Graph sampling algorithms from the paper 'Constraints and spandrels of interareal connectomes'.
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README.md
loop_sa.c
mleme_constraint_model.m
rand_mt.c
simann_constraint_model.m

README.md

cnm-code

Graph sampling algorithms from Rubinov (2016) Constraints and spandrels of interareal connectomes. Nature Communications 7 13812. See the matlab files for detailed help and contact Mika Rubinov (rubinovm at janelia.hhmi.org) for additional questions or suggestions.

simann_constraint_model.m: Constrained randomization of empirical networks mleme_constraint_model.m: Exact maximum-likelihood estimation of maximum-entropy/exponential random-graph models
Type of sampling Uniform sampling of networks with hard constraints: the constraints are satisfied with high accuracy for each individual sampled network. Unbiased sampling of networks with soft constraints: the constraints are satisfied on average for the network ensemble, but not, in general, for each individual network.
Method of sampling Specification of constraint-error function, and sampling of individual networks via numerical minimization (with simulated annealing) of this function. Maximum-likelihood estimation of network probability distribution by numerical solution of systems of nonlinear equations, and sampling of individual networks directly from this distribution.
Type of constraints Weighted and binary node-strength, module-weight, and wiring-cost constraints. In addition, all empirical connection weights are automatically preserved. Weighted node-strength and module-weight constraints. Empirical connection weights are not preserved.
Accuracy A small normalized constraint error. Constraint errors are guaranteed to vanish in the limit of the full network ensemble.
Disadvantages Uniform sampling is possible but not formally guaranteed. Sampled distributions may not be representative of target distributions.
Implementation mex file called from a matlab wrapper (the mex file needs to be compiled once before execution). Native matlab implementation (requires the optimization toolbox).