From 8b750e01b022ec9066daa9ee4e618e11db6cab10 Mon Sep 17 00:00:00 2001 From: Ryan Gibson Date: Sat, 1 Jun 2024 13:06:02 -0400 Subject: [PATCH] Add basic documentation on multilayer topologies This closes https://github.com/ragibson/ModularityPruning/issues/12. --- utilities/parameter_estimation_utilities.py | 12 ++++++++++++ 1 file changed, 12 insertions(+) diff --git a/utilities/parameter_estimation_utilities.py b/utilities/parameter_estimation_utilities.py index 34b94e8..8daff0a 100644 --- a/utilities/parameter_estimation_utilities.py +++ b/utilities/parameter_estimation_utilities.py @@ -534,6 +534,18 @@ def prune_to_multilayer_stable_partitions(G_intralayer, G_interlayer, layer_vec, parameter estimates are within the provided ``gamma_start``, ``gamma_end``, ``omega_start``, and ``omega_end`` bounds. + There are three network layer topology models available, all from Pamfil et al. + + * **"temporal"**: Interlayer edges always connect copies of a node from one layer to the next, often representing + interactions that change over time. + * **"multilevel"**: Interlayer edges connect a hierarchy of monolayer networks from one layer to the next. This is + more general than temporal networks, as nodes can connect arbitrarily to nodes in the next layer. These often + represent inclusion relationships, such as cities to counties, counties to states, and states to countries. + * **"multiplex"**: Each layer represents a type of interaction, making the entire multilayer network akin to an + edge-colored multigraph (each type of edge has its own layer). This model is unique in that there is no natural + ordering of layers, and the resulting theory requires some analytical simplifications, making the resulting + parameter estimation the least robust of the three models. + See https://doi.org/10.1038/s41598-022-20142-6 for more details. NOTE: This method truncates omega estimates to ``omega_end - 1e-3`` in order to properly identify stable partitions