[igraph] Generation of Random Graphs According to Some Rules

[Lorenzo Isella]

Dear All,
I would like to test the features of a real network against some null 
models, meant as random network sharing only some statistical properties 
of the real network. Below you find a list of quantities of interest 
whose distribution should be preserved by the igraph-generated network

(1) The random network should have a given P(k) [this question of mine 
was actually answered on the mailing list some time ago]

In addition to (1), I would like each time one of the following 
properties of the original graph to be preserved in the randomized network

(2) the average nearest neighbor degree distribution k_nn(k) or
(3) the vertex betweenness distribution or
(4) the local transitivity coefficient distribution (also called 
clustering coefficient distribution) or
(5) the neighborhood distribution (loosely speaking), meant as the 
number of nodes I can reach by making n steps from any node in the graph

I have no idea of how to deal with requirements (2) to (5) [it does not 
sound trivial to me] hence any suggestion is really appreciated.
Many thanks

Lorenzo