Tailored graph ensembles as proxies or null models for real networks II: results on directed graphs
New mathematical tools quantify the topological structure of large directed networks which describe how genes interact within a cell.
Journal of Physics A 44, 275002 (2011)
E. Roberts, T. Schlitt, A. Coolen

We generate new mathematical tools with which to quantify the macroscopic topological structure of large directed networks. This is achieved via a statistical mechanical analysis of constrained maximum entropy ensembles of directed random graphs with prescribed joint distributions for in- and out-degrees and prescribed degree–degree correlation functions. We calculate exact and explicit formulae for the leading orders in the system size of the Shannon entropies and complexities of these ensembles, and for information-theoretic distances. The results are applied to data on gene regulation networks.
More in Intelligence of graphs
Exactly solvable random graphs
An explicit analytical solution reproduces the main features of random graph ensembles with many short cycles under strict degree constraints.
Entropies of graph ensembles
Explicit formulae for the Shannon entropies of random graph ensembles provide measures to compare and reproduce their topological features.
Unbiased randomization
Unbiased randomisation processes generate sophisticated synthetic networks for modelling and testing the properties of real-world networks.
Spin systems on Bethe lattices
Exact equations for the thermodynamic quantities of lattices made of d-dimensional hypercubes are obtainable with the Bethe-Peierls approach.
Random graphs with short loops
The analysis of real networks which contain many short loops requires novel methods, because they break the assumptions of tree-like models.