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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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