Reference

MLNConfig(
    seed::Union{Int,Nothing},
    n::Int,
    edges_cor::String,
    layer_params::String,
    d_max_iter::Int,
    c_max_iter::Int,
    t::Int,
    eps::Float64,
    d::Int,
    edges_filename::String,
    communities_filename::String)
    ::MLNConfig

Creates MLNABCD configuration struct.

Arguments

• filename::String configuration file name

parse_config(filename::String)::MLNConfig

Parse configuration file into MLNABCD configuration struct.

Arguments

• filename::String configuration file name

write_edges(cfg::MLNConfig, edges::Vector{Set{Tuple{Int,Int}}})

Saves edges of multilayer network in cfg.edges_filename file.

Arguments

• cfg::MLNConfig MLNABCD configuration
• edges::Vector{Set{Tuple{Int,Int}}} edges between agents in each layer

write_communities(cfg::MLNConfig, coms::Vector{Vector{Int}})

Saves communities of multilayer network in cfg.communities_filename file.

Arguments

• cfg::MLNConfig MLNABCD configuration
• coms::Vector{Vector{Int}} assignment of agents to communities for each layer

generate_active_nodes(cfg::MLNConfig)::Vector{Vector{Int}}

Samples active nodes for each layer.

Arguments

• cfg::MLNConfig MLNABCD configuration

sample_ranking(vs::Vector{Int}, n::Int, sigma::AbstractFloat)::Vector{Vector{Int}}

Returns ranking of samples of random variables N(v/n,sigma).

Arguments

• vs::Vector{Int} vector with IDs of active agents
• n::Int number of agents
• sigma::AbstractFloat standard deviation of normal distribution N(v/n,sigma)

find_ranking(ns::Int, n::Int, tau::AbstractFloat, verbose::Bool=false, limit::Int=20)

Finds ordering of labels of agents which has tau Kendall-tau correlation with ordered labels sequence.

Arguments

• ns::Int number of active agents
• n::Int number of agents
• tau::AbstractFloat desired Kendall-tau correlation value
• verbose::Bool=false verbose logging flag
• limit::Int=20 number of rankings sampled to find the best correlation match

degrees_correlation(
    cfg::MLNConfig,
    degs::Vector{Vector{Int}},
    active_nodes::Vector{Vector{Int}},
    verbose::Bool=false)
    ::Vector{Vector{Int}}

Creates correlated sequences of degrees for all layers of the network.

Arguments

• cfg::MLNConfig MLNABCD configuration
• degs::Vector{Vector{Int}} sorted (input) sequences of degrees
• active_nodes::Vector{Vector{Int}} IDs of active nodes
• verbose::Bool=false verbose logging flag

generate_degrees(cfg::MLNConfig,
    active_nodes::Vector{Vector{Int}},
    verbose::Bool=false)
    ::Vector{Vector{Int}}

Samples sequences of degrees from truncated power-law distribution and reorder the sequences to correlate layers.

Arguments

• cfg::MLNConfig MLNABCD configuration
• active_nodes::Vector{Vector{Int}} IDs of active nodes
• verbose::Bool=false verbose logging flag

sample_points(n::Int, d::Int)::Matrix{Float64}

Samples normalized points in d-dimensional space.

Arguments

• n::Int number of points
• d::Int number of dimensions

assign_points(x::Matrix{Float64}, c::Vector{Int})::Vector{Vector{Int}}

Assigns points to communities based on the proximity in Euclidian space.

Arguments

• x::Matrix{Float64} coordinates of points
• c::Vector{Int} sizes of communities

shuffle_communities(r::Float64, a::Vector{Vector{Int}})::Vector{Vector{Int}}

Shuffles assignment of nodes to communities to introduce correlation r between the layer and reference layer

Arguments

• r::Float64 desired correlation between the layer and reference layer
• a::Vector{Vector{Int}} assignment of nodes to communities

communities_correlation(
    n::Int,
    coms_sizes::Vector{Vector{Int}},
    rs::Vector{Float64},
    active_nodes::Vector{Vector{Int}},
    d::Int)
    ::Vector{Vector{Int}}

Shuffles communities assignment to match correlations rs between network layers and hidden reference layer.

Arguments

• n::Int number of agents
• coms_sizes::Vector{Vector{Int}} sizes of communities
• rs::Vector{Float64} vector of desired correlations between each network layer and reference layer
• active_nodes::Vector{Vector{Int}} IDs of active nodes
• d::Int number of dimensions in reference space

generate_communities(cfg::MLNConfig, active_nodes::Vector{Vector{Int}})

Samples sequences of community sizes from truncated power-law distribution. Then, assigns nodes to communities and shuffles the assignment to correlate layers. Returns sizes of communities and assignment of nodes to communities.

Arguments

• cfg::MLNConfig MLNABCD configuration
• active_nodes::Vector{Vector{Int}} IDs of active nodes

generate_abcd(cfg::MLNConfig, degs::Vector{Vector{Int}},
    coms_sizes::Vector{Vector{Int}}, coms::Vector{Vector{Int}})
    ::Vector{Set{Tuple{Int,Int}}}

Generates edges of multilayer network using ABCD model.

Arguments

• cfg::MLNConfig MLNABCD configuration
• degs::Vector{Vector{Int}} degree sequences for active nodes
• coms_sizes::Vector{Vector{Int}} community sizes
• coms::Vector{Vector{Int}} assignment of active nodes to communities

map_edges_to_agents(edges::Vector{Set{Tuple{Int64,Int64}}}, active_nodes::Vector{Vector{Int64}})

Translates edges to agent-based representation.

Arguments

• edges::Vector{Set{Tuple{Int64,Int64}}} edges based on layer-specific node labels
• active_nodes::Vector{Vector{Int64}} IDs of active agents

map_communities_to_agents(
    n_agents::Int,
    communities::Vector{Vector{Int64}},
    active_nodes::Vector{Vector{Int64}})

Translates communities assignment to agent-based representation and imputes 0 for non-active agents.

Arguments

• n_agents::Int number of agents
• communities::Vector{Vector{Int64}} assignment of nodes to communities
• active_nodes::Vector{Vector{Int64}} IDs of active agents

common_agents_dict(active_nodes::Vector{Vector{Int64}})

Finds common active agents between all pairs of layers.

Arguments

• active_nodes::Vector{Vector{Int64}} IDs of active agents

common_agents_edges(
    edges_agents::Vector{Set{Tuple{Int64,Int64}}},
    common_agents_dict::Dict{Tuple{Int,Int},Set{Int}})

Finds edges including only common active agents for all pairs of layers.

Arguments

• edges_agents::Vector{Set{Tuple{Int64,Int64}}} agent-based edges of multilayer network
• common_agents_dict::Dict{Tuple{Int,Int},Set{Int}} mapping of common active agents between layers

map_neighbours(edges::Set{Tuple{Int,Int}}, coms::Vector{Int})

Finds neigbhours of each agent within and outside of given node community.

Arguments

• edges::Set{Tuple{Int,Int}} agent-based edges of multilayer network
• coms::Vector{Int} assignment of nodes to communities

map_communities(edges::Set{Tuple{Int,Int}}, coms::Vector{Int})

Finds edges within communities and background graph.

Arguments

• edges::Set{Tuple{Int,Int}} agent-based edges of multilayer network
• coms::Vector{Int} assignment of nodes to communities

neighbours_common_agents_edges(
    edges_common_agents::Dict{Tuple{Int,Int},Vector{Set{Tuple{Int,Int}}}},
    coms_agents::Vector{Vector{Int64}})

Finds neighbours of each agent in graphs induced by common agents between layers.

Arguments

• edges_common_agents::Dict{Tuple{Int,Int},Vector{Set{Tuple{Int,Int}}}} graphs induced by common agents between layers
• coms_agents::Vector{Vector{Int64}} assignment of nodes to communities in each layer

edges_in_communities_common_agents_edges(
    edges_common_agents::Dict{Tuple{Int,Int},Vector{Set{Tuple{Int,Int}}}},
    coms_agents::Vector{Vector{Int64}})

Finds edges within communities and background graph in graphs induced by common agents between layers.

Arguments

• edges_common_agents::Dict{Tuple{Int,Int},Vector{Set{Tuple{Int,Int}}}} graphs induced by common agents between layers
• coms_agents::Vector{Vector{Int64}} assignment of nodes to communities in each layer

calculate_edges_cor(
    edges_common_agents::Dict{Tuple{Int,Int},Vector{Set{Tuple{Int,Int}}}},
    desired_cor::Matrix{Float64})

Calculates correlation between edges in each pair of layers, difference between desired correlation and distance between desired correlation matrix and current correlation matrix.

Arguments

• edges_common_agents::Dict{Tuple{Int,Int},Vector{Set{Tuple{Int,Int}}}} graphs induced by common agents between layers
• desired_cor::Matrix{Float64} input correlation matrix between layers

pick_cor_to_improve(cor_diff::Matrix{Float64}, method::String="weighted")

Selects entry of correlation matrix to improve in next batch.

Arguments

• cor_diff::Matrix{Float64} difference between desired and current correlation matrices
• method::String="weighted" method of entry selection

write_cor_diff_to_file(io::IOStream, cor_diff::Matrix{Float64}, cor_dist::Float64)

Writes differences between current and desired correlation matrices entries to file. Used to track changes in empirical correlation between batches.

Arguments

• io::IOStream IO handler to a file
• cor_diff::Matrix{Float64} difference between desired and current correlation matrices
• cor_dist::Float64 distance between desired and current correlation matrices

increase_edges_correlation!(layers::Tuple{Int,Int},
    edges::Vector{Set{Tuple{Int,Int}}},
    edges_common::Vector{Set{Tuple{Int,Int}}},
    neighbours::Vector{Dict{Int,Set{Int}}},
    coms_agents::Vector{Vector{Int}},
    perc_rewire::Float64,
    verbose::Bool=false)

Increases correlation between edges in two selected layers.

Arguments

• layers::Tuple{Int,Int} IDs of modified layers
• edges::Vector{Set{Tuple{Int,Int}}} edges of multilayer network modified in-place to keep state between batches
• edges_common::Vector{Set{Tuple{Int,Int}}} edges on common active agents between layers
• neighbours::Vector{Dict{Int,Set{Int}}} mapping of neighbours of agents
• coms_agents::Vector{Vector{Int}} assignment of agents to communities
• perc_rewire::Float64 fraction of edges to be used for rewiring attempt
• verbose::Bool=false verbose logging flag

decrease_edges_correlation!(layers::Tuple{Int,Int},
    edges::Vector{Set{Tuple{Int,Int}}},
    edges_common::Vector{Set{Tuple{Int,Int}}},
    neighbours::Vector{Dict{Int,Set{Int}}},
    coms_agents::Vector{Vector{Int}},
    perc_rewire::Float64,
    verbose::Bool=false)

Decreases correlation between edges in two selected layers.

Arguments

• layers::Tuple{Int,Int} IDs of modified layers
• edges::Vector{Set{Tuple{Int,Int}}} edges of multilayer network modified in-place to keep state between batches
• edges_common::Vector{Set{Tuple{Int,Int}}} edges on common active agents between layers
• edges_in_coms::Vector{Dict{Int,Set{Tuple{Int,Int}}}} mapping of edges withing communities and background graph
• coms_agents::Vector{Vector{Int}} assignment of agents to communities
• perc_rewire::Float64 fraction of edges to be used for rewiring attempt
• verbose::Bool=false verbose logging flag

adjust_edges_correlation(cfg::MLNConfig,
    edges::Vector{Set{Tuple{Int,Int}}},
    coms::Vector{Vector{Int}},
    active_nodes::Vector{Vector{Int}},
    verbose::Bool=false,
    save_cor_change_to_file::Bool=false)

Run cfg.t rewiring batches to match edges correlation between layers with desired cfg.edges_cor_matrix correlation matrix.

Arguments

• cfg::MLNConfig MLNABCD configuration
• edges::Vector{Set{Tuple{Int,Int}}} agent-based edges of multilayer network before rewiring
• coms::Vector{Vector{Int}} assignment of nodes to communities in each layer
• active_nodes::Vector{Vector{Int}} IDs of active agents
• verbose::Bool=false verbose logging flag
• save_cor_change_to_file::Bool=false correlation changes file logging flag