Reference

landmarks(edges::Array{Int,2},vweights::Vector{Float64}, clusters::Vector{Vector{Int}},
    embedding::Array{Float64,2}, verbose::Bool, land::Int, forced::Int, method::Function)

Arguments

• edges::Array{Int,2} array with edges definition (two whitespace separated vertices ids)
• weights::Vector{Float64} edges weights
• vweights::Vector{Float64} vertices weights
• clusters::Vector{Vector{Int}} vector of vectors indicating an initial 1-based cluster

assignment of vertices.

• embedding::Array{Float64,2} array with vertices embeddings
• comm::Array{Int,2} assignment of vertices to communities
• verbose::Bool verbose switch, if true prints additional processing information
• land::Int number of landmarks to generate
• forced::Int required maximum number of forced splits of a cluster
• method::Function method used to generate landmarks
• directed::Bool flag for directed version of landmark-based graph creation

runsplit(embedding, w, initial_clusters, n, s, rule)

Take embedding with weights w where each column is a single observation and initial_clusters is a vector of vectors indicating an initial 1-based cluster assignment of vertices. Return a vector of 0-based assignments of vertices to n groups. Each cluster is guaranteed to be split to at most s landmarks (may be less if its size is less than s).

split_cluster_diameter(m, w)

Splits cluster m with weights w into two clusters along its first principal component so as to make both clusters have approximately the same diameter along the first principal component.

split_cluster_size(m, w)

Splits cluster m with weights w into two clusters along its first principal component so as to make the clusters have equal size (number of edges).

split_cluster_rss(m, w)

Splits cluster m with weights w into two clusters along its first principal component so as to minimize maximum RSS of one of the resulting clusters.

split_cluster_rss2(m, w)

Splits cluster m with weights w into two clusters along its first principal component so as to minimize maximum RSS of one of the resulting clusters.

This is a second slower version of the algorithm using sorting. Retained for testing purposes.

wGCL(edges::Array{Int,2}, weights::Vector{Float64}, comm::Array{Int,2}, embed::Array{Float64,2}, distances::Vector{Float64}, verbose::Bool = false)

Calculates Weighted Geometric Chung-Lu model and divergence score for graph and embedding.

Arguments

• edges::Array{Int,2} array with edges definition (two whitespace separated vertices ids)
• eweights::Vector{Float64} edges weights
• comm::Array{Int,2} assignment of vertices to communities
• embed::Array{Float64,2} array with vertices embeddings
• distances::Vector{Float64} distances between vertices
• vweights::Vector{Float64} landmarks total weights - used only with landmarks approximation
• init_vweights::Vector{Float64} vector with original (full) vertices weights - used only with landmarks approximation
• v_to_l::Vector{Int} mapping from vertices to landmarks (landmarks membership) - used only with landmarks approximation
• init_edges::Array{Int,2} array with original (full) graph edges - used only with landmarks approximation
• init_eweights::Vector{Float64} vector with original (full) edges weights - used only with landmarks approximation
• init_embed::Matrix{Float64} array with original embedding for full graph - used only with landmarks approximation
• split::Bool indicator for splitting JS divergence score (global score)
• seed::Int RNG seed for local measure score
• auc_samples::Int no. samples for local measure score
• verbose::Bool verbose switch, if true prints additional processing information

wGCL_directed(edges::Array{Int,2}, weights::Vector{Float64}, comm::Array{Int,2}, embed::Array{Float64,2}, distances::Vector{Float64}, verbose::Bool = false)

Calculates directed Weighted Geometric Chung-Lu model and divergence score for graph and embedding.

Arguments

• edges::Array{Int,2} array with edges definition (two whitespace separated vertices ids)
• eweights::Vector{Float64} edges weights
• comm::Array{Int,2} assignment of vertices to communities
• embed::Array{Float64,2} array with vertices embeddings
• distances::Vector{Float64} distances between vertices
• vweights::Vector{Float64} landmarks total weights - used only with landmarks approximation
• init_vweights::Vector{Float64} vector with original (full) vertices weights - used only with landmarks approximation
• v_to_l::Vector{Int} mapping from vertices to landmarks (landmarks membership) - used only with landmarks approximation
• init_edges::Array{Int,2} array with original (full) graph edges - used only with landmarks approximation
• init_eweights::Vector{Float64} vector with original (full) edges weights - used only with landmarks approximation
• init_embed::Matrix{Float64} array with original embedding for full graph - used only with landmarks approximation
• split::Bool indicator for splitting JS divergence score (global score)
• seed::Int RNG seed for local measure score
• auc_samples::Int no. samples for local measure score
• verbose::Bool verbose switch, if true prints additional processing information

dist(i::Int, j::Int, embed::Array{Float64,2})

Calculates Euclidian distance between two vectors from embedding array.

Arguments

• v1::Int index of first vector
• v2::Int index of second vector
• embed::Array{Float64,2} graph embedding array

JS(vC::Vector{Float64}, vB::Vector{Float64},
    vI::Vector{Int}, internal::Int, vLen::Int)

Jensen-Shannon divergence with Dirichlet-like prior.

Arguments

• vC::Vector{Float64} first distribution of edges within and between communities
• vB::Vector{Float64} second distribution of edges within and between communities
• vI::Vector{Int} indicator of internal (1) and external (0) edges w.r.t. communities, if empty compute overall JS distance
• internal::Int internal JS distance switch, if 1 return internal, else return external

Change 2-dimensional into 1-dim index

louvain_clust(edges::String)

Calculate communities in graph using Louvain algoritm

Arguments

• edges::String name of file with edges definition

louvain_clust(filename::String, edges::Array{Int,2}, weights::Array{Float64,1}))

Calculate communities in weighted graph using Louvain algoritm

Arguments

• filename::String name of file with edges definition
• edges::Array{Int,2} list of edges
• weights::Array{Float64,1} array of edges' weights