What is a network?

What is a network?

Network Analysis is for the analysis of relational data

There are four basic assumptions:

1. Nodes and interactions are interdependent*
2. Edges allow flow between nodes
3. Network models on indiviuals both constrain and provide opportunity for action
4. Network models conceptualize structure as representation of lasting patterns of relations between actors

What can we do with it?

What can we do with it?

What can we do with it?

Historical Foundations

Modern Foundations of Network Analysis

Sociophysics (1990s)

• Graph theory
• Information theory
• Computing
• Used to study
  • Internet
  • Power grid
  • Transportation networks

Seminal Articles

• Watts & Strogratz "Collective dynamics of small world networks" Nature (1998)
• Page, Brin, Motwani, & Winograd "The PageRank citation ranking: Bringing order to the web" Stanford InfoLab (1999)

Important Takeaways from History

Two main camps

Statistical -> hypothesis testing

Graph theoretic -> network models and simulation

Network Data in R

## 5 x 5 sparse Matrix of class "dgCMatrix"
##               
## [1,] . 1 1 1 1
## [2,] 1 . . . .
## [3,] 1 . . . .
## [4,] 1 . . . 1
## [5,] 1 . . 1 .

Network Data in R

## [[1]]
## + 4/5 edges from ddd0978:
## [1] 1--2 1--3 1--4 1--5
## 
## [[2]]
## + 1/5 edge from ddd0978:
## [1] 1--2
## 
## [[3]]
## + 1/5 edge from ddd0978:
## [1] 1--3
## 
## [[4]]
## + 2/5 edges from ddd0978:
## [1] 1--4 4--5
## 
## [[5]]
## + 2/5 edges from ddd0978:
## [1] 1--5 4--5

What does this mean in terms of learning R?

• We need to know something about the different types of data!

What you need to know about R?

• R is the programming language.
• RStudio is the Integrated Development Environment (IDE)
• Posit.cloud is an online version of the IDE
• Packages: groups of functions that are developed as open source
• Base R
  • The group of packages preloaded into R
• Tidyverse
  • Family of packages that are designed with the theory that programming should be readable by humans.
• igraph
  • Package that is very useful for doing network analyses

Lets do this!

Lets Take a Tour of RStudio IDE

Let's Install Some Packages

You'll only need to do this once.

In Console

To install tidyverse package...

install.packages("tidyverse")

Repeat this with the following packages:

igraph tidygraph here ggraph

Let's Load Some Packages

You'll need to do this every time you restart R.

In Console

To load tidyverse package...

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

Once you have done this, you will want to put include a code chunk with all of your libraries into your markdown document so that you don't have to type this every time.

Let's get data into R.

In this workshop, you have the data from the survey to make things as easy as possible. However, this is not typical. You will have to find ways to get your data into R but that is sort of different depending on where you are running R (posit.cloud or a local machine)

If you have loaded the package "here" this should just work. If you have not loaded the "here" package you will need to set the working directory.

Again, you will want to include this as a code chunk in your RMD file.

#This loads the csv and saves it as a dataframe titled WorkshopData
WorkshopData <- read_csv(here("data", "AnonSurveyData.csv"))

Let's have a look at the data

glimpse(WorkshopData)

## Rows: 34
## Columns: 18
## $ ID                      <dbl> 5106, 6633, 7599, 4425, 2495, 6355, 8810, 3877…
## $ StartDate               <dttm> 2020-07-30 12:15:20, 2020-07-30 12:18:50, 202…
## $ EndDate                 <dttm> 2020-07-30 12:18:59, 2020-07-30 12:20:21, 202…
## $ Status                  <chr> "IP Address", "IP Address", "IP Address", "IP …
## $ Progress                <dbl> 100, 100, 100, 100, 100, 100, 100, 100, 100, 1…
## $ `Duration (in seconds)` <dbl> 219, 91, 137, 97, 127, 233, 97, 144, 103, 231,…
## $ Finished                <lgl> TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE…
## $ RecordedDate            <dttm> 2020-07-30 12:18:59, 2020-07-30 12:20:22, 202…
## $ SurveyID                <chr> "R_ssTGHZwy5EpQaNX", "R_2fv9VCk0tjdrDOr", "R_1…
## $ ExternalReference       <lgl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA…
## $ DistributionChannel     <chr> "email", "email", "email", "email", "email", "…
## $ UserLanguage            <chr> "EN", "EN", "EN", "EN", "EN", "EN", "EN", "EN"…
## $ Q2                      <chr> "morning person.", "morning person.", "night o…
## $ Q3                      <chr> "Brownies", "I don't care for dessert.", "Ice …
## $ Q4                      <chr> "Coffee,Water,The tears of my enemies", "Coffe…
## $ Q5                      <dbl> 350, 12, 300, 0, 264, 4, 289, 550, 349, 300, 4…
## $ Q6                      <dbl> 350, 56, 5000, 50, 286, 250, 76, 185, 108, 220…
## $ `as.character(Q5)`      <dbl> 350, 12, 300, 0, 264, 4, 289, 550, 349, 300, 4…

Let's start cleaning up.

First, we don't need most of that data

There is a ton of data there that doesn't make sense for us to keep around.

We will use the '%>%' (pipe) operator and the verb select

WorkshopData %>%
  select(ID,Q2:Q6) -> WorkshopData
glimpse(WorkshopData)

## Rows: 34
## Columns: 6
## $ ID <dbl> 5106, 6633, 7599, 4425, 2495, 6355, 8810, 3877, 1554, 7743, 8353, 2…
## $ Q2 <chr> "morning person.", "morning person.", "night owl.", "morning person…
## $ Q3 <chr> "Brownies", "I don't care for dessert.", "Ice Cream", "I don't care…
## $ Q4 <chr> "Coffee,Water,The tears of my enemies", "Coffee,Tea,Water,Milk", "F…
## $ Q5 <dbl> 350, 12, 300, 0, 264, 4, 289, 550, 349, 300, 424, 426, 231, 290, 10…
## $ Q6 <dbl> 350, 56, 5000, 50, 286, 250, 76, 185, 108, 220, 500, 350, 412, 1135…

Let's start cleaning up.

Now we should actually take a look at the data

WorkshopData %>%
  head()

## # A tibble: 6 × 6
##      ID Q2              Q3                        Q4                    Q5    Q6
##   <dbl> <chr>           <chr>                     <chr>              <dbl> <dbl>
## 1  5106 morning person. Brownies                  Coffee,Water,The …   350   350
## 2  6633 morning person. I don't care for dessert. Coffee,Tea,Water,…    12    56
## 3  7599 night owl.      Ice Cream                 Fruit Juice,Tea,W…   300  5000
## 4  4425 morning person. I don't care for dessert. Fruit Juice,Coffe…     0    50
## 5  2495 morning person. Brownies                  Coffee,Water         264   286
## 6  6355 night owl.      Ice Cream                 Fruit Juice,Tea,W…     4   250

Let's check out the power of R

I am going to blast through these next slides, to show you some of the things that you might want to do with R

Let's start visualizing the data

For categorical data, you might want to get some counts.

Here is code to do this for the question about morning or night person.

WorkshopData %>%
  select(Q2) %>%
  group_by(Q2) %>%
  tally()

## # A tibble: 2 × 2
##   Q2                  n
##   <chr>           <int>
## 1 morning person.    19
## 2 night owl.         15

Let's start visualizing the data

For categorical data, you might want to get a histogram.

Here is code to do this for the favorite dessert type.

WorkshopData %>%
  select(Q3) %>%
  group_by(Q3) %>% 
  tally()

## # A tibble: 5 × 2
##   Q3                                      n
##   <chr>                               <int>
## 1 Brown Butter Chocolate Chip Cookies     2
## 2 Brownies                                9
## 3 Cheese                                  3
## 4 I don't care for dessert.               3
## 5 Ice Cream                              17

WorkshopData %>%
  select(Q3) %>%
  ggplot(aes(y = Q3)) + 
  geom_bar()

Let's explore beverage choices

WorkshopData %>%
  select(ID, Q4) %>%
  head()

## # A tibble: 6 × 2
##      ID Q4                                  
##   <dbl> <chr>                               
## 1  5106 Coffee,Water,The tears of my enemies
## 2  6633 Coffee,Tea,Water,Milk               
## 3  7599 Fruit Juice,Tea,Water,Fizzy Water   
## 4  4425 Fruit Juice,Coffee,Water            
## 5  2495 Coffee,Water                        
## 6  6355 Fruit Juice,Tea,Water

Notice, these are not tidy data, more than one variable per line

Let's dummy code the beverage data

WorkshopData %>%
  select(ID, Q4) %>%
  separate_rows(Q4, sep = ",") %>%
  head(10)

## # A tibble: 10 × 2
##       ID Q4                     
##    <dbl> <chr>                  
##  1  5106 Coffee                 
##  2  5106 Water                  
##  3  5106 The tears of my enemies
##  4  6633 Coffee                 
##  5  6633 Tea                    
##  6  6633 Water                  
##  7  6633 Milk                   
##  8  7599 Fruit Juice            
##  9  7599 Tea                    
## 10  7599 Water

WorkshopData %>%
  select(ID, Q4) %>%
  separate_rows(Q4, sep = ",") %>%
  mutate(Checked = 1) %>%
  pivot_wider(names_from = Q4,
              values_from = Checked,
              values_fill = 0)

## # A tibble: 34 × 11
##       ID Coffee Water `The tears of my enemies`   Tea  Milk `Fruit Juice`
##    <dbl>  <dbl> <dbl>                     <dbl> <dbl> <dbl>         <dbl>
##  1  5106      1     1                         1     0     0             0
##  2  6633      1     1                         0     1     1             0
##  3  7599      0     1                         0     1     0             1
##  4  4425      1     1                         0     0     0             1
##  5  2495      1     1                         0     0     0             0
##  6  6355      0     1                         0     1     0             1
##  7  8810      1     0                         1     0     0             0
##  8  3877      0     1                         1     1     1             0
##  9  1554      0     1                         1     0     0             1
## 10  7743      0     1                         0     1     1             1
## # ℹ 24 more rows
## # ℹ 4 more variables: `Fizzy Water` <dbl>,
## #   `A delicious 12 year single malt scotch from the Scottish lowlands with notes of apple` <dbl>,
## #   ` cinnamon` <dbl>, ` and dried fruit served with a single ice cube` <dbl>

Let's look at some quantitative data

First, let's summarize the reading data.

WorkshopData %>%
  select(Q5) %>%
  summarize(Ave = mean(Q5, na.rm = TRUE), 
            SD = sd(Q5, na.rm = TRUE))

## # A tibble: 1 × 2
##     Ave    SD
##   <dbl> <dbl>
## 1  327.  247.

Let's investigate groups

WorkshopData %>%
  select(Q2, Q5) %>%
  group_by(Q2) %>%
  summarize(Ave = mean(Q5),
            SD = sd(Q5))

## # A tibble: 2 × 3
##   Q2                Ave    SD
##   <chr>           <dbl> <dbl>
## 1 morning person.  321   215.
## 2 night owl.       335.  289.

WorkshopData %>%
  select(Q2, Q5) %>%
  ggplot(., aes(x = Q2, y = Q5)) +
  geom_boxplot()

Let's look at readers vs. blueberries

Is there a relationship between length of book and estimates on number of blueberries?

WorkshopData %>%
  select(Q5:Q6) %>%
  mutate(Q5 = as.numeric(Q5), Q6 = as.numeric(Q6)) %>%
  ggplot(aes(x = Q5, y = Q6)) +
  geom_point()

Let's look at readers vs. blueberries

Is there a relationship between length of book and estimates on number of blueberries?

Or you could do a linear model

summary(lm(Q6 ~ Q5, data = WorkshopData))

## 
## Call:
## lm(formula = Q6 ~ Q5, data = WorkshopData)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -365.6 -313.8 -179.1  -98.8 4563.5 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)
## (Intercept) 382.9414   249.7136   1.534    0.135
## Q5            0.1785     0.6126   0.291    0.773
## 
## Residual standard error: 867.6 on 32 degrees of freedom
## Multiple R-squared:  0.002647,    Adjusted R-squared:  -0.02852 
## F-statistic: 0.08492 on 1 and 32 DF,  p-value: 0.7726

Let's prep our data for SNA

We will need to prep two separate files...

1. An edgelist
2. A file of attributes of the nodes.

Let's make an edgelist

There is an issue here.

I wanted to make these data anonymous (so we don't know who likes scotch)

But to do that I had to make the edgelist for you.

So I sent you an edgelist as a csv. Sorry.

Check out the edgelist

EL = read_csv(here("data", "AnonEL.csv"))
head(EL)

## # A tibble: 6 × 2
##      ID Connections
##   <dbl>       <dbl>
## 1  5106        5106
## 2  6633        6196
## 3  7599        5462
## 4  4425        7743
## 5  2495        3940
## 6  6355        6355

Let's assemble our node attributes

Before we can convert our Edgelist to a network, we should add in the attributes.

We have several candidate attributes:

• Morning vs. Night
• Dessert Type
• Pages in book

We will develop a separate dataframe for the attributes.

WorkshopData %>%
  select(ID, Q2, Q3, Q5) -> AttributeDf

Let's assemble our node attributes

Experience tells me that when you try to add attributes that you often make a mistake where the number attributes don't match up well to the number of nodes...but lets see.

gr <- graph_from_data_frame(EL, directed = TRUE)
plot(gr)

gr = as_tbl_graph(gr)

Let's add some attributes

So actually the easiest way to add the attributes is to add them while you make the graph.

But that isn't as easy as it seems

gr %>%
  activate(nodes) %>%
  mutate(AMPM = AttributeDf$Q2)

But that isn't as easy as it seems...

Let's sort out these attributes.

The warning was: "Input AMPM must be size 60 or 1, not 34."

What this means is we need to take our attributes dataframe and make sure all the nodes are listed.

To do this we need to:

• Compile a dataframe of all nodes listed in the graph
• Use a join to add attributes to this dataframe

Let's sort out these attributes (pt 2)

#This will get a vector of all nodes
gr %>%
  activate(nodes) %>%
  as_tibble() %>%
  transmute(ID = name) %>%
  mutate(ID = as.numeric(ID))-> GrNodes
#Now we pull in the attributes using a left_join
NodeAttributes = left_join(GrNodes, AttributeDf, by = "ID")

You should inspect Node Attributes

Let's sort out these attributes (pt 3)

Inspect the head

head(NodeAttributes)

## # A tibble: 6 × 4
##      ID Q2              Q3                           Q5
##   <dbl> <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

Let's sort out these attributes (pt 4)

Inspect the tail

tail(NodeAttributes)

## # A tibble: 6 × 4
##      ID Q2    Q3       Q5
##   <dbl> <chr> <chr> <dbl>
## 1  7128 <NA>  <NA>     NA
## 2  1050 <NA>  <NA>     NA
## 3  3799 <NA>  <NA>     NA
## 4  1651 <NA>  <NA>     NA
## 5  8984 <NA>  <NA>     NA
## 6  1958 <NA>  <NA>     NA

Let's finally assemble this graph.

gr %>%
  as_tbl_graph() %>%
  activate(nodes) %>%
  mutate(AMPM = NodeAttributes$Q2) %>%
  mutate(Dessert = NodeAttributes$Q3) %>%
  mutate(Pages = NodeAttributes$Q5) -> gr
summary(gr)

## IGRAPH 0971b7b DN-- 60 101 -- 
## + attr: name (v/c), AMPM (v/c), Dessert (v/c), Pages (v/n)

Let's finally assemble this graph.

Take a look at your graph

## # 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

Let's make our plots look a bit better

```r
ggraph(gr) +
  geom_edge_link() +
  geom_node_point()
```

Let's make our plots look a bit better

```r
ggraph(gr, layout = 'circle') +
  geom_edge_link() +
  geom_node_point()
```

Let's make our plots look a bit better

```r
ggraph(gr, layout = 'circle') +
  geom_edge_link() +
  geom_node_point(aes(shape = AMPM))
```

Let's make our plots look a bit better

```r
ggraph(gr, layout = 'circle') +
  geom_edge_link() +
  geom_node_point(aes(color = Dessert))
```

Let's make our plots look a bit better

```r
ggraph(gr, layout = 'circle') +
  geom_edge_link() +
  geom_node_point(aes(size = Pages))
```

Let's make our plots look a bit better

```r
ggraph(gr, layout = 'circle') +
  geom_edge_link() +
  geom_node_point(aes(shape = AMPM, 
                      color = Dessert, 
                      size = Pages))
```

Let's save our data so that we can access it easily

```r
write_rds(gr, here("data", "WorkshopNetwork.rds"))
```