In mabafaba/frequentgraphs: Frequentist Hypothesis Tests For Graph Statistics

knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>",
  warning = FALSE,
  message = FALSE
)

library(igraph)
library(frequentgraphs)
library(magrittr)

Example graphs

# runif(1)
set.seed(0.8662903)

lattice <- make_lattice(dimvector = c(20,20))
star <- make_star(n = 15)

Example scalar graph statistic

Say we're interested in the mean closeness of largest connected component of the graph:

mean_closeness<-function(g,...){
  giant_comp <- g_largest_component(g)
  mean(closeness(giant_comp,...))
  }

Hypothesis test

# lattice
lattice_test <- g_test_scalar(g = lattice,
                              simulation.n = 300,
                              scalar.graph.statistic = mean_closeness)

lattice_test$observed
lattice_test$simulated.mean
lattice_test$p.value
lattice_test$normality.condition.met

The lattice has a much smaller mean closeness than the largest component of same size graphs with a uniformly random edge distribution on average. The probability that a uniform random distribution of edges produces an average degree centrality as high as the lattice is < r ceiling(lattice_test$p.value*1000)/1000.

The test statistic is not normally distributed, so this result should not be taken too serious. We should have a look at the distribution:

g_test_scalar_plot(lattice_test)

In comparison, a Barabasi-Albert model graph:

g <- igraph::ba.game(100,m = 3)
plot(g)
  g_test_scalar(g,
                simulation.n = 100,
                scalar.graph.statistic = mean_closeness,
                na.rm = TRUE) %>% 
  g_test_scalar_plot

In comparison, a Geometric random graph:

g <- igraph::grg.game(100,radius = 0.5)
plot(g)
  g_test_scalar(g,
                simulation.n = 100,
                scalar.graph.statistic = mean_closeness,
                na.rm = TRUE) %>% 
  g_test_scalar_plot