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pitmonticone committed Jan 7, 2023
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Multiple theoretical frameworks have been proposed to formally subsume all instances of multilayer graphs [^1].

Multilayer graphs have been adopted to model the structure and dynamics of a wide spectrum of high-dimensional, non-linear, multi-scale, time-dependent complex systems including physical, chemical, biological, neuronal, socio-technical, epidemiological, ecological and economic networks[^2].
Multilayer graphs have been adopted to model the structure and dynamics of a wide spectrum of high-dimensional, non-linear, multi-scale, time-dependent complex systems including physical, chemical, biological, neuronal, socio-technical, epidemiological, ecological and economic networks [^2].

MultilayerGraphs.jl is an integral part of the [JuliaGraphs](https://github.com/JuliaGraphs) ecosystem extending [Graphs.jl](https://github.com/JuliaGraphs/Graphs.jl) so all the methods and metrics exported by Graphs.jl work for multilayer graphs, but due to the special nature of multilayer graphs the package features a peculiar implementation that maps a standard integer-labelled vertex representation to a more user-friendly framework exporting all the objects an experienced practitioner would expect such as nodes ([`Node`](@ref)), vertices ([`MultilayerVertex`](@ref)), layers ([`Layer`](@ref)), interlayers ([`Interlayer`](@ref)), etc.

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configuration_multilayergraph = MultilayerGraph(empty_layers, empty_interlayers, truncated(Normal(10), 0.0, 20.0));
```

Note that this is not an implementation of a fully-fledged configuration model, which would require to be able to specify a degree distribution for every dimension of multiplexity. Moreover, it stil lacks the abilty to specify a minimum discrepancy (w.r.t. a yet-to-be-chosen metric) between the empirical distributions of the sampled sequence and the provided thorietical disribution. Please refer to [Future Developments](@ref).
Note that this is not an implementation of a fully-fledged configuration model, which would require to be able to specify a degree distribution for every dimension of multiplexity. Moreover, it still lacks the ability to specify a minimum discrepancy (w.r.t. a yet-to-be-chosen metric) between the empirical distributions of the sampled sequence and the provided theoretical distribution. Please refer to [Future Developments](@ref).

There is a similar constructor for `MultilayerDiGraph` which requires both the indegree distribution and the outdegree distribution. Anyway due to current performance limitations in the graph realization algorithms, it is suggested to provide two "similar" distributions (similar mean or location parameter, similar variance or shape parameter), in order not to incur in lengthy computational times.

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8. Artime et al. (2022) [Multilayer Network Science: From Cells to Societies](https://doi.org/10.1017/9781009085809). *Cambridge University Press*;
9. De Domenico (2022) [Multilayer Networks: Analysis and Visualization](https://doi.org/10.1007/978-3-030-75718-2). *Springer Cham*.

[^1]: [De Domenico et al. (2013)](https://doi.org/10.1103/physrevx.3.041022); [Kivelä et al. (2014)](https://doi.org/10.1093/comnet/cnu016); [Boccaletti et al. (2014)](https://doi.org/10.1016/j.physrep.2014.07.001); [Lee et al. (2015)](https://doi.org/10.1140/epjb/e2015-50742-1); [Aleta and Moreno (2019)](https://doi.org/10.1146/annurev-conmatphys-031218-013259); [Bianconi (2018)](https://doi.org/10.1093/oso/9780198753919.001.0001); [Cozzo et al. (2018)](https://doi.org/10.1007/978-3-319-92255-3); [Artime et al. (2022)](https://doi.org/10.1017/9781009085809); [De Domenico (2022)](https://doi.org/10.1007/978-3-030-75718-2)
[^1]: [De Domenico et al. (2013)](https://doi.org/10.1103/physrevx.3.041022); [Kivelä et al. (2014)](https://doi.org/10.1093/comnet/cnu016); [Boccaletti et al. (2014)](https://doi.org/10.1016/j.physrep.2014.07.001); [Lee et al. (2015)](https://doi.org/10.1140/epjb/e2015-50742-1); [Aleta and Moreno (2019)](https://doi.org/10.1146/annurev-conmatphys-031218-013259); [Bianconi (2018)](https://doi.org/10.1093/oso/9780198753919.001.0001); [Cozzo et al. (2018)](https://doi.org/10.1007/978-3-319-92255-3); [Artime et al. (2022)](https://doi.org/10.1017/9781009085809); [De Domenico (2022)](https://doi.org/10.1007/978-3-030-75718-2).

[^2]: [Cozzo et al. (2013)](https://doi.org/10.1103/physreve.88.050801); [Granell et al. (2013)](https://doi.org/10.1103/physrevlett.111.128701); [Massaro and Bagnoli (2014)](https://doi.org/10.1103/physreve.90.052817); [Estrada and Gomez-Gardenes (2014)](https://doi.org/10.1103/physreve.89.042819); [Azimi-Tafreshi (2016)](https://doi.org/10.1103/physreve.93.042303); [Baggio et al. (2016)](https://doi.org/10.1073/pnas.1604401113); [DeDomenico et al. (2016)](https://doi.org/10.1038/nphys3865); [Amato et al. (2017)](https://doi.org/10.1038/s41598-017-06933-2); [DeDomenico (2017)](https://doi.org/10.1093/gigascience/gix004); [Pilosof et al. (2017)](https://doi.org/10.1038/s41559-017-0101); [de Arruda et al. (2017)](https://doi.org/10.1103/physrevx.7.011014); [Gosak et al. (2018)](https://doi.org/10.1016/j.plrev.2017.11.003); [Soriano-Panos et al. (2018)](https://doi.org/10.1103/physrevx.8.031039); [Timteo et al. (2018)](https://doi.org/10.1038/s41467-017-02658-y); [Buldú et al. (2018)](https://doi.org/10.1162/netn_a_00033); [Lim et al. (2019)](https://doi.org/10.1038/s41598-019-39243-w); [Mangioni et al. (2020)](https://doi.org/10.1109/tnse.2018.2871726); [Aleta et al. (2020)](https://doi.org/10.1038/s41562-020-0931-9); [Aleta et al. (2022)](https://doi.org/10.1073/pnas.2112182119))
[^2]: [Cozzo et al. (2013)](https://doi.org/10.1103/physreve.88.050801); [Granell et al. (2013)](https://doi.org/10.1103/physrevlett.111.128701); [Massaro and Bagnoli (2014)](https://doi.org/10.1103/physreve.90.052817); [Estrada and Gomez-Gardenes (2014)](https://doi.org/10.1103/physreve.89.042819); [Azimi-Tafreshi (2016)](https://doi.org/10.1103/physreve.93.042303); [Baggio et al. (2016)](https://doi.org/10.1073/pnas.1604401113); [DeDomenico et al. (2016)](https://doi.org/10.1038/nphys3865); [Amato et al. (2017)](https://doi.org/10.1038/s41598-017-06933-2); [DeDomenico (2017)](https://doi.org/10.1093/gigascience/gix004); [Pilosof et al. (2017)](https://doi.org/10.1038/s41559-017-0101); [de Arruda et al. (2017)](https://doi.org/10.1103/physrevx.7.011014); [Gosak et al. (2018)](https://doi.org/10.1016/j.plrev.2017.11.003); [Soriano-Panos et al. (2018)](https://doi.org/10.1103/physrevx.8.031039); [Timteo et al. (2018)](https://doi.org/10.1038/s41467-017-02658-y); [Buldú et al. (2018)](https://doi.org/10.1162/netn_a_00033); [Lim et al. (2019)](https://doi.org/10.1038/s41598-019-39243-w); [Mangioni et al. (2020)](https://doi.org/10.1109/tnse.2018.2871726); [Aleta et al. (2020)](https://doi.org/10.1038/s41562-020-0931-9); [Aleta et al. (2022)](https://doi.org/10.1073/pnas.2112182119)).

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