintance" means and let us think that "acquaintance" in life is the same as in fb.<br />In this view, what we did is precisely what Milgram wanted to do.<br /><br />Reading his papers (and the papers that inspired his work, in particular the one by Rapoport and Horvitz), it is clear that his "experiment" was just an attempt to circumvent the problem of not being able to access acquaintance information directly. <br />This way, he obtained a completely different measure, that I may call "routing distance" and that is, in a sense, much more interesting than simple "shortest-path distance". This is what you are probably thinking of in your note.<br /><br />The mathematical relation between the two measures is clear: ours is a lower bound for his. The practical implications of the two measures are anyway completely different. The problem with Milgram's experiment in the proper sense is that I don't see a way to replicate it without the intervention of human beings, or without a firm mathematically precise notion of "knowledge" or "information" that we currently miss.<br /><br />There is still one point that is worth being discussed: the existence non-completed chains.<br />In our setting, non-completed chains do not exist, at least as long as the graph is connected; in Milgram's experiment most of the chains where uncompleted (more than 2/3). He spends many pages to try to understand why those chains stopped at some point. Well, the bare truth is that we will never know, but the explanation is probably of larger interest to sociologists than it is to me. I can make thousands wild guesses, probably all of them wrong.Paolohttps://www.blogger.com/profile/13310238923650038234noreply@blogger.comtag:blogger.com,1999:blog-6314876008291942531.post-602223629870263062011-11-29T23:35:13.655-08:002011-11-29T23:35:13.655-08:00My understanding (as usually uneducated :) in the ...My understanding (as usually uneducated :) in the FB case these "degrees" are simply an statistical estimation of the graph diameter and nothing else.MaxGubinhttps://www.blogger.com/profile/02398899442487152363noreply@blogger.com