• Data activity (10 min)
• Introduction to Networks (10 min)
• Building our first networks (20 min)
• Measures of Centrality (15 min)
• Break (5 min)
• IPCC Report Authorship (25 min)
• Final project time (Remainder)

print.data.frame(groups)

##                   group 1             group 2               group 3
## 1      Jun, Ernest Ng Wei       Ning, Zhi Yan       Tan, Zheng Yang
## 2            Shah, Jainam           Su, Barry           Tian, Zerui
## 3         Gnanam, Akash Y        Gupta, Umang        Somyurek, Ecem
## 4 Alsayegh, Aisha E H M I Andrew Yu Ming Xin, Leong, Wen Hou Lester
##                     group 4                          group 5
## 1   Spindler, Laine Addison             Dotson, Bianca Ciara
## 2             Cai, Qingyuan Ramos, Jessica Andria Potestades
## 3 Saccone, Alexander Connor           Cortez, Hugo Alexander
## 4          Wan Rosli, Nadia                                 
##                 group 6                  group 7
## 1   Premkrishna, Shrish Huynh Le Hue Tam, Vivian
## 2       Knutson, Blue C                         
## 3         Lim, Fang Jan             Ng, Michelle
## 4 Widodo, Ignazio Marco      Albertini, Federico

• Task: communicate a message about the data using a visual approach of your choosing.
• Consider: which information is most important? how much can you display graphically?
• Visualization does not need to be complete!

• Understand network structure (node vs. edge, directed vs. undirected)
• Learn how to plot networks using igraph
• Understand different types of centrality and what these mean
• Motivate examination of IPCC authorship network

• Two elements:

1. Nodes
2. Edges

Network example. From Nykamp DQ, “An introduction to networks”.

• Two types of edges:

1. Directed

• e.g. cash payments, job applications, academic citations, etc.

1. Undirected

Directed Network. From Nykamp DQ, “An introduction to networks”.

• Two types of edges:

1. Directed
2. Undirected

• e.g. friendship ties, common board members, shared destinations, etc.

Undirected Network. From Nykamp DQ, “An introduction to networks”.

• We can modify the nodes and edges according to various characteristics to make our visuals more interesting

• Nodes are users
• Edges are twitter interactions
• Colors based on opinions

• Nodes are actors
• Edges are information shared
• Color based on agreement with ‘There should be an international binding commitment on all nations to reduce GHG emissions’.

• Special case: two-mode network
• Small nodes are actors, large nodes are organizations

• Can represent this as one-mode network
• Now ties represent shared actors
• Colors represent funding from Koch/Exxon (green) or not (red)

• Let’s create a network!
• We’ll represent friendship ties among 7 people
• We’ll call it el for “edge list”
• Notice how the data structure is different
• Needs to be a matrix

el <- data.frame(person_1 = c("Lionel", "Frederica", "Garrett", "Lina",
                               "Sampson", "Garrett", "Frederica", "Lionel",
                              "Frederica", "Frederica", "Ahmad"),
                  person_2 = c("Lina", "Charlotte", "Lina", "Sampson",
                               "Charlotte", "Lionel", "Lina", "Sampson",
                               "Sampson", "Garrett", "Garrett")) %>%
  as.matrix()
# take a look
el

##       person_1    person_2   
##  [1,] "Lionel"    "Lina"     
##  [2,] "Frederica" "Charlotte"
##  [3,] "Garrett"   "Lina"     
##  [4,] "Lina"      "Sampson"  
##  [5,] "Sampson"   "Charlotte"
##  [6,] "Garrett"   "Lionel"   
##  [7,] "Frederica" "Lina"     
##  [8,] "Lionel"    "Sampson"  
##  [9,] "Frederica" "Sampson"  
## [10,] "Frederica" "Garrett"  
## [11,] "Ahmad"     "Garrett"

• We can use igraph to create a network object
• Should it be directed?

library(igraph)

# create network from edge list
net <- graph_from_edgelist(el)

• Let’s assume friendships are bidirectional (undirected)

library(igraph)

# create network from edge list
net <- graph_from_edgelist(el, directed = FALSE)

• Let’s try plotting our network!

# plot network
plot(net)

• We can adjust the graph using arguments that start with vertex and edge

# customize network plot
plot(net, vertex.size = 30, 
     vertex.color = "lavender", 
     vertex.frame.color = NA, 
     vertex.label.cex = .7, 
     edge.curved = .05, 
     edge.arrow.size = .3, 
     edge.width = .7, 
     edge.color = "gray1")

• Degree Centrality
• Based on number of edges, node with most edges is most central

• Betweenness Centrality
• Based on “shortest paths” between nodes, node involved in most “shortest paths” is most central

• Closeness Centrality
• Based on “shortest paths” between nodes, node with lowest average “shortest path” to the others is most central

• Eigenvalue Centrality
• Based on the degree of adjacent nodes, node with “friends in high places” is most central

• Group activity:
• Which point(s) have the highest degree centrality? (most edges)
• Betweenness centrality? (involved in most “shortest paths”)
• Closeness centrality? (lowest average “shortest path” to others)
• Eigenvalue Centrality? (“friends in high places”)

• IPCC has written 6 climate assessments since 1990 (FAR - AR6)
• Three working groups:
• WGI: physical and scientific basis of climate change
• WGII: vulnerability of natural and social systems to climate change
• WGIII: mitigation strategies and policy recommendations
• All of these influence global policies and mitigation strategies
• Geographic bias? Most authors come from “Global North” countries

• Let’s take a look at the WGIII authors

ipcc_authors <- read_csv("IPCC_co_authorship.csv",
                         skip = 1)

• Need to clean up data

library(dplyr)
# reorder column names to match rows
ipcc_authors %<>%
  select(order(colnames(.)))


# turn dataframe into matrix
ipcc_authors %<>%
  select(-Author) %>%
  as.matrix()

• Now we can turn it into a network!

ipcc_net <- graph_from_adjacency_matrix(ipcc_authors,
                                        mode = "undirected")

• Try plotting

plot(ipcc_net, vertex.size = 2, 
     vertex.color = "lavender", 
     vertex.frame.color = NA, 
     vertex.label.cex = .5, 
     edge.curved = .05, 
     edge.width = .1, 
     edge.color = "gray1")

• Let’s only look at \(\ge2\) collaborations

# replace 1s with 0s
ipcc_authors[ipcc_authors == 1] = 0

# replace NAs with 0s
ipcc_authors[is.na(ipcc_authors)] = 0

• Let’s remove authors who did not collaborate with anyone

# vector of authors who do not collaborate with others
no_colab <- which(apply(ipcc_authors, 1, sum, na.rm = TRUE) == 0)


# then we can remove these from ipcc_authors
ipcc_authors <- ipcc_authors[-no_colab,
                             -no_colab]

• Now let’s try again

# create network, again
ipcc_net <- graph_from_adjacency_matrix(ipcc_authors,
                                        mode = "undirected")

plot(ipcc_net, vertex.size = 2, 
     vertex.color = "lavender", 
     vertex.frame.color = NA, 
     vertex.label.cex = .5, 
     edge.curved = .05, 
     edge.width = .1, 
     edge.color = "gray1")

• We can set network characteristics using V()

# add betweenness centrality
V(ipcc_net)$betweenness <- betweenness(ipcc_net)

• We can use network characteristics to format plot

plot(ipcc_net, 
     vertex.size = V(ipcc_net)$betweenness/max(V(ipcc_net)$betweenness) * 20, 
     vertex.color = "lavender", 
     vertex.frame.color = NA, 
     vertex.label.cex = .5, 
     edge.curved = .05, 
     edge.width = .1, 
     edge.color = "gray1")

• Touch base with me on final project if you have not yet!
• Grading rubrics up on Canvas

• Data activity (10 min)
• IPCC Report Authorship (25 min)
• Discussion on networks (10 min)
• Break (5 min)
• Interactive network plots (15 min)
• Migration and chord diagrams (5 min)
• Final Reflections (10 min)
• Final project time (Remainder)

print.data.frame(groups)

##                   group 1             group 2               group 3
## 1      Jun, Ernest Ng Wei       Ning, Zhi Yan       Tan, Zheng Yang
## 2            Shah, Jainam           Su, Barry           Tian, Zerui
## 3         Gnanam, Akash Y        Gupta, Umang        Somyurek, Ecem
## 4 Alsayegh, Aisha E H M I Andrew Yu Ming Xin, Leong, Wen Hou Lester
##                     group 4                          group 5
## 1   Spindler, Laine Addison             Dotson, Bianca Ciara
## 2             Cai, Qingyuan Ramos, Jessica Andria Potestades
## 3 Saccone, Alexander Connor           Cortez, Hugo Alexander
## 4          Wan Rosli, Nadia                                 
##                 group 6                  group 7
## 1   Premkrishna, Shrish Huynh Le Hue Tam, Vivian
## 2       Knutson, Blue C                         
## 3         Lim, Fang Jan             Ng, Michelle
## 4 Widodo, Ignazio Marco      Albertini, Federico

• Task: communicate a message about the data using a visual approach of your choosing.
• Consider: which information is most important? how much can you display graphically?
• Visualization does not need to be complete!

• Plot networks with node/edge attributes
• Consider cases of network data in issues relating to climate change and society
• Consider uses of interactive networks and chord diagrams
• Reflect on class

• Review of what we’ve done:
• (no need to run again if you have ipcc_authors in your environment)
• First, read in data

ipcc_authors <- read_csv("IPCC_co_authorship.csv",
                         skip = 1)

• Clean it up!

library(dplyr)
# reorder column names to match rows
ipcc_authors %<>%
  select(order(colnames(.)))


# turn dataframe into matrix
ipcc_authors %<>%
  select(-Author) %>%
  as.matrix()

• Let’s only look at \(\ge2\) collaborations

# replace 1s with 0s
ipcc_authors[ipcc_authors == 1] = 0

# replace NAs with 0s
ipcc_authors[is.na(ipcc_authors)] = 0

• We removed authors who did not collaborate with anyone

# vector of authors who do not collaborate with others
no_colab <- which(apply(ipcc_authors, 1, sum, na.rm = TRUE) == 0)


# then we can remove these from ipcc_authors
ipcc_authors <- ipcc_authors[-no_colab,
                             -no_colab]

• Create new igraph object
• Can change weighted = TRUE to weight by collaborations

# create network, again
ipcc_net <- graph_from_adjacency_matrix(ipcc_authors,
                                        mode = "undirected",
                                        weighted = TRUE)

• We set network characteristics using V()

# add betweenness centrality
V(ipcc_net)$betweenness <- betweenness(ipcc_net)

• We can examine the “most central” authors, according to betweeenness scores

# show authors in descending order
V(ipcc_net)[order(V(ipcc_net)$betweenness, decreasing = TRUE)]

## + 148/148 vertices, named, from cd68747:
##   [1] Shukla             Schaeffer          Smith             
##   [4] Edenhofer          Price              Carraro           
##   [7] Uerge-Vorsatz      Krey               Riahi             
##  [10] Clarke             Rogner             Lutz              
##  [13] Kahn-Ribeiro       Nakicenovic        Winkler           
##  [16] Hoehne             Paltsev            Michaelowa        
##  [19] Strachan           Sathaye            Faaij             
##  [22] Hourcade           Ravindranath       Halsnaes          
##  [25] Bosetti            Zhang              Skea              
##  [28] Den-Elzen          Lecocq             Fischedick        
## + ... omitted several vertices

• We can specify that we want edge width to be proportional to weights:

# plot network
plot(ipcc_net, 
   edge.width=(E(ipcc_net)$weight)/5,
    vertex.size = V(ipcc_net)$betweenness/max(V(ipcc_net)$betweenness) * 20, 
     vertex.color = "lavender", 
     vertex.alpha = 0.5,
     vertex.frame.color = NA, 
     vertex.label.cex = .5, 
     edge.curved = .05, 
     edge.width = .1, 
     edge.color = "gray1")

• We can specify that we want edge width to be proportional to weights:

• What else could we add to the plot?

• We could add region to examine differences in network centrality

# read in cv data
ipcc_cvs <- read_csv("IPCC_cv.csv")

# define global regions
ipcc_cvs %<>%
  mutate(region = case_match(`IPCC representing country (i.e. Country of residence from IPCC doc)`,
                             # Europe will be green
                             c("Austria", "Belgium", "Denmark", "Finland", 
                               "France", "Germany", "Greece", "Hungary", "Italy",
                               "Netherlands", "Norway", "Spain", "Sweden", 
                               "Switzerland", "UK") ~ "green4", 
                             # North America will be red
                             c("Canada", "USA", "Mexico") ~ "tomato",
                             # BRICS will be blue
                             c("Brazil", "Russia", "India", "China", 
                               "South Africa") ~ "steelblue", 
                             # Other countries will be gold
                             .default = "gold"))

• Define region variable for the vertices

# define country variable
V(ipcc_net)$region <- ipcc_cvs$region

• Can change vertex color using vertex.color

# plot network
plot(ipcc_net, 
   edge.width=(E(ipcc_net)$weight)/5,
    vertex.size = V(ipcc_net)$betweenness/max(V(ipcc_net)$betweenness) * 20, 
     vertex.color = V(ipcc_net)$region, 
     vertex.alpha = 0.5,
     vertex.frame.color = NA, 
     vertex.label.cex = .5, 
     edge.curved = .05, 
     edge.width = .1, 
     edge.color = "gray1")

• Finally, we can add a legend manually

# add legend
legend(
  "bottomright",
  legend = c("Europe", "North America", "BRICS", "Other"),
  pt.bg  = c("green4", "tomato", "steelblue", "gold"),
  pch    = 21,
  cex    = 1,
  title  = "Region"
  )

• Finally, we can add a legend manually

• Much of the social dimensions of reactions to and opinions on climate topics have network structures
• We’ll discuss three of these, and how they relate to inequality in resources/beliefs

• First, networks matter for climate resilience

• Second, networks matter for post-disaster inequalities

“local network capacities of Lower Ninth Ward residents relative to those of the more affluent Lakeview neighborhood dissipated before, during, and after the disaster to erode the life chances of individual residents and the neighborhood they once constited.” (Elliott, Haney, & Sams-Abiodun, 2010:624)

“For example, if a translocal tie can help one find housing during evacuation, this assistance may be useful only for those who also possess the financial capital needed to travel there and pay market rent; otherwise, such translocal assistance may be much less useful and therefore go unutilized.” (Elliott et al., 2010:630)

• Third, networks matter for how we form our beliefs around issues like climate change

• In groups discuss:

1. What is an example of a network structure related to climate change and society?
2. What are the nodes? What are the edges?
3. Is centrality in this network important? Which measure(s) best capture(s) this?

• First, transform igraph object to networkd3 object

library(networkD3)

# create dataframe for networkD3
ipcc_d3 <- igraph_to_networkD3(ipcc_net, group = V(ipcc_net)$region)

• Next, set color palette (optional)

# set color scale
ColourScale <- 'd3.scaleOrdinal()
            .domain(["Europe", "North America", "BRICS", "Other"])
           .range(["#07C343", "#D2140C", "#0C4AD2", "#C7D20C"]);'

• Then use forceNetwork() to build interactive network

p <- forceNetwork(Links = ipcc_d3$links,
                  Nodes = ipcc_d3$nodes,
                  Group = "group",
                  height="400px", width="800px",
                  NodeID = "name",
                  fontSize = 14,
                  colourScale = JS(ColourScale),
                  zoom = TRUE)

• Plot network!

# plot network!
p

• First, read in migration data

# read migration data
ca_migration <- read_csv("ca_migration.csv")

## Rows: 28 Columns: 3
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr (2): from, to
## dbl (1): value
## 
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.

• Set up chord diagram
• Code modified from r-graph-gallery.com

library(circlize)
library(stringr)
library(viridis)

# create chord diagram
chordDiagram(ca_migration,
             transparency = 0.25,
              grid.col = inferno(7),
  directional = 1,
  direction.type = c("arrows", "diffHeight"), 
  diffHeight  = -0.04,
  annotationTrack = "grid", 
  annotationTrackHeight = c(0.05, 0.1),
  link.arr.type = "big.arrow", 
  link.sort = TRUE, 
  link.largest.ontop = TRUE)

• Add stylistic choices

# Add text and axis
circos.trackPlotRegion(
  track.index = 1, 
  bg.border = NA, 
  panel.fun = function(x, y) {
    
    xlim = get.cell.meta.data("xlim")
    sector.index = get.cell.meta.data("sector.index")
    
    # Add names to the sector. 
    circos.text(
      x = mean(xlim), 
      y = 2.2, 
      labels = sector.index, 
      facing = "bending", 
      cex = 0.8
      )

  }
)

• When can we use chord diagrams?

• On the first day, we defined climate change and data science
• Think back to how you defined these!
• In groups: have your definitions changed during this class?
• What has led your conceptions of these topics to change or remain stable?
• What are the possibilities for using data science tools to think about climate change? What are the challenges?

• Fixed typo in question 3 (betweenness and eigenvalue scores switched)
• Bookdown is correct now
• Won’t take points off if you’ve already turned it in and misinterpreted this

• 12 minutes slides (max!)
• 5-8 minutes Q&A
• We will start promptly at 1:30! Recommend getting here early so we can leave on time
• Can present on own computers (hdmi cord w/ adapter) or email slides to me