Welcome Back!

Our project is about building and analyzing the Workshop network

We will continue to use the WorkshopNetwork.rds data file.

library(tidyverse) #tools for cleaning data 
library(igraph)  #package for doing network analysis
library(tidygraph) #tools for doing tidy networks
library(here) #tools for project-based workflow
library(ggraph) #plotting tools for networks
library(boot)  #to do resampling

Let's load our data

gr <- readRDS(here("data", "WorkshopNetwork.rds"))

Let's plot it quickly

And get some important features of the graph.

```r
GrLayout <- create_layout(gr,
                          layout = "kk")
ggraph(GrLayout) +
  geom_edge_link() +
  geom_node_point() +
  theme(legend.position="bottom")
```

gr

## # A tbl_graph: 60 nodes and 101 edges
## #
## # A directed multigraph with 8 components
## #
## # A tibble: 60 × 4
##   name  AMPM            Dessert                   Pages
##   <chr> <chr>           <chr>                     <dbl>
## 1 5106  morning person. Brownies                    350
## 2 6633  morning person. I don't care for dessert.    12
## 3 7599  night owl.      Ice Cream                   300
## 4 4425  morning person. I don't care for dessert.     0
## 5 2495  morning person. Brownies                    264
## 6 6355  night owl.      Ice Cream                     4
## # ℹ 54 more rows
## #
## # A tibble: 101 × 2
##    from    to
##   <int> <int>
## 1     1     1
## 2     2    35
## 3     3    14
## # ℹ 98 more rows

Note, there are 60 nodes and 101 edges

Orient

Let's decide if our network is unique

What is the big problem with the network that we have collected?

1. We have one network.
2. There is no variance in the metrics.
3. What is the null hypothesis/model?

Let's talk about camps

This is a place where there are sort of two camps of network analysis

Let's compare two networks

GrLayout <- create_layout(gr,
                          layout = "kk")
ggraph(GrLayout) +
  geom_edge_link() +
  geom_node_point() +
  theme(legend.position="bottom")

er_gr <- play_erdos_renyi(n = 60, m = 101, loops = FALSE)
GrLayoutER <- create_layout(er_gr,
                          layout = "kk")
ggraph(GrLayoutER) +
  geom_edge_link() +
  geom_node_point() +
  theme(legend.position="bottom")

Let's talk about how you might compare

What are some ways you can think of to compare these two graphs?

Let's compare based on metrics

Why don't we try density

edge_density(gr)

## [1] 0.02853107

edge_density(er_gr)

## [1] 0.02853107

Well that isn't any fun!

Let's compare based on metrics

Here is diameter, note that with tidygraph you have to use the with_graph() function, and specify the graph and function graph_diameter()

with_graph(gr, graph_diameter())

## [1] 6

with_graph(er_gr, graph_diameter())

## [1] 12

Ok, so the numbers are different...does that mean the graphs are different?

Let's try this 1000 times

#Start by setting up a vector to hold our results.
diameter_results <- c()
for(i in 1:1000) {
  tmp <- play_erdos_renyi(n=60, m = 101)
  diameter_results[i] = with_graph(tmp, graph_diameter())
}
#Convert to dataframe
diameter_results_df <- tibble(diam = diameter_results)
#and plot our results
ggplot(diameter_results_df, aes(diam)) +
  geom_bar() +
  geom_vline(xintercept = with_graph(gr, graph_diameter()),
             color = 'red',
             size = 2)

Let's get a confidcence interval

If we want to estimate the confidence with which we think our measured network is different on any metrics, we can look for the percentiles.

Let's see if the measured diameter falls within the 95% of the simulated network....

mean(diameter_results_df$diam)

## [1] 13.608

sd(diameter_results_df$diam)

## [1] 2.450376

quantile(diameter_results_df$diam, probs = c(0.025, 0.975))

##  2.5% 97.5% 
##    10    19

Since the measured diameter of 6 is outside of this range, we can say pretty confidently that the measured network is not a random network!

Let's summarize

Let's assign attributes

In order to compare homophily, we need our ER_gr to have the same attributes.

There is a file that has a random graph with the attributes assigned to it.

ER_gr_attr <- readRDS(here("data", "RandomGraph.rds"))

## # A tbl_graph: 58 nodes and 101 edges
## #
## # A directed simple graph with 1 component
## #
## # A tibble: 58 × 3
##   name  AMPM            Dessert                  
##   <chr> <chr>           <chr>                    
## 1 5106  morning person. Brownies                 
## 2 6633  morning person. I don't care for dessert.
## 3 7599  night owl.      Ice Cream                
## 4 4425  morning person. I don't care for dessert.
## 5 2495  morning person. Brownies                 
## 6 6355  night owl.      Ice Cream                
## # ℹ 52 more rows
## #
## # A tibble: 101 × 2
##    from    to
##   <int> <int>
## 1     1    12
## 2     1    25
## 3     1    33
## # ℹ 98 more rows

Now you get to try!

• Choose a network simulator (think about why you chose it)
• Decide on a metric (better yet - create a function to look at many at once).
• Simulate networks -- Measure chosen metrics -- Store metrics in data frame

Let's reflect

Let's note what we missed

Let's be thankful