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On 12-01-2016 11:36, LEVALLOIS Clément wrote:
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> 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.

Vladimir Batagelj
  IMFM - Institute of Mathematics, Physics and Mechanics
  Jadranska 19, 1000 Ljubljana, Slovenia
  University of Primorska, Andrej Marušič Institute, Koper
T: +386 1 4766 672

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