3  Graph Properties

3.1 Sample some data

We’ve previously computed the network graphs of a couple student, but lets just sample out a handful more for some visualizations here.

Code

sample_of_graphs <- sample_n(course_graphs, 5)

3.1.1 Vanilla visualization

For reference here’s a visualization with no colorings. It’s a real eyesore to me but hey it makes the other graphs look better by comparison, eh?

3.1.2 Coloring some nodes

Code

# lets use a blue-red spectrum here to show our centrality
# high values -> red
# low values -> blue
palette <- diverging_hcl(100, palette = "Blue-Red-3")
color_key <- palette %>% enframe() %>% rename(index = name, color = value)

colored_vanilla_graph <- vanilla_graph %>% 
  activate(nodes) %>% 
  mutate(color = case_when(
    str_detect(course, "BIO") ~ palette[1],
    str_detect(course, "CHEM") ~ palette[100],
    .default = palette[50]))

visualize_graph(colored_vanilla_graph)

3.2 Edge Ratios

3.3 Centrality

Code

normalize2 <- function(x, na.rm = T) (x  / max(x, na.rm = T))

centrality_graph <- vanilla_graph %>% 
  activate(nodes) %>%
  mutate(centrality = centrality_alpha()) %>% 
  mutate(normalized_centrality_1 = centrality, 
         normalized_centrality_2 = centrality) %>% 
  mutate_at('normalized_centrality_1', ~ scale(.)) %>% 
  mutate_at('normalized_centrality_2', normalize2) %>% 
  mutate(color_index = floor(normalized_centrality_2 * 100)) %>% 
  mutate(color = NULL) %>% 
  left_join(color_key, by = join_by(color_index == index)) %>%
  arrange(desc(centrality))

visualize_graph(centrality_graph)

3.4 Flow

3.5 Cycles