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This concept needs to define "friendship" in connections/nodes to have any merit at all
It purposes plays of the nebulousness between "friendship" being a one or two way connection. I am a proponent for deletion of this article.
- On the contrary, it explicitly assumes (for the purposes of mathematical modeling) that it is only a two way connection and, rather than being nebulous, consists of rigorously proven mathematics. What reason do you have for thinking it should be deleted? —David Eppstein (talk) 20:24, 27 August 2013 (UTC)
Friendship paradox explanation
I would like the following comment regarding the "solution" of the paradox:
The paradox is not explained as described because if one thinks that it is more likely to be friends with someone who has more friends, the same thinking will be also done by that someone! So that sort of thinking is self-contradictory! —Preceding unsigned comment added by Alsims (talk • contribs) 11:11, 18 August 2010 (UTC)
- It's not a contradiction, because it's only true in general. There will be individuals whose friends have fewer friends than they have, but there will be many more whose friends have more friends than they have. MartinPoulter (talk) 12:42, 18 August 2010 (UTC)
I think it would help to make it clearer if the article had one image (or more) showing how most people in a sample can have less friends than their friends. --TiagoTiago (talk) 00:39, 25 October 2011 (UTC)
- Couldn't agree more, this is practically screaming for a graph. --188.8.131.52 (talk) 18:55, 7 January 2012 (UTC)
Examples where the law fails?
Right now the article makes the following claim: "there exist undirected graphs (such as the graph formed by removing a single edge from a large complete graph) that are unlikely to arise as social networks but in which most vertices have higher degree than the average of their neighbors' degrees." I don't believe this is true. It certainly contradicts the formula above, because mu and sigma are positive. Can someone provide an example where this statement is true? --keepinitraw, 29 February 2012 —Preceding undated comment added 17:48, 29 February 2012 (UTC).
- A very explicit example is given in the sentence that you quoted. Let G have n vertices, with one pair st not connected and all other pairs of vertices connected, and with n ≥ 5. Then most vertices have degree n-1 and their neighbors have average degree ((n-3)(n-1)+2(n-2))/(n-1) < n-1. The only two vertices for which this is not true are s and t. —David Eppstein (talk)
I see, however, some holes in here
First of all, this paradox is driven, by the assumption that there is such a thing as "friend of a friend", thus: a friend in the second degree; this is - of course - wishful thinking. Most second degree, or third degree 'friends' we rarely have contact with. The assumption of 'mutual friendship' is also hypothetic; this need not be the case.
Second, this - mathematical - phenomenon is highly influenced by the possibility of one individiual having many friends: this is explained by 'so-called' popularity; this also - of course - a very hypothetic assumption. Most people with large networks have very few real friends, to be realistic.
In short: we are considering mathematical proportions of unbalanced networks; we are talking about nodes, not real friends. So we must skip the philosophical bit; we are not talking about real people, we are talking about nodes, and degrees. We are not talking about real friendships here.
We are talking about the behaviour of networks, formed by Social Media, not Social Behaviour. That is the real paradox, here.
Misuse of phrase "average person"
Does anyone see a difference between the phrases "Average number of friends" and "Average person's number of friends"..? Given:
- Larry has 1 friend
- Curly has 2 friends
- Moe has 6 friends
The average number of friends is (1+2+6)/3=3. The average person is Curly, who has 2 friends; thus the average person has 2 friends.
When I saw this on a slate.com article, it read "most people have fewer friends than their friends," which is ambiguous. The whole "paradox" is built up from a misunderstanding of the best metric for the situation, which is median rather than mean.
Who's with me?
"In everyday language, we use the word "average" to mean "most people," or the most representative person (as in, "The average person doesn't read classic literature" or "The average Joe can't afford to dress like Prince"). But then when they start using the word "average" to talk about statistics, you get weird results, like the fact that 67 percent of people in the USA make less than the "average" income."
- Your use of "average" conflates arithmetic mean (as in "average number") and "median" (as in "average person"). Please note that the paradox talks about "most", which refers to mode (statistics). Paradoctor (talk) 05:31, 17 January 2014 (UTC)