partition_undirected_graph {tip}

Partition an undirected graph

Description

A function that iteratively applies the transformation max(0, .graph_matrix - cutoff) until there are <.num_components> graph components where cutoff = cutoff + .step_size. This is used to generate the one-cluster graph and plot.

Usage

partition_undirected_graph(.graph_matrix, .num_components, .step_size)

Arguments

.graph_matrix

Matrix: a symmetric matrix that the analyst wishes to decompose into <.num_components> components.

.num_components

Positive integer: the number of components that the analyst wishes to decompose <.graph_matrix> into.

.step_size

Positive numeric: the size of the update for the cutoff in the transformation max(0, .graph_matrix - cutoff) where cutoff = cutoff + .step_size.

Value

List with three elements:

graph_component_members

Vector. A vector of positive integers: the (i)th element is the graph component assignment for the (i)th subject.

cutoff

Numeric. The value max(0, g_i,j - cutoff) so that there are <.num_components> components in the graph.

partitioned_graph_matrix

Matrix. The graph with <.num_components> components (parts).

Examples

# Import the tip library
library(tip)

# Choose an arbitrary random seed to generate the data
set.seed(4*8*15*16*23*42)

# Generate a symmetric posterior probability matrix
# Each element is the probability that the two subjects belong
# to the same cluster
n1 <- 10
posterior_prob_matrix <- matrix(NA, nrow = n1, ncol = n1)
for(i in 1:n1){
  for(j in i:n1){
    if(i != j){
      posterior_prob_matrix[i,j] <- runif(n=1,min=0,max=1)
      posterior_prob_matrix[j,i] <- posterior_prob_matrix[i,j]
    }else{
      posterior_prob_matrix[i,j] <- 1.0
    }
  }
}

# Generate a one-cluster graph (i.e., partitioned_graph_matrix)
partition_undirected_graph(.graph_matrix = posterior_prob_matrix,
                           .num_components = 1,
                           .step_size = 0.001)