More specifically, we consider graphs whose edges are associated with a +1, a -1 or a 0 and propose an iterative method to correctly sample a set of four ensembles of signed networks, i.e. those associated with both the free-topology and the fixed-topology versions of the Random Graph Model and the Configuration Model: in the former case, signs are shuffled along with the edges while, in the latter, signs are permuted on a set of connections that, instead, are kept fixed. In words, the benchmarks belonging to the first basket are designed to model situations where agents can choose both with whom and how to interact while the benchmarks belonging to the second basket are designed to model situations where agents can solely choose how to interact. Since our approach relies upon exact maximum-entropy distributions, it is inherently unbiased, even for highly heterogeneous networks.
The binary, undirected, signed models implemented by the present package are introduced and solved in the paper by Gallo, Garlaschelli, Lambiotte, Saracco, Squartini "Testing structural balance theories in heterogeneous signed networks" Comm. Phys. 7, 154 (2024) a summary of which can be found here. For what concerns the theoretical methodology lying at the basis of the entropy-based canonical models, see the paper by Park and Newman "Statistical mechanics of networks" Phys. Rev. E 70, 66117 (2004) and the paper by Squartini and Garlaschelli "Analytical maximum-likelihood method to detect patterns in real networks" New J. Phys. 13, 083001 (2011).