average degree

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devide sum of degrees by number of nodes \[ \bar d_G = \frac{1}{n}\sum_V\text{deg}_Gv \] or equivalently, \[ \bar d_G = \frac{2m}{n} \]

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density of a network G is the quantity \[ \bar e = \frac{m}{C^n_2} \] interpretations are:

  • ratio of existing links and all possible links between all nodes(hence combination of 2 among n elements)
  • normalized average degree, as the definition could be transformed to \[ \bar e = \frac{\bar d_G}{n-1} \]

Author: Linfeng He

Created: 2024-04-03 Wed 23:22