Another Game of Thrones network analysis - this time with tidygraph and ggraph

What can network analysis tell us?

Network analysis can e.g. be used to explore relationships in social or professional networks. In such cases, we would typically ask questions like:

• How many connections does each person have?
• Who is the most connected (i.e. influential or “important”) person?
• Are there clusters of tightly connected people?
• Are there a few key players that connect clusters of people?
• etc.

These answers can give us a lot of information about the patterns of how people interact.

So, how do we find out who the most important characters are in this network? We consider a character “important” if he has connections to many other characters. There are a few network properties, that tell us more about this, like node centrality and which characters are key-players in the books.

A word of caution before you read on: BEWARE of SPOILERS for all books!

A Song of Ice and Fire character network across all five books; find out how I made it by following the code below…

library(readr)     # fast reading of csv files
library(tidyverse) # tidy data analysis
library(tidygraph) # tidy graph analysis
library(ggraph)    # for plotting

The Data

I obtained the following data by cloning this Github repository from Andrew Beveridge:

Character Interaction Networks for George R. R. Martin’s “A Song of Ice and Fire” saga These networks were created by connecting two characters whenever their names (or nicknames) appeared within 15 words of one another in one of the books in “A Song of Ice and Fire.” The edge weight corresponds to the number of interactions. You can use this data to explore the dynamics of the Seven Kingdoms using network science techniques. For example, community detection finds coherent plotlines. Centrality measures uncover the multiple ways in which characters play important roles in the saga.

Andrew already did a great job analyzing these character networks and you can read all his conclusions on his site https://networkofthrones.wordpress.com. Here, I don’t aim to replicate his analyses but I want to show how you could do this or similar analyses with tidygraph and ggraph. Thus, I am also not going to use all of his node and edge files.

path <- "/Users/shiringlander/Documents/Github/Data/asoiaf/data/"
files <- list.files(path = path, full.names = TRUE)
files

##  [1] "/Users/shiringlander/Documents/Github/Data/asoiaf/data//asoiaf-all-edges.csv"   
##  [2] "/Users/shiringlander/Documents/Github/Data/asoiaf/data//asoiaf-all-nodes.csv"   
##  [3] "/Users/shiringlander/Documents/Github/Data/asoiaf/data//asoiaf-book1-edges.csv" 
##  [4] "/Users/shiringlander/Documents/Github/Data/asoiaf/data//asoiaf-book1-nodes.csv" 
##  [5] "/Users/shiringlander/Documents/Github/Data/asoiaf/data//asoiaf-book2-edges.csv" 
##  [6] "/Users/shiringlander/Documents/Github/Data/asoiaf/data//asoiaf-book2-nodes.csv" 
##  [7] "/Users/shiringlander/Documents/Github/Data/asoiaf/data//asoiaf-book3-edges.csv" 
##  [8] "/Users/shiringlander/Documents/Github/Data/asoiaf/data//asoiaf-book3-nodes.csv" 
##  [9] "/Users/shiringlander/Documents/Github/Data/asoiaf/data//asoiaf-book4-edges.csv" 
## [10] "/Users/shiringlander/Documents/Github/Data/asoiaf/data//asoiaf-book4-nodes.csv" 
## [11] "/Users/shiringlander/Documents/Github/Data/asoiaf/data//asoiaf-book45-edges.csv"
## [12] "/Users/shiringlander/Documents/Github/Data/asoiaf/data//asoiaf-book45-nodes.csv"
## [13] "/Users/shiringlander/Documents/Github/Data/asoiaf/data//asoiaf-book5-edges.csv" 
## [14] "/Users/shiringlander/Documents/Github/Data/asoiaf/data//asoiaf-book5-nodes.csv"

Characters across all books

The first data set I am going to use are the character interactions in all five books. I am not using the node files here, because I find the edge names sufficient for this demonstration. If you wanted to have nice name labels, you could use the node files.

cooc_all_edges <- read_csv(files[1])

Because there are so many characters in the books, many of them minor, I am subsetting the data to the 100 characters with the most interactions across all books. The edges are undirected, therefore there are no redundant Source-Target combinations; because of this, I gathered Source and Target data before summing up the weights.

main_ch <- cooc_all_edges %>%
  select(-Type) %>%
  gather(x, name, Source:Target) %>%
  group_by(name) %>%
  summarise(sum_weight = sum(weight)) %>%
  ungroup()

main_ch_l <- main_ch %>%
  arrange(desc(sum_weight)) %>%
  top_n(100, sum_weight)
main_ch_l

## # A tibble: 100 x 2
##    name               sum_weight
##    <chr>                   <int>
##  1 Tyrion-Lannister         2873
##  2 Jon-Snow                 2757
##  3 Cersei-Lannister         2232
##  4 Joffrey-Baratheon        1762
##  5 Eddard-Stark             1649
##  6 Daenerys-Targaryen       1608
##  7 Jaime-Lannister          1569
##  8 Sansa-Stark              1547
##  9 Bran-Stark               1508
## 10 Robert-Baratheon         1488
## # ... with 90 more rows

cooc_all_f <- cooc_all_edges %>%
  filter(Source %in% main_ch_l$name & Target %in% main_ch_l$name)

tidygraph and ggraph

Both tidygraph and ggraph have been developed by Thomas Lin Pedersen:

With tidygraph I set out to make it easier to get your data into a graph and perform common transformations on it, but the aim has expanded since its inception. The goal of tidygraph is to empower the user to formulate complex questions regarding relational data as simple steps, thus enabling them to retrieve insights directly from the data itself. The central idea this all boils down to is this: you don’t have to plot a network to understand it. While I absolutely love the field of network visualisation, it is in many ways overused in data science — especially when it comes to extracting knowledge from a network. Just as you don’t need a plot to tell you which car in a dataset is the fastest, you don’t need a plot to tell you which pair of friends are the closest. What you do need, instead of a plot, is a tool that allow you to formulate your question into a logic sequence of operations. For many people in the world of rectangular data, this tool is increasingly dplyr (and friends), and I do hope that tidygraph can take on the same role in the world of relational data. https://www.data-imaginist.com/2018/tidygraph-1-1-a-tidy-hope/

The first step is to convert our edge table into a tbl_graph object structure. Here, we use the as_tbl_graph() function from tidygraph; it can take many different types of input data, like data.frame, matrix, dendrogram, igraph, etc.

Underneath the hood of tidygraph lies the well-oiled machinery of igraph, ensuring efficient graph manipulation. Rather than keeping the node and edge data in a list and creating igraph objects on the fly when needed, tidygraph subclasses igraph with the tbl_graph class and simply exposes it in a tidy manner. This ensures that all your beloved algorithms that expects igraph objects still works with tbl_graph objects. Further, tidygraph is very careful not to override any of igraphs exports so the two packages can coexist quite happily. https://www.data-imaginist.com/2017/introducing-tidygraph/

A central aspect of tidygraph is that you can directly manipulate node and edge data from this tbl_graph object by activating nodes or edges. When we first create a tbl_graph object, the nodes will be activated. We can then directly calculate node or edge metrics, like centrality, using tidyverse functions.

as_tbl_graph(cooc_all_f, directed = FALSE)

## # A tbl_graph: 100 nodes and 798 edges
## #
## # An undirected simple graph with 1 component
## #
## # Node Data: 100 x 1 (active)
##   name                           
##   <chr>                          
## 1 Aemon-Targaryen-(Maester-Aemon)
## 2 Aeron-Greyjoy                  
## 3 Aerys-II-Targaryen             
## 4 Alliser-Thorne                 
## 5 Arianne-Martell                
## 6 Arya-Stark                     
## # ... with 94 more rows
## #
## # Edge Data: 798 x 5
##    from    to Type          id weight
##   <int> <int> <chr>      <int>  <int>
## 1     1     4 Undirected    43      7
## 2     1    13 Undirected    44      4
## 3     1    28 Undirected    52      3
## # ... with 795 more rows

We can change that with the activate() function. We can now, for example, remove multiple edges. When you are using RStudio, start typing ?edge_is_ and wait for the autocomplete function to show you what else is possible (or go to the tidygraph manual).

as_tbl_graph(cooc_all_f, directed = FALSE) %>%
  activate(edges) %>%
  filter(!edge_is_multiple())

## # A tbl_graph: 100 nodes and 798 edges
## #
## # An undirected simple graph with 1 component
## #
## # Edge Data: 798 x 5 (active)
##    from    to Type          id weight
##   <int> <int> <chr>      <int>  <int>
## 1     1     4 Undirected    43      7
## 2     1    13 Undirected    44      4
## 3     1    28 Undirected    52      3
## 4     1    32 Undirected    53     20
## 5     1    34 Undirected    54      5
## 6     1    41 Undirected    56      5
## # ... with 792 more rows
## #
## # Node Data: 100 x 1
##   name                           
##   <chr>                          
## 1 Aemon-Targaryen-(Maester-Aemon)
## 2 Aeron-Greyjoy                  
## 3 Aerys-II-Targaryen             
## # ... with 97 more rows

as_tbl_graph(cooc_all_f, directed = FALSE) %>%
  activate(nodes) %>% 
  mutate(n_rank_trv = node_rank_traveller()) %>%
  arrange(n_rank_trv)

## # A tbl_graph: 100 nodes and 798 edges
## #
## # An undirected simple graph with 1 component
## #
## # Node Data: 100 x 2 (active)
##   name             n_rank_trv
##   <chr>                 <int>
## 1 Gendry                    1
## 2 Hot-Pie                   2
## 3 Lem                       3
## 4 Beric-Dondarrion          4
## 5 Eddard-Stark              5
## 6 Ramsay-Snow               6
## # ... with 94 more rows
## #
## # Edge Data: 798 x 5
##    from    to Type          id weight
##   <int> <int> <chr>      <int>  <int>
## 1    44    46 Undirected    43      7
## 2    44    45 Undirected    44      4
## 3    44    92 Undirected    52      3
## # ... with 795 more rows

as_tbl_graph(cooc_all_f, directed = FALSE) %>%
  activate(nodes) %>% 
  mutate(neighbors = centrality_degree()) %>%
  arrange(-neighbors)

## # A tbl_graph: 100 nodes and 798 edges
## #
## # An undirected simple graph with 1 component
## #
## # Node Data: 100 x 2 (active)
##   name              neighbors
##   <chr>                 <dbl>
## 1 Tyrion-Lannister        54.
## 2 Cersei-Lannister        49.
## 3 Joffrey-Baratheon       49.
## 4 Robert-Baratheon        47.
## 5 Jaime-Lannister         45.
## 6 Sansa-Stark             44.
## # ... with 94 more rows
## #
## # Edge Data: 798 x 5
##    from    to Type          id weight
##   <int> <int> <chr>      <int>  <int>
## 1    41    42 Undirected    43      7
## 2    41    60 Undirected    44      4
## 3    41    63 Undirected    52      3
## # ... with 795 more rows

as_tbl_graph(cooc_all_f, directed = FALSE) %>%
  activate(nodes) %>% 
  mutate(group = group_infomap()) %>%
  arrange(-group)

## # A tbl_graph: 100 nodes and 798 edges
## #
## # An undirected simple graph with 1 component
## #
## # Node Data: 100 x 2 (active)
##   name              group
##   <chr>             <int>
## 1 Arianne-Martell       7
## 2 Doran-Martell         7
## 3 Davos-Seaworth        6
## 4 Melisandre            6
## 5 Selyse-Florent        6
## 6 Stannis-Baratheon     6
## # ... with 94 more rows
## #
## # Edge Data: 798 x 5
##    from    to Type          id weight
##   <int> <int> <chr>      <int>  <int>
## 1    32    33 Undirected    43      7
## 2    32    34 Undirected    44      4
## 3    32    36 Undirected    52      3
## # ... with 795 more rows

as_tbl_graph(cooc_all_f, directed = FALSE) %>%
  activate(nodes) %>% 
  mutate(center = node_is_center(),
         keyplayer = node_is_keyplayer(k = 10))

## # A tbl_graph: 100 nodes and 798 edges
## #
## # An undirected simple graph with 1 component
## #
## # Node Data: 100 x 3 (active)
##   name                            center keyplayer
##   <chr>                           <lgl>  <lgl>    
## 1 Aemon-Targaryen-(Maester-Aemon) FALSE  FALSE    
## 2 Aeron-Greyjoy                   FALSE  FALSE    
## 3 Aerys-II-Targaryen              FALSE  FALSE    
## 4 Alliser-Thorne                  FALSE  FALSE    
## 5 Arianne-Martell                 FALSE  FALSE    
## 6 Arya-Stark                      FALSE  FALSE    
## # ... with 94 more rows
## #
## # Edge Data: 798 x 5
##    from    to Type          id weight
##   <int> <int> <chr>      <int>  <int>
## 1     1     4 Undirected    43      7
## 2     1    13 Undirected    44      4
## 3     1    28 Undirected    52      3
## # ... with 795 more rows

Node pairs

Some statistics are a measure between two nodes, such as distance or similarity between nodes. In a tidy context one of the ends must always be the node defined by the row, while the other can be any other node. All of the node pair functions are prefixed with node_* and ends with _from/_to if the measure is not symmetric and _with if it is; e.g. there’s both a node_max_flow_to() and node_max_flow_from() function while only a single node_cocitation_with() function. The other part of the node pair can be specified as an integer vector that will get recycled if needed, or a logical vector which will get recycled and converted to indexes with which(). This means that output from node type functions can be used directly in the calls. https://www.data-imaginist.com/2017/introducing-tidygraph/

as_tbl_graph(cooc_all_f, directed = FALSE) %>%
  activate(nodes) %>% 
  mutate(dist_to_center = node_distance_to(node_is_center()))

## # A tbl_graph: 100 nodes and 798 edges
## #
## # An undirected simple graph with 1 component
## #
## # Node Data: 100 x 2 (active)
##   name                            dist_to_center
##   <chr>                                    <dbl>
## 1 Aemon-Targaryen-(Maester-Aemon)             1.
## 2 Aeron-Greyjoy                               2.
## 3 Aerys-II-Targaryen                          1.
## 4 Alliser-Thorne                              1.
## 5 Arianne-Martell                             2.
## 6 Arya-Stark                                  1.
## # ... with 94 more rows
## #
## # Edge Data: 798 x 5
##    from    to Type          id weight
##   <int> <int> <chr>      <int>  <int>
## 1     1     4 Undirected    43      7
## 2     1    13 Undirected    44      4
## 3     1    28 Undirected    52      3
## # ... with 795 more rows

as_tbl_graph(cooc_all_f, directed = FALSE) %>%
  activate(edges) %>% 
  mutate(centrality_e = centrality_edge_betweenness())

## # A tbl_graph: 100 nodes and 798 edges
## #
## # An undirected simple graph with 1 component
## #
## # Edge Data: 798 x 6 (active)
##    from    to Type          id weight centrality_e
##   <int> <int> <chr>      <int>  <int>        <dbl>
## 1     1     4 Undirected    43      7         1.00
## 2     1    13 Undirected    44      4        30.2 
## 3     1    28 Undirected    52      3        42.1 
## 4     1    32 Undirected    53     20         0.  
## 5     1    34 Undirected    54      5        35.2 
## 6     1    41 Undirected    56      5        18.9 
## # ... with 792 more rows
## #
## # Node Data: 100 x 1
##   name                           
##   <chr>                          
## 1 Aemon-Targaryen-(Maester-Aemon)
## 2 Aeron-Greyjoy                  
## 3 Aerys-II-Targaryen             
## # ... with 97 more rows

The complete code

Now let’s combine what we’ve done above in true tidyverse fashion:

cooc_all_f_graph <- as_tbl_graph(cooc_all_f, directed = FALSE) %>%
  mutate(n_rank_trv = node_rank_traveller(),
         neighbors = centrality_degree(),
         group = group_infomap(),
         center = node_is_center(),
         dist_to_center = node_distance_to(node_is_center()),
         keyplayer = node_is_keyplayer(k = 10)) %>%
  activate(edges) %>% 
  filter(!edge_is_multiple()) %>%
  mutate(centrality_e = centrality_edge_betweenness())

We can also convert our active node or edge table back to a tibble:

cooc_all_f_graph %>%
  activate(nodes) %>% # %N>%
  as.tibble()

## # A tibble: 100 x 7
##    name         n_rank_trv neighbors group center dist_to_center keyplayer
##    <chr>             <int>     <dbl> <int> <lgl>           <dbl> <lgl>    
##  1 Aemon-Targa…          7       13.     2 FALSE              1. FALSE    
##  2 Aeron-Greyj…         85        5.     5 FALSE              2. FALSE    
##  3 Aerys-II-Ta…         59       12.     1 FALSE              1. FALSE    
##  4 Alliser-Tho…          6       13.     2 FALSE              1. FALSE    
##  5 Arianne-Mar…         95        4.     7 FALSE              2. FALSE    
##  6 Arya-Stark           34       37.     1 FALSE              1. FALSE    
##  7 Asha-Greyjoy         87        7.     5 FALSE              1. FALSE    
##  8 Balon-Greyj…         86       11.     5 FALSE              2. FALSE    
##  9 Barristan-S…         91       23.     3 FALSE              1. FALSE    
## 10 Belwas               42        6.     3 FALSE              2. FALSE    
## # ... with 90 more rows

cooc_all_f_graph %>%
  activate(edges) %>% # %E>%
  as.tibble()

## # A tibble: 798 x 6
##     from    to Type          id weight centrality_e
##    <int> <int> <chr>      <int>  <int>        <dbl>
##  1     1     4 Undirected    43      7         1.00
##  2     1    13 Undirected    44      4        30.2 
##  3     1    28 Undirected    52      3        42.1 
##  4     1    32 Undirected    53     20         0.  
##  5     1    34 Undirected    54      5        35.2 
##  6     1    41 Undirected    56      5        18.9 
##  7     1    42 Undirected    57     25         0.  
##  8     1    48 Undirected    58    110         0.  
##  9     1    58 Undirected    60      5        24.5 
## 10     1    71 Undirected    62      5        17.0 
## # ... with 788 more rows

layout <- create_layout(cooc_all_f_graph, 
                        layout = "fr")

ggraph(layout) + 
    geom_edge_density(aes(fill = weight)) +
    geom_edge_link(aes(width = weight), alpha = 0.2) + 
    geom_node_point(aes(color = factor(group)), size = 10) +
    geom_node_text(aes(label = name), size = 8, repel = TRUE) +
    scale_color_brewer(palette = "Set1") +
    theme_graph() +
    labs(title = "A Song of Ice and Fire character network",
         subtitle = "Nodes are colored by group")

cols <- RColorBrewer::brewer.pal(3, "Set1")

ggraph(layout) + 
    geom_edge_density(aes(fill = weight)) +
    geom_edge_link(aes(width = weight), alpha = 0.2) + 
    geom_node_point(aes(color = factor(center), size = dist_to_center)) +
    geom_node_text(aes(label = name), size = 8, repel = TRUE) +
    scale_colour_manual(values = c(cols[2], cols[1])) +
    theme_graph() +
    labs(title = "A Song of Ice and Fire character network",
         subtitle = "Nodes are colored by centeredness")

Characters devided by books

The second data set I am going to use is a comparison of character interactions in the five books.

A little node on the side: My original plan was to loop over the separate edge files for each book, concatenate them together with the information from which book they are and then plot them via faceting. This turned out to be a bad solution because I wanted to show the different key-players in each of the five books. So, instead of using one joined graph, I created separate graphs for every book and used the bind_graphs() and facet_nodes() functions to plot them together.

for (i in 1:5) {
  cooc <- read_csv(paste0("/Users/shiringlander/Documents/Github/Data/asoiaf/data//asoiaf-book", i, "-edges.csv")) %>%
    mutate(book = paste0("book_", i)) %>%
    filter(Source %in% main_ch_l$name & Target %in% main_ch_l$name)
  
  assign(paste0("coocs_book_", i), cooc)
}

The concepts are the same as above, here I want to know the key-players in each book:

cooc_books_1_graph <- as_tbl_graph(coocs_book_1, directed = FALSE) %>%
  mutate(book = "Book 1: A Game of Thrones",
         keyplayer = node_is_keyplayer(k = 10))

cooc_books_2_graph <- as_tbl_graph(coocs_book_2, directed = FALSE) %>%
  mutate(book = "Book 2: A Clash of Kings",
         keyplayer = node_is_keyplayer(k = 10))

cooc_books_3_graph <- as_tbl_graph(coocs_book_3, directed = FALSE) %>%
  mutate(book = "Book 3: A Storm of Swords",
         keyplayer = node_is_keyplayer(k = 10))

cooc_books_4_graph <- as_tbl_graph(coocs_book_4, directed = FALSE) %>%
  mutate(book = "Book 4: A Feast for Crows",
         keyplayer = node_is_keyplayer(k = 10))

cooc_books_5_graph <- as_tbl_graph(coocs_book_5, directed = FALSE) %>%
  mutate(book = "Book 5: A Dance with Dragons",
         keyplayer = node_is_keyplayer(k = 10))

And let’s combine and plot the key-players:

cooc_books_1_graph %>% 
  bind_graphs(cooc_books_2_graph)  %>%
  bind_graphs(cooc_books_3_graph)  %>%
  bind_graphs(cooc_books_4_graph)  %>%
  bind_graphs(cooc_books_5_graph)  %>%
  ggraph(layout = "fr") + 
    facet_nodes( ~ book, scales = "free", ncol = 1) +
    geom_edge_density(aes(fill = weight)) +
    geom_edge_link(aes(edge_width = weight), alpha = 0.2) + 
    geom_node_point(aes(color = factor(keyplayer)), size = 3) +
    geom_node_text(aes(label = name), color = "black", size = 3, repel = TRUE) +
    theme_graph() +
    scale_colour_manual(values = c(cols[2], cols[1]))

The networks and key-players of the five different books also offer a few surprises but also a lot that reflects the narrative quite well. I’m not going to go into details here as that would go a bit too far for an R-related blog - but if you are interested in in-depth discussions about the books, email me… ;-)

More info

You can find more info about

• tidygraph here
• ggraph here
• influenceR here
• and DataCamp has a Python project for the same data set here

sessionInfo()

## R version 3.4.3 (2017-11-30)
## Platform: x86_64-apple-darwin15.6.0 (64-bit)
## Running under: macOS High Sierra 10.13.4
## 
## Matrix products: default
## BLAS: /Library/Frameworks/R.framework/Versions/3.4/Resources/lib/libRblas.0.dylib
## LAPACK: /Library/Frameworks/R.framework/Versions/3.4/Resources/lib/libRlapack.dylib
## 
## locale:
## [1] de_DE.UTF-8/de_DE.UTF-8/de_DE.UTF-8/C/de_DE.UTF-8/de_DE.UTF-8
## 
## attached base packages:
## [1] methods   stats     graphics  grDevices utils     datasets  base     
## 
## other attached packages:
##  [1] bindrcpp_0.2       ggraph_1.0.1       tidygraph_1.1.0   
##  [4] forcats_0.3.0      stringr_1.3.0      dplyr_0.7.4       
##  [7] purrr_0.2.4        tidyr_0.8.0        tibble_1.4.2      
## [10] ggplot2_2.2.1.9000 tidyverse_1.2.1    readr_1.1.1       
## 
## loaded via a namespace (and not attached):
##  [1] nlme_3.1-131.1     bitops_1.0-6       lubridate_1.7.3   
##  [4] RColorBrewer_1.1-2 httr_1.3.1         prabclus_2.2-6    
##  [7] rprojroot_1.3-2    tools_3.4.3        backports_1.1.2   
## [10] utf8_1.1.3         R6_2.2.2           KernSmooth_2.23-15
## [13] lazyeval_0.2.1     colorspace_1.3-2   trimcluster_0.1-2 
## [16] nnet_7.3-12        withr_2.1.1.9000   tidyselect_0.2.4  
## [19] gridExtra_2.3      mnormt_1.5-5       compiler_3.4.3    
## [22] cli_1.0.0          rvest_0.3.2        TSP_1.1-5         
## [25] influenceR_0.1.0   xml2_1.2.0         labeling_0.3      
## [28] bookdown_0.7       diptest_0.75-7     caTools_1.17.1    
## [31] scales_0.5.0.9000  DEoptimR_1.0-8     robustbase_0.92-8 
## [34] mvtnorm_1.0-7      psych_1.7.8        digest_0.6.15     
## [37] foreign_0.8-69     rmarkdown_1.8      pkgconfig_2.0.1   
## [40] htmltools_0.3.6    rlang_0.2.0.9000   readxl_1.0.0      
## [43] rstudioapi_0.7     bindr_0.1          jsonlite_1.5      
## [46] mclust_5.4         gtools_3.5.0       dendextend_1.7.0  
## [49] magrittr_1.5       modeltools_0.2-21  Rcpp_0.12.15      
## [52] munsell_0.4.3      viridis_0.5.0      stringi_1.1.6     
## [55] whisker_0.3-2      yaml_2.1.17        MASS_7.3-49       
## [58] flexmix_2.3-14     gplots_3.0.1       plyr_1.8.4        
## [61] grid_3.4.3         parallel_3.4.3     gdata_2.18.0      
## [64] ggrepel_0.7.0      crayon_1.3.4       udunits2_0.13     
## [67] lattice_0.20-35    haven_1.1.1        hms_0.4.1         
## [70] knitr_1.20         pillar_1.2.1       igraph_1.1.2      
## [73] fpc_2.1-11         stats4_3.4.3       reshape2_1.4.3    
## [76] codetools_0.2-15   glue_1.2.0         gclus_1.3.1       
## [79] evaluate_0.10.1    blogdown_0.5       modelr_0.1.1      
## [82] tweenr_0.1.5       foreach_1.4.4      cellranger_1.1.0  
## [85] gtable_0.2.0       kernlab_0.9-25     assertthat_0.2.0  
## [88] xfun_0.1           ggforce_0.1.1      broom_0.4.3       
## [91] class_7.3-14       viridisLite_0.3.0  seriation_1.2-3   
## [94] iterators_1.0.9    registry_0.5       units_0.5-1       
## [97] cluster_2.0.6