Temporal multilayer network with global relax rates

Data set

A temporal multilayer network. Each layer is a host-parasite bipartite network. Intralayer edges between a parasite species and a host species are the number of parasite individuals divided by the number of host individuals. Interlayer coupling edges connect each physical node to itself in the next layer (e.g., host A in layer 1 to host A in layer 2), and are calculated as the number of individuals in layer l+1 divided by the number of individuals in layer l. They therefore represent population dynamics. Interlayer edges only go one way (l-->l+1) because time flow one way. We represented the undirected edges within each layer as directed edges that go both ways (with the same weight) to be able to have a directed flow. This does not affect the calculation of L. This data set was taken from Pilosof S, Porter MA, Pascual M, Kéfi S. The multilayer nature of ecological networks. Nature Ecology & Evolution. 2017;1: 0101.

Data sets in infomapecology:

# Get data
data("siberia1982_7_links")
data("siberia1982_7_nodes")

Input

A multilayer link-list format. With this format, a random walker moves within a layer and with a given relax rate r jumps to another layer without recording this movement, such that the constraints from moving in different layers can be gradually relaxed. If the *Inter exists, then interlayer edges can be used. However, if a relax rate is also used (Infomap input parameter --multilayer-relax-rate), the interlayer edges are ignored. Here we only include *Intra.

# A network in multilayer format
*Intra
#layer node node weight
1 1 23 0.15853658536585366
1 1 25 0.024390243902439025
1 1 27 0.0975609756097561
... some more cases ...
6 22 63 0.8181818181818182
6 22 67 0.09090909090909091
6 22 77 0.18181818181818182

R Code

The description of functions create_multilayer_object and run_infomap_multilayer in the infomapecology package contains everything you need to know. The for loop performs a sensitivity analysis to examine how structure changes with increasing relax rates.

# Get data
NEE2017 <- create_multilayer_object(extended = siberia1982_7_links, nodes = siberia1982_7_nodes, intra_output_extended = F, inter_output_extended = F)

# Ignore interlayer edges
NEE2017$inter <- NULL

#Run Infomap and return the network's modular structure at increasing relax-rates.
relaxrate_modules <- NULL
for (r in seq(0.001,1, by = 0.0999)){
  print(r)
  modules_relax_rate <- run_infomap_multilayer(NEE2017, relax = T, silent = T, trials = 50, seed = 497294, multilayer_relax_rate = r, multilayer_relax_limit_up = 1, multilayer_relax_limit_down = 0, temporal_network = T)
  modules_relax_rate$modules$relax_rate <- r
  relaxrate_modules <- rbind(relaxrate_modules, modules_relax_rate$modules)
}

Infomap

Under the hood, the function run_infomap_multilayer runs:

./Infomap infomap_multilayer.txt . -2 --seed 497294 -N 50 -i multilayer --multilayer-relax-rate 0.15 --multilayer-relax-limit-up 1 --multilayer-relax-limit-down 0 --silent

Explanation of key arguments:

• -i multilayer indicates a multilayer input format, which is automatically recognised as a multilayer link list (and not as a general link list).
• --multilayer-relax-rate 0.15 defines the relax rate (here 0.15).
• multilayer-relax-limit-up 1 --multilayer-relax-limit-down 0 limits relaxation to a single layer upwards (l to l+1), but never downwards, because time flows one-way.

Output

For multilayer network the output file has a _states suffix, with the following format. This output is as in 5. Temporal multilayer network with interlayer edges.

# path flow name stateId physicalId layerId
1:1 0.000516265 "0" 0 1 1
1:2 0.000211504 "8" 8 44 1
1:3 0.000225137 "19" 19 75 1
1:4 0.000124064 "20" 20 76 1

This output is parsed by run_infomap_multilayer to obtain a table in which each state node (combination of a physical node in a layer) is assigned to a module. This can be obtained by:

NEE2017_modules$modules