title: Correct way to standardize/scale/normalize multiple variables following power law distribution for use in linear combination
body: <p>I'd like to combine a few metrics of nodes in a social network graph into a single value for rank ordering the nodes:     </p>
  
  <p><code>in_degree + betweenness_centrality = informal_power_index</code></p>
  
  <p>The problem is that <code>in_degree</code> and <code>betweenness_centrality</code> are measured on different scales, say 0-15 vs 0-35000 and follow a power law distribution (at least definitely not the normal distribution)</p>
  
  <p>Is there a good way to rescale the variables so that one won't dominate the other in determining the <code>informal_power_index</code>?  </p>
  
  <p>Three obvious approaches are:</p>
  
  <ul>
  <li>Standardizing the variables (subtract <code>mean</code> and divide by <code>stddev</code>). This seems it would squash the distribution too much, hiding the massive difference between a value in the long tail and one near the peak.</li>
  <li>Re-scaling variables to the range [0,1] by subtracting <code>min(variable)</code> and dividing by <code>max(variable)</code>. This seems closer to fixing the problem since it won't change the shape of the distribution, but maybe it won't really address the issue?  In particular the means will be different.</li>
  <li>Equalize the means by dividing each value by <code>mean(variable)</code>. This won't address the difference in scales, but perhaps the mean values are more important for the comparison?</li>
  </ul>
  
  <p>Any other ideas?</p>