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Hello,
I have a similar question to what Seok-Woo has asked:  is there any way to compare node level centrality scores, across ego-networks with different sizes and densities?
One approach can be: using ranked centrality scores. For each ego-network, I calculate the centrality scores for all nodes (e.g. betweenness), rank them and then normalize them; the resulted score for each node will be something between 0 and 1.

I am looking for suggestions on this question and the proposed approach. Do you think it is an appropriate way to solve this problem?
Any comment or help is appreciated.
Regards,
Mahin

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Mahin Raissi
PhD Student
Australian Demographic and Social Research Institute (ADSRI)
Coombs 9, Australian National University, ACT 0200, Australia

-----Original Message-----
Sent: Sunday, 8 February 2015 5:14 PM
Subject: Re: [SOCNET] comparing centrality scores across networks

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On Sun, Feb 08, 2015 at 12:02:44AM +0000, Thomas William Valente wrote:
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>
> Seok-Woo
> The major centrality measures, degree, closeness and betweenness, all have a nodal version and a normalized one which corrects for the network size.  For example, degree centrality can be a count of the number of links for each node (the nodal version) and the count divided by network size minus one which is the maximum possible degree score for any network.  This latter measure is the normalized degree centrality and can be compared between different networks and it ranges from zero to one.   If the networks are approximately equal there should be no problem making such comparisons.  However it is conceivable that there is an association between centrality and network size in the sense that it may be possible to have very central nodes in very small networks but unlikely in large ones. For example, a team of 10 people may readily agree who is the most popular or who is a natural leader, but a group of 100 or a 1,000 would have considerably more variability on who is the m!
os!
>  t popular.
> UCINET readily provides these measures.

Hi,

If I can add my humble opinion to the discussion, I would personally refrain, at least in general, from comparing the values of node centrality in different networks. In most of the cases, it is not just a matter of number of nodes. Just to make an example, two nodes may have the same normalised degree centrality in two different networks, but if the two networks have different edge densities then the normalised degree does not tell the whole story. And IMHO a direct comparison of the values of node centralities is even less grounded if we move to eigenvector centrality, betweenness, closeness and so forth, especially when the networks are large, have different sizes/order, and/or heteregeneous degree distributions.

Nevertheless, in some special cases, namely when the networks have exactly the same size because they represent different kinds of relationships among the same actors, comparing the rankings induced by a given centrality measure (not just the bare values) on different networks can be OK.

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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Hello,

I am wondering if I can compare centrality measures across networks. For example, node A from network 1 has a centrality score of 3 and node B from network 2 has a centrality score of 1, (and the two networks are not related and different in size). Can I still conclude that A is more central in network 1 than B is in network 2? Or does this depend on what kinds of centrality we are talking about?

Also, if this conclusion is misleading, is there a normalized centrality score that can be compared across networks? I am hoping someone on this list can help.

Thanks.

==============================
Seok-Woo Kwon
Assistant Professor
Dept. of Strategic Management