Distributions of Node Size

Power law: P(k links) proportional to k-g
  for some positive g

g is about 2.1 for the World Wide Web
  new nodes prefer to link to large nodes

Modified power law with cutoff for networks with limited nodes
  human acquaintanceship network, limited capacity and life

Exponential law: P(k links) proportional to a-k
  for some a > 1.0
  e.g., neural network of C. elegans

Irregular networks have small diameter with any of these laws