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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:


Some variations on the proposed widespread measure

  W  = |U  union N(U)| / |V|

1. option - consider also the size of set U

  W1  = (|U  union N(U)| . |U|) / | V |**2

attains its maximum value 1 iff U = V.

2. option - dominating set 

  W2  = (|U  union N(U)| . |V setminus U|) / (|V|.(|V|-1))

attains its maximum value 1 iff U is the center of a star (a single node
linked to all other nodes).

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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