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Re: How to measure the distribution of an attribute among the nodes of a network?

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Tue, 12 Jan 2016 12:18:36 +0100

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 ```***** To join INSNA, visit http://www.insna.org ***** On 12-01-2016 11:36, LEVALLOIS Clément wrote: > ***** To join INSNA, visit http://www.insna.org ***** > > Dear List members, > > I need to have a measure of how widespread is the distribution of a > node attribute in a network. Let me explain: > > My nodes have a textual attribute, let's say "preferred flavor for ice > cream" > > I would like to know to what extent the flavor "raspberry" is a value > which is evenly distributed in the network, or to the contrary, just > found in one community. A low value would mean that only nodes from a > subregion of the network have this taste, a higher value would show an > even distribution of the value across the whole network. I imagine > that a difficulty is to account for the frequency of the attribute: if > many nodes of the network have "raspberry" for the value of the > attribute, it will tend to make this value distributed more widely.    A possible measure could be the following:    let V be the set of nodes and U the set of nodes with given    attribute value. Then we define the widespread of attribute as       W = | U union N(U) | / | V |    where N(U) is the set of nodes neighboring some node of U .    | | denotes the cardinality (number of elements) of the set.    Vlado -- Vladimir Batagelj   IMFM - Institute of Mathematics, Physics and Mechanics   Jadranska 19, 1000 Ljubljana, Slovenia and   University of Primorska, Andrej Marušič Institute, Koper T: +386 1 4766 672 W: http://vladowiki.fmf.uni-lj.si/doku.php?id=vlado _____________________________________________________________________ SOCNET is a service of INSNA, the professional association for social network researchers (http://www.insna.org). To unsubscribe, send an email message to [log in to unmask] containing the line UNSUBSCRIBE SOCNET in the body of the message.```