Models for graphs representing real-life networks I am interested in basic models of graphs (stochastic or deterministic) that are offered for real-life networks (like social networks, the Internet, neuron networks).
I will be thankful for answers that will describe the actual model and not just link to some reference. (Such links can be useful in comments.)
 A: There is considerable work on modeling automobile traffic flows via directed graphs.
One high-level article is

Frank Kelly. "The mathematics of traffic in networks." The Princeton Companion to Mathematics (2008). (PDF download link.)

The graph modeling is not sophisticated: just a directed graph representing
routes between (e.g.) towns.
What is more interesting is modeling driver route choices.
One natural model is to seek a Wardrop equilibrium:
"Only when they cannot find alternative, quicker routes
will drivers not have an incentive to change routes."
The defining characteristic of a Wardrop equilibrium is that,
"if a route $r$ is actively used, then it achieves
the minimum delay over all routes serving its source–destination pair."

The result does not mean that average delays in the
  network will be minimal: a striking illustration of this
  fact is provided by Braess’s paradox.


         


But then Kelly goes on to argue that

with the
  imposition of appropriate tolls, it is possible for the
  self-interested behavior of drivers to lead to an equilibrium
  pattern of flow that minimizes total delay.

A: There are different models for terrorist or other criminal networks. I can only give references.
Roy H. A. Lindelauf (Royal Dutch Defense Academy) et al., "The Influence of Secrecy on the Communication Structure of Covert Networks"
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1096057
Steven Brams (New York University) et al., "Influence in Terrorist Networks: From Undirected to Directed Graphs"
http://www.rit.edu/cos/sms/cmmc/literature/Brams_etal_2006.pdf
Jonathan David Farley, "Toward a Mathematical Theory of Counterterrorism"
http://www.rit.edu/cos/sms/cmmc/literature/Proteus.pdf
This model was actually used by the head of Jamaica's National Intelligence Bureau.
Mariagiovanna Baccara and Heski Bar-Isaac (New York University), "How to Organize Crime"
http://apps.olin.wustl.edu/faculty/baccara/crimeRES.pdf
