Comparing Networks of Different Size

There was a good discussion on the Political Networks listserve last week on how to compare networks of different sizes.  Here are some of the comments.

Wojciech Gryc (wojciech@gmail.com) wrote:

A few papers I’ve explored when dealing with a similar question:

  1. “Comparing Networks Across Space and Time, Size and Species”, by Faust and Skvoretz, 2002.
  2. “Network Motifs: simple building blocks of complex networks”, by Milo et al., 2002.
  3. “Correlation profiles and motifs in complex networks”, by Maslov et al., 2003. (In the Handbook of Graphs and Networks.)

The common theme behind all these papers is that you build a (mathematical, statistical) model of what your network is expected to look like, in terms of number of different types of dyads, triads, and other subgraph structures… Then you compare to see if the networks you have in your data set are statistically significantly different from what is expected in the statistical / mathematical model.

Mason Alexander Porter (porterm@MATHS.OX.AC.UK) wrote:

One thing to do is to also compute the relevant quantities for a random network (using an appropriate null model) of the sizes to see how those quantities scale with size.  Another thing to do is use permutation tests.

Valdis Krebs (valdis@orgnet.com) wrote:

We normalize all network metrics in InFlow, yet it does not adjust well for all metrics.   A 1% density in a thousand node network is normal, but is not prevalent in a 100 node network.  Normalizing works well if the networks are close in size… again, a 0.333 betweenness  may be found in a 70 node network,  but is not likely to be found in a 700 node network.

Carter T. Butts (buttsc@uci.edu) wrote:

See B.S. Anderson et al., “The Interaction of Size and Density with Graph Level Indices,”  Social Networks, 21(3), 239-267.  If you happen to use the sna library for R, you can perform certain tests of difference for GLIs between graphs of different sizes using cugtest(), by setting FUN=gliop (see the cugtest and gliop help for more details).  In other packages, procedures may vary.

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