Chapter 7 Networks and Inequality

In this section, we will look at a network analysis. Networks emerged from a combination of sociological theory, linear algebra, statistics, and graph theory. They present a totally different way of thinking about data than most of previous topics. Here, we’ll cover different types of networks and methods for viewing them. Substantively, we will consider inequality in networks as this relates to disasters and changes in the environment.

7.1 What Are Networks?

Networks have two elements: nodes and edges. Nodes, or vertices, are points, and edges, or links, are the connections between the nodes. We can illustrate these with a simple network graph:

Network example. From [Nykamp DQ, "An introduction to networks"](https://mathinsight.org/network_introduction).

Figure 7.1: Network example. From Nykamp DQ, “An introduction to networks”.

Importantly, a network’s edges can be directed or undirected. Directed edges constitute flows from one node to another; the order matters. These could be cash payments, academic citations, school transfers, social media follows, or anything else where the direction of the edge would matter. A directed network graph could look like the figure below. Notice how each edge is unidirectional, and that a pair of nodes can have two edges between them.

Directed Network. From [Nykamp DQ, "An introduction to networks"](https://mathinsight.org/network_introduction).

Figure 7.2: Directed Network. From Nykamp DQ, “An introduction to networks”.

Undirected edges constitute bidirectional ties, in which the order does not matter. These could be friendships or romantic partnerships, classes that students have taken together, bills that congresspeople have written together, companies that share a board member, or anything else where the connection is the same for both parties. A possible undirected network is shown here:

Undirected Network. From [Nykamp DQ, "An introduction to networks"](https://mathinsight.org/network_introduction).

Figure 7.3: Undirected Network. From Nykamp DQ, “An introduction to networks”.

For both directed and undirected networks, we may want to modify the edges according to characteristics of the ties (for example, are these strong or weak connections?), and we may want to modfiy the nodes according to their characteristics as well (for example, what group is each member from?). We can do this by changing the color, shape, line width, and so on of our network, as we might do for other types of visualization.

7.2 A Broader View of Climate Change, Networks, and Inequality

Networks are relevant to the changing climate in several ways. Here, I’ll focus on a few major ways in which network analysis can contribute to our understand of, and our mitigation of the climate crisis.

First, networks matter in disasters. In the book Heat Wave, Eric Klinenberg notes the protective role of social networks in the 1995 Chicago Heat Wave. In an article that we read, this is how Klinenberg describes a poor neighborhood in Chicago with strong social networks:

“Older people there belonged to block clubs; residents assured me they knew who they had to keep tabs on during the heat wave.”

By checking in on each other during the heat wave, the residents ensured that they were taking precautionary measures and that they would notice early warning signs. Klinenberg contrasts this to another neighborhood in which residents are far more isolated, and therefore tended to face the heat wave on their own. In the latter case, social isolation meant that residents had no one checking in on them, contributing to much higher mortality rates.

Second, social networks can explain a link between disasters and social inequalities. People affected by disasters like hurricanes often stay with family or friends in the aftermath. Families with higher socioeconomic status are more likely to be able to stay with other affluent families in regions farther from the disaster, contributing to more stability in their recovery trajectories. Fothergill and Peek detail this in their book, Children of Katrina.

Finally, networks of information are vital to understanding how people think about climate change. We’ve discussed the role of Twitter bots in spreading climate misinformation. But networks of climate uncertainty go far beyond Twitter bots: this study looks at contrarian information networks across board executives, politicians, and think tanks in the U.S. It finds that “successful production and diffusion of contrarian information has a particular network structure and corporate influence.” That is, there are particular actors and elite funders that are central to disseminating contrarion information about climate change in the U.S. This article further expands on networks of the “climate change countermovement,” and its ties to oil and coal companies.

In sum, networks help to explain some of the most pressing questions relating to climate change and climate disasters: why do outcomes differ across places, and across social groups? And why does uncertainty about climate change persist, despite vast scientific evidence? In the following sections, we’ll learn how to build our own networks, and how to apply these to authorship of climate change reports and migration flows between counties.

7.3 Building And Visualizing Networks

Let’s first create a network. We’ll make a dataframe where every row represents an edge, and the two variables represent from which node the edge goes to (and from). You’ll notice that the names can appear more than once - we can think about this as friendship ties, each person could have multiple friends, which would be represented as unique rows. We’ll need to put the data in matrix form in order for our later network functions to perform correctly. We’ll call this el, for “edge list.”

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"

Now we can convert our data to a network with igraph. We can specify here whether our network is directed or not. This choice is meaningful: if our network simply represents friendship ties, this would best be represented as an undirected network (assuming the friendships are bidirectional). However, it could be that our network represents aid given to friends after a disaster (e.g. who let who stay at their home after a hurricane). In the latter case, person_1 may represent the person who is displaced and person_2 may represent the person hosting. For now, we will consider our edges to simply represent bidirectional frienships, so our network will be undirected.

library(igraph)

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

Great! Now let’s try to visualize our network.

# plot network
plot(net)

We can make the graph more visually appealing by changing some of the default settings.

# 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")

7.4 Measures of Centrality

We may be interested in measuring how central each node is to the entire network. We will focus on the following four measures of network centrality:

  • Degree Centrality
  • Betweenness Centrality
  • Eigenvector Centrality
  • Closeness Centrality

These four measures are similar, but measure slightly different concepts. These differences are illustrated here:

Degree Centrality counts how many edges each node has. The node with the most edges, therefore, is most central. This is a straightforward approach to understanding centrality that is easily communicated: in a friendship network, the most “central” actor would simply be the person with the most friends. This would capture the most popular actor, in some sense.

We can calculate degree centrality using the degree() function. In our network, Lina, Frederica, Garrett, and Sampson are all tied for the highest degree centrality.

degree(net)
##    Lionel      Lina Frederica Charlotte   Garrett   Sampson     Ahmad 
##         3         4         4         2         4         4         1

Betweenness Centrality considers how important nodes are to the flow of information (or other resources) between nodes. Betweenness similarity measures the shortest path between every combination of nodes. It then counts how many “shortest paths” each node is involved in, and the node with the most is considered most central. We might want to use this measure if we are interested in actors that connect different groups: for example, it could be that the most popular politician is also immersed in an echochamber, and we would not want to consider them central to the functioning of the entire network. In this case we could use the betweenness centrality to get a sense of who is a “bridging tie” between the most members of the entire network.

Betweenness centrality can be calculated using the betweenness() function. According to this metric, Garrett reigns supreme! This is mostly because Garrett has the sole tie to Ahmad, and thus is involved in every “shortest path” involving Ahmad.

betweenness(net)
##    Lionel      Lina Frederica Charlotte   Garrett   Sampson     Ahmad 
## 0.6666667 1.0000000 3.1666667 0.0000000 5.3333333 1.8333333 0.0000000

Closeness Centrality similarly makes use of the “shortest paths” between nodes. Closeness centrality is measured by averaging the values of these shortest paths from one node to all others (farness), and then taking the reciprocal of this. We might want to use this if we are interested in not necessarily the flow of information, but in which members may have access to all other members of the network.

Closeness centrality can be calculated using the closeness() function. By this metric, Lina, Frederica, and Garrett are all at equally central positions (but not Sampson, as was the case in the degree centrality measure. This is because the shortest path from Sampson to Ahmad involves 3 edges).

closeness(net)
##     Lionel       Lina  Frederica  Charlotte    Garrett    Sampson      Ahmad 
## 0.11111111 0.12500000 0.12500000 0.09090909 0.12500000 0.11111111 0.07692308

Eigenvector Centrality considers not only the ties of the node of interest (or ego), but also the ties of nodes that they are connected to (their alters). The Eigenvector Centrality measure rewards alters with lots of connections. Perhaps if we are looking at a network of politicians and lobbyists, we want to consider not just individual’s ties, but whether they are tied to powerful people. An influential member might only have a few ties, but each of these ties would be extremely popular.

We can calculate Eigenvector Centrality using the evcent() function. We also need to specify that we want the $vector result. According to this metric, Lina is the most central! This is because Lina is close to other popular people, who have lots of social ties themselves.

evcent(net)$vector
##    Lionel      Lina Frederica Charlotte   Garrett   Sampson     Ahmad 
## 0.7910018 1.0000000 0.9429201 0.5334790 0.8472419 0.9304545 0.2412682

We can compare these four measures of centrality all together with the code below:

library(tidyr)
library(ggplot2)
# create dataframe with similarity scores
central_df <- data.frame(degree = degree(net),
                         betweenness = betweenness(net),
                         closeness = closeness(net),
                         eigenvector = evcent(net)$vector)

# all the measures are on different scales, we can standardize them with scale()
central_df %<>%
  mutate_all(scale)

# pivot so that the type of score is a variable and the value is another variable
central_df %<>%
  mutate(name = rownames(.)) %>%
  pivot_longer(-c(name),
               names_to = "centrality",
               values_to = "standardized value")

# now plot the centrality scores
ggplot(central_df, aes(name, `standardized value`))+
  geom_point(aes(col = centrality), size = 2)+
  theme_bw()

There are other measures of centrality, such as Bonacich Centrality and Google’s Page Rank, which go beyond the scope of this course. Hoffman’s “Methods for Network Analysis” bookdown has more information on these.

7.5 Co-Authorship Patterns

We’ll now turn to an example involving authors of the Intergovernmental Panel on Climate Change’s (IPCC) climate reports. The IPCC has written six assessment reports since 1990, each detailing the state of climate change and governmental actions which exacerbate or mitigate its effects. These reports garner much media attention and are influential in global plans to curtain the worst effects of the changing climate. In recent years, scholars have begun to examine geographic biases in representation in authorship of these reports, with most authors coming from the Global North.

Here, we will work with the data from this paper, which analyzes networks of co-authorship in the fifth assessment report (AR5). Specifically, the paper examines authorship on the third working group’s (WGIII) contribution to the report, which details mitigation of climate impacts. The authors of the study have calculated the number of co-authorships between the researchers on the WGIII (i.e. the number of times that these researchers published scientific papers together, outside of the AR5). I’ve added this data file to Canvas, but you can also download all the data from the paper in the Supplementary Information.

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

We can then view the co-authorship:

Table 7.1: IPCC AR5 Co-Authors
Author Victor Zhou_Dadi Ahmed Olivier Rogner Yamaguchi Gruebler Bosetti Cooke Dutt Gupta_Shreekant Ha-Duong Held Kunreuther Linnerooth-Bayer Patt Shittu Weber Attzs Broome Bruvoll Fullerton Gollier Hanemann Hassan Jotzo Urama Kolstad Kverndokk Meyer Mundaca Okereke Bolwig Corbera Fleurbaey Kartha Lecocq Lutz Muylaert-de-Araujo Norgaard Pinguelli-Rosa Ruth Sathaye Gerlagh Barrett Nakicenovic Pathak Rice_Jake Stern Suh Verbruggen de Coninck Mathur Ofosu-Ahenkorah Pan Toth Rose Akimoto Clarke Fisher-Vanden Hourcade Krey Kriegler Loeschel Paltsev Tavoni Van-Vuuren Blanford Jiang_Kejun Chen_Wenying Van-der-Zwaan Weyant Wiser Bruckner Chum De-La-Vega-Navarro Edmonds Faaij Fungtammasan Hertwich Honnery Infield Kim_Suduk Mulugetta Nimir Parikh_Kirit Riahi Skea Strachan Kainuma Zhang Creutzig Cruz-Nunez DAgosto Deakin Dimitriu Figueroa-Meza Fulton Kahn-Ribeiro McKinnon Newman Ouyang Schaeffer Schauer Sims Sperling_Daniel Akbari Brown Cabeza Eyre Gadgil Harvey Jiang_Yi Murakami_Shuzo Parikh_Jyoti Uerge-Vorsatz Vilarino Zain-Ahmed Lucon Abdel-Aziz Acquaye Allwood Ceron Clift Fischedick Kheshgi Lanza Price Roy Santalla Tanaka Yetano-Roche Ahammad Bustamante Clark Elsiddig Haberl Harper Jafari Krug Masera-Cerutti Mbow Nabuurs Rice_Charles Smith Tubiello Bigio Blanco_Hilda Cervero Delgado-Ramos Dhakal Inaba Kansal Lwasa McMahon Mueller Murakami_Jin Nagendra Ramaswami Seto Paterson Brewer Conte-Grand Finus Gupta_Joyeeta Hoehne Ivanova-Boncheva Michaelowa Morgan Den-Elzen Stavins Wiener Winkler Agrawala Cottier Guan Gutierrez-Espeleta Halsnaes Jiang_Leiwen Klasen Lewis Rauscher Venables Barreto-Gomez Somanathan Sugiyama Sterner Zylicz Chimanikire Dubash Goulder Jaffe Jaenicke Labandeira Managi Mitchell Montero Seroa-da-Motta Barua Carraro Frankel Gomez-Echeverri Gupta_Sujata Harnisch Karrouk Kopp Lefevre Machado-Filho Massetti Perez-Arriaga Haites Edenhofer Pichs-Madruga Sokona Yamba Zatari Muvundika Acosta-Moreno Bashmakov Bertoldi Bouille Carino-Olvera Dadhich El-Gizouli Essandoh-Yeddu Geng Huang_Yongfu Ling Liphoto Nzunda Perczyk Pyke Ramakrishna Robledo-Abad Romanovskaya Sagar Sheinbaum Tiwari Torres-Martinez Zou Babiker Sheikho Llanes-Regueiro Chen_Ying Blanco_Gabriel Diaz-Morejon Richels Zhou_Peter Gomes Shukla Garg Khennas Kobayashi Mirasgedis Palvolgy Nenov Dong Ravindranath Sperling_Frank Dewar Huang_Luxin Lee Wen Demkine Gamez-Vazquez Kim_Yong-Gun Messouli Uddin Suliman Fifita Teng Chingambo Garrido-Vazquez
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Vilarino 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 NA 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Weber 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 1 0 NA 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Wen 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 NA 0 0 0 0 0 0 0 0 0 0
Weyant 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 5 0 0 1 0 0 0 0 1 0 0 0 0 NA 0 0 0 0 4 0 0 0 0 0 0 0 0 1 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Wiener 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 NA 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Winkler 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 2 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 0 0 0 2 0 0 NA 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Wiser 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 NA 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Yamaguchi 0 0 0 0 1 NA 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Yamba 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 NA 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Yetano-Roche 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 NA 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Zain-Ahmed 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 NA 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Zatari 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Zhang 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 NA 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Zhou_Dadi 0 NA 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Zhou_Peter 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 NA 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Zou 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 NA 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Zycliz 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 NA 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

We notice that this network data has a different structure than the dataframe that we used earlier. This structure is called an adjacency matrix. It is also a sparse matrix because most of the values are 0.

To create a network from these data, we’ll transform it from a dataframe to a matrix object, and use graph_from_adjacency_matrix().

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


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

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

Great! Let’s try plotting the network.

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 notice that there are several authors who have not co-authored with anyone else in the group, and then a large clump of authors who do collaborate with each other (but it is hard to tell exactly how much or who might be central players within this group). There are also many periphery authors who may have collaborated with just one or two others.

To examine the network in further detail, we can increase the threshold for an edge: as is done in the Nature Climate Change paper, we will only consider two or more co-authorships to constitute edges. We can do this by changing all the 1’s in our adjacency matrix to 0’s. Since ipcc_authors is a matrix, we will do this using base R’s index (rather than dplyr’s mutate functions, which only work with dataframes).

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

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

We can also remove all the authors who don’t collaborate with anyone else. We’ll do this by creating a vector of these indices, and then removing them from both the rows and columns of the matrix (remember that the matrix is symmetric).

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

# we can see the names of these authors by changing the margin to 2
which(apply(ipcc_authors, 2, sum, na.rm = TRUE) == 0)
##         Abdel-Aziz      Acosta-Moreno            Ahammad              Ahmed 
##                  1                  2                  5                  6 
##            Akimoto              Attzs              Barua              Bigio 
##                  8                 10                 14                 17 
##     Blanco_Gabriel       Blanco_Hilda            Bouille             Brewer 
##                 18                 19                 23                 24 
##             Broome            Bruvoll             Cabeza       Chen_Wenying 
##                 25                 28                 30                 35 
##        Chimanikire          Chingambo              Clark              Clift 
##                 37                 38                 40                 42 
##        Conte-Grand              Cooke            Corbera            Cottier 
##                 43                 44                 45                 46 
##           Creutzig         Cruz-Nunez De-La-Vega-Navarro         de Coninck 
##                 47                 48                 51                 52 
##      Delgado-Ramos            Demkine              Dewar           Dimitriu 
##                 54                 55                 57                 60 
##             Dubash         El-Gizouli           Elsiddig     Essandoh-Yeddu 
##                 62                 66                 67                 68 
##             Fifita              Finus          Fleurbaey            Frankel 
##                 71                 73                 76                 77 
##          Fullerton             Fulton       Fungtammasan    Garrido-Vazquez 
##                 78                 79                 80                 84 
##    Gomez-Echeverri Gutierrez-Espeleta             Harvey             Hassan 
##                 89                 96                104                105 
##            Honnery        Huang_Luxin       Huang_Yongfu              Inaba 
##                109                111                112                113 
##            Infield           Jaenicke             Jafari            Karrouk 
##                114                116                117                126 
##             Kartha            Khennas          Kim_Suduk       Kim_Yong-Gun 
##                127                128                130                131 
##             Klasen            Kolstad         Labandeira                Lee 
##                132                134                141                144 
##            Lefevre               Ling            Liphoto    Llanes-Regueiro 
##                145                147                149                150 
##           Loeschel              Lwasa      Machado-Filho             Mathur 
##                151                154                155                159 
##           McKinnon           Messouli              Meyer            Montero 
##                161                163                164                168 
##             Morgan          Mulugetta            Mundaca     Murakami_Shuzo 
##                169                171                172                174 
##          Muvundika              Nenov             Newman              Nimir 
##                175                180                181                182 
##             Nzunda    Ofosu-Ahenkorah            Okereke            Olivier 
##                184                185                186                187 
##             Ouyang                Pan       Parikh_Jyoti       Parikh_Kirit 
##                188                191                192                193 
##           Paterson            Perczyk      Perez-Arriaga               Pyke 
##                194                197                198                202 
##        Ramakrishna           Rauscher       Robledo-Abad       Romanovskaya 
##                203                205                211                213 
##              Sagar           Santalla     Seroa-da-Motta            Sheikho 
##                217                218                222                224 
##             Shittu         Somanathan    Sperling_Daniel     Sperling_Frank 
##                226                232                233                234 
##            Suliman               Teng             Tiwari    Torres-Martinez 
##                241                244                245                246 
##              Uddin           Venables           Vilarino                Wen 
##                249                254                257                259 
##             Wiener       Yetano-Roche         Zain-Ahmed             Zatari 
##                261                266                267                268 
##          Zhou_Dadi         Zhou_Peter                Zou             Zylicz 
##                270                271                272                273
# then we can remove these from ipcc_authors
ipcc_authors <- ipcc_authors[-no_colab,
                             -no_colab]

The dimensions of ipcc_authors have now changed from 273 x 273 to 148 x 148.

# 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")

This looks a bit better. We can see that there are peripheral clusters of authorship, as well as a central cluster. However, we still can’t really see who the main actors may be. To make this more visible, we’ll add a variable to the vertices on our network graph with their betweenness scores. We’ll also standardize the betweenness scores by dividing all of them by the maximum and then multiplying by 20.

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


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")

We see that there are several “central” authors. Still, it’s hard to see their names here. We can display the authors’ names, in descending order based on their betweenness scores, using the following code:

# show authors in descending order
V(ipcc_net)[order(V(ipcc_net)$betweenness, decreasing = TRUE)]
## + 148/148 vertices, named, from a9b8e22:
##   [1] Nakicenovic        Smith              Shukla            
##   [4] Price              Edenhofer          Schaeffer         
##   [7] Krey               Bosetti            Carraro           
##  [10] Riahi              Hourcade           Uerge-Vorsatz     
##  [13] Rogner             Sathaye            Van-Vuuren        
##  [16] Clarke             Victor             Faaij             
##  [19] Lutz               Michaelowa         Paltsev           
##  [22] Strachan           Edmonds            Den-Elzen         
##  [25] Hoehne             Zhang              Skea              
##  [28] Kopp               Stavins            Kahn-Ribeiro      
## + ... omitted several vertices

This reveals that Nakicenovic is the “most central” author, at least according to the betweenness metric.

We might want to modify our graph edges to represent the number of collaborations, not just the fact that two authors have collaborated. We can do this by creating a weighted network, and using the weights as edge widths:

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

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

# 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 may also want to modify the attributes of our nodes according to their characteristics. Since geographic biases in IPCC authorship has been raised, let’s start there. We can add the countries that each author represents to our data by joining the IPCC_cv data.

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

Great! However, remember that we removed authors with less than 2 collaborations. So let’s remove these from our CV data too. We’ll use the slice() function, and add a negative in front of no_colab to specify that we don’t want these indices.

# remove authors who did not collaborate
ipcc_cvs %<>%
  slice(-no_colab)

We notice that there are several variables around the country of origin, country of employment, and country representing at the IPCC, as well as other characteristics such as gender and institutional affiliations. We’ll define a new variable indicating the region of the world each author is representing.

# 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"))

Now let’s define a variable for our vertices named region:

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

And let’s try plotting our network with the nodes colored according to country:

# 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")

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

7.6 Interactive Network Visualizations

You might notice that in the previous graphs, it’s still hard to read any names! If only there were a way to create an interactive chart, where one could zoom in on different parts of the network … Here, we will use the networkD3 package to create such an interactive visualization. The package has a igraph_to_networkD3 function which allows us to transform our network into an object that the package can handle. We will specify the vertex feature region as our grouping variable, as we will want to color the nodes by this variable later (but if we were ok with the nodes all being the same color, then we wouldn’t need the group argument).

library(networkD3)

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

Great. Next, we’ll set a color scale for our visualization. part of this code draws from JavaScript, so it looks a bit different from what we’ve done so far. For more information, see here.

If you want to set different colors, just change the hex values in the range row. For a hex color finder, you can see here. You can also label the domain row values however you like (just make sure that the number of items matches that in the range row).

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

Now we can make our interactive network. We’ll specify the nodes and links from our ipcc_d3 object (this is easy since we have already converted it to networkD3 format). we will also note our nodeID, “name” and our Group, “group.” We’ll make the font a bit larger than the default so we can read names, we’ll add our color scale (which will be applied to the groups), and we’ll set zoom=TRUE to enable this feature.

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)

And finally, we can plot our network! Try zooming in on different parts, and highlighting the nodes to see their names.

# plot
p

7.7 Migration Flows

We can also display networks in other forms. For example, we might want to show reciprocal (or non-reciprocal) migration flows between counties. Here, we’ll select Butte County, which experienced the 2018 Camp Fire, as well as the surrounding counties of Colusa, Glenn, Plumas, Sierra, Tehama, and Yuba.

The ca_migration data below represents migration patterns between these counties, as measured by the U.S. Census’ American Community Survey. The full data can be downloaded here. I use migration flows between 2016 and 2020.

We can create a chord diagram using the code below. The R Graph Gallery has similar examples of chord diagrams.

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 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
      )

  }
)

We notice that the flows in and out of Butte County are fairly even, and similar to other counties in the region. Sierra County is smaller and more peripheral than the others, and therefore only has migration flows with Plumas County.

While we might expect to see large out-migration of Butte County, this is not visible, at least in these data. Many evacuees fled to nearby Chico within Butte County, and others traveled much farther. While we know that the Camp Fire disrupted migration patterns on various scales, we don’t see strong evidence of this at the county level during the 2016-2020 period.

7.8 Problem Set 7

Recommended Resources:

Methods for Network Analysis

  1. Download the “class_activities.csv” file from Canvas. Using igraph, create a network diagram based on who has worked with who in our class activities this quarter (you may want to use graph_from_data_frame()). Then plot the network.

  2. Choose a centrality measure, and explain how you would interpret this in the context of the class activities data. Who is/are the most central actor(s) according to this measure?

  3. Using the IPCC co-authorship data, create a network graph of all co-authors who share at least 2 publications together, excluding those with no network ties, similar to what we do in section 7.5. Graph the data using eigenvector scores, rather than betweenness scores, to plot the vertex sizes. Does this make a difference in our interpretation of the network? (Try comparing the top 5 most central authors, using the different measures of centrality).

  4. Let’s say you want to give one of the IPCC authors a memo to disseminate to the others. Who would you choose? Which measure of centrality would help you arrive at your answer?

  5. Finally, plot the IPCC co-authorship data, but change the color/shape of the vertices so that these correspond to authors’ gender. Describe what you see. (Note that you will need the IPCC_cv.csv dataset, which is on Canvas, to get author gender. You don’t need to remove non-collaborators from the IPCC_cv data, this has already been done).