<p>Work by Leskovec, Kleinberg, and Faloutsos has examined this question specifically [<a href="http://www.cs.cmu.edu/afs/cs/Web/People/jure/pubs/powergrowth-kdd05.pdf" rel="nofollow">1</a>,<a href="http://arxiv.org/pdf/physics/0603229.pdf" rel="nofollow">2</a>]. They find:</p>

<blockquote>
  <p>"First, graphs densify over time, with the number of edges crowing super-linearly in the number of nodes. Second, the average distance between nodes often shrinks over time, in contrast to the conventional wisdom that such distance parameters should increase slowly as a function of the number of nodes."</p>
</blockquote>
Any ideas about the variation of the diameter of a network/graph as the number of nodes increases?
<p>My question is with regard to the increase/decrease of the diameter of a network. I'm thinking that as one adds more nodes to an existing network, the density should effectively increase and the probability of the edges created by the new nodes could result in higher degree of clustering. If this is the case, my assumption is that the diameter of the network should decrease as we add more nodes, owing to the probability that shorter geodesic paths can now exist and become the new diameter. Am I wrong with this logic? Or is there a better explanation or perhaps something I'm missing?</p>