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Yep. That's precisely the thought process. Well the sample itself is not a cycle--I was simply trying to get an estimate of the uniqueness of the friend/follower relationships without relying on homophily or clustering, so I wanted to reduce my collected network (as a test) to N nodes with K edges where k in K only occurs once (k is an edge from a to b in N) thinking that this would be a test for uniqueness of edges, but by reducing the network to begin with to that form I reduce it to N nodes, K edges where N=K.

Yep, we're on the same page. It was nonsense to begin with. Thanks for your help.
Joe


-----Original Message-----
From: Vincenzo Nicosia [mailto:[log in to unmask]] 
Sent: Wednesday, July 29, 2015 2:03 PM
To: [log in to unmask]
Cc: [log in to unmask]
Subject: Re: [SOCNET] Estimating Unique Indegree in a Social Media Network

On Wed, Jul 29, 2015 at 05:53:12PM +0000, [log in to unmask] wrote:
> Hi Enzo,
> 
> Thank you very much for your prompt answer, and I guess your answer just made me rethink my question. My network is in closed form (1 component) so I just realized my question is nonsense, because if I assume no node follows more than one other node (thus unique) the number of unique followers would just be n, and the average I'm after would just be n/n which is 1. Sorry!

Hi Joseph,

I dont' know if this is related, but in your original email you said that each node in your graph could follow many other nodes and be followed by many (more) other nodes, hence I assumed that the total number of edges K would be different from the total number of nodes N. Since the twitter "follow" relationship between nodes "a" and "b"
is just binary (i.e., either a follows b, or it does not), the average number of unique followers is equal to the average number of followers, which is equal to the average number of incoming edges in a node (which in turn is equal by definition to the average number of outgoing edges), which in general is K/N.

If in your specific case you have K=N, then your network is simply a cycle or order N, which is a quite unusual Twitter sample :)

My2Cents

Enzo

--
[ Enzo Nicosia - School of Mathematical Sciences - Queen Mary UL ] [ -- v.nicosia [at] qmul.ac.uk -- katolaz [at] yahoo [dot] it -- ] [ -- web @QMUL: http://maths.qmul.ac.uk/~vnicosia/index.html  -- ] [ twitter:@KatolaZ -- jabber:[log in to unmask] - skype: katolaz ]

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