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On Sun, Feb 08, 2015 at 12:02:44AM +0000, Thomas William Valente wrote:
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> 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 mos!
> t popular.
> UCINET readily provides these measures.
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.
[ 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 -- ]
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