meme-orooni

[j4]

And another one. This cliques one makes no sense:

I am a member of 5 cliques of size 16

• j4, lnr, ewx, fanf, crazyscot, acronym, mobbsy, timeplease, kaet, ceb, emperor, senji, angoel, meirion, simont, cjwatson


• j4, lnr, ewx, fanf, crazyscot, acronym, mobbsy, timeplease, kaet, ceb, emperor, senji, angoel, meirion, simont, sion_a


• j4, lnr, ewx, fanf, crazyscot, acronym, mobbsy, timeplease, kaet, ceb, emperor, senji, angoel, simont, cjwatson, rmc28


• j4, lnr, ewx, fanf, crazyscot, acronym, mobbsy, timeplease, kaet, ceb, emperor, senji, simont, cjwatson, rmc28, mpinna


• j4, lnr, ewx, fanf, crazyscot, acronym, mobbsy, timeplease, kaet, emperor, senji, angoel, meirion, simont, sion_a, dreamingchristi

Find the largest clique containing:

(Enter your livejournal username here).

How are these my "cliques"? Some of them contain people I haven't spoken to for over a year.

Comments

[sparrowsion]

"Clique" in the mathematical sense of fully interconnected graph.

[rmc28]

They're groups of people who are all on each other's LiveJournal Friends lists. See http://www.livejournal.com/users/hukuma/63723.html for an explanation.

[rysmiel.livejournal.com]

It keeps timing out when I try it, I wonder if the biggest set of cross-connecting people for me is too big for it to evaluate.

[bopeepsheep.livejournal.com]

Same here - when I have got something approximating a result it's never been full enough to do anything with. (I got the same with the 'best friend' meme - clearly a big friends list is a disadvantage.)

[liv]

I got it to work for you. (I was trying because I was looking for a clique bigger than mine, and thought you were a likely candidate.) To my surprise it only came up with 11s, and only a couple at that. I should have thought of j4; luckily she posted the meme! It is slow and I'm not at all surprised it's timing out.

I also don't know how far to trust its negatives. I don't understand what it's doing well enough to know whether it is likely to miss cliques.

[ewx.livejournal.com]

The number of combinations to check is exponential in the number of nodes; you have over 50 mutual friends which is pretty clearly more than it can check in anything even vaguely approaching a reasonable period of time, so I would say it is practically guaranteed to miss some.

[kaet.livejournal.com]

Mathematicians (perhaps unfortunately) have an idea of a "clique" (they only borrowed the word, usually the cliques in question are things like telephone exhanges or girders). That kind of clique is a set of nodes in a graph where all nodes are connected to all others. A pentagram in a circle is the clique of size 5, each of the five nodes connected to the four others, and so on. So in each of the cliques listed, everyone is friends with each other.

If you take the top two, they're the same except one contains Colin and the other contains Sion. The only way that can happen is that all the links for a clique of size 17 are there except Colin and Sion are not mutual friends.

The core of all five of those cliques, in all five is: j4, lnr, ewx, fanf, crazyscot, acronym, mobbsy, timeplease, kaet, emperor, senji, simont. The other nodes are almost completely connected to this core, or are completely connected to it, but to few other people who are almost completely connected to it: ceb, angoel, meirion, simont, cjwatson, sion_a, rmc28, mpinna, dreamingchristi.

I doubt it tells you much about real social networks, or of "cliques" as we know and love the word, without much more processing and real-world knowledge.

[ewx.livejournal.com]

I think it's slightly naughty of the originator to use a technical term which also has a relevant real-world meaning without any marking (even the 'how it works' link doesn't state the definition). Hardly a failing exclusive to users of mathematical terminology, though.

[cjwatson]

If you take the top two, they're the same except one contains Colin and the other contains Sion. The only way that can happen is that all the links for a clique of size 17 are there except Colin and Sion are not mutual friends.

50% of which is an oversight on my part, now corrected :-)

[lnr]

Still need the other 50% though :-)