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:
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.
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:
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.
Great! Now let’s try to visualize our network.
We can make the graph more visually appealing by changing some of the default settings.
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.
## 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.
## 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).
## 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 $vector
result. According to this metric, Lina is the most central! This is because Lina is close to other popular people, who have lots of social ties themselves.
## Lionel Lina Frederica Charlotte Garrett Sampson Ahmad
## 0.7910018 1.0000000 0.9429201 0.5334790 0.8472419 0.9304545 0.2412682
We can compare these four measures of centrality all together with the code below:
library(tidyr)
library(ggplot2)
# create dataframe with similarity scores
central_df <- data.frame(degree = degree(net),
betweenness = betweenness(net),
closeness = closeness(net),
eigenvector = evcent(net)$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.
We can then view the co-authorship:
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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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
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)$betweenness) * 20,
vertex.color = "lavender",
vertex.frame.color = NA,
vertex.label.cex = .5,
edge.curved = .05,
edge.width = .1,
edge.color = "gray1")
We see that there are several “central” authors. Still, it’s hard to see their names here. We can display the authors’ names, in descending order based on their betweenness scores, using the following code:
## + 148/148 vertices, named, from a9b8e22:
## [1] Nakicenovic Smith Shukla
## [4] Price Edenhofer Schaeffer
## [7] Krey Bosetti Carraro
## [10] Riahi Hourcade Uerge-Vorsatz
## [13] Rogner Sathaye Van-Vuuren
## [16] Clarke Victor Faaij
## [19] Lutz Michaelowa Paltsev
## [22] Strachan Edmonds Den-Elzen
## [25] Hoehne Zhang Skea
## [28] Kopp Stavins Kahn-Ribeiro
## + ... omitted several vertices
This reveals that Nakicenovic is the “most central” author, at least according to the betweenness metric.
We might want to modify our graph edges to represent the number of collaborations, not just the fact that two authors have collaborated. We can do this by creating a weighted network, and using the weights as edge widths:
# create network, again
ipcc_net <- graph_from_adjacency_matrix(ipcc_authors,
mode = "undirected",
weighted = TRUE)
# add betweenness centrality
V(ipcc_net)$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)$betweenness) * 20,
vertex.color = "lavender",
vertex.alpha = 0.5,
vertex.frame.color = NA,
vertex.label.cex = .5,
edge.curved = .05,
edge.width = .1,
edge.color = "gray1")
We may also want to modify the attributes of our nodes according to their characteristics. Since geographic biases in IPCC authorship has been raised, let’s start there. We can add the countries that each author represents to our data by joining the IPCC_cv data.
Great! However, remember that we removed authors with less than 2 collaborations. So let’s remove these from our CV data too. We’ll use the slice()
function, and add a negative in front of no_colab
to specify that we don’t want these indices.
We notice that there are several variables around the country of origin, country of employment, and country representing at the IPCC, as well as other characteristics such as gender and institutional affiliations. We’ll define a new variable indicating the region of the world each author is representing.
# define global regions
ipcc_cvs %<>%
mutate(region = case_match(`IPCC representing country (i.e. Country of residence from IPCC doc)`,
# Europe will be green
c("Austria", "Belgium", "Denmark", "Finland",
"France", "Germany", "Greece", "Hungary", "Italy",
"Netherlands", "Norway", "Spain", "Sweden",
"Switzerland", "UK") ~ "green4",
# North America will be red
c("Canada", "USA", "Mexico") ~ "tomato",
# BRICS will be blue
c("Brazil", "Russia", "India", "China",
"South Africa") ~ "steelblue",
# Other countries will be gold
.default = "gold"))
Now let’s define a variable for our vertices named region
:
And let’s try plotting our network with the nodes colored according to country:
# plot network
plot(ipcc_net,
edge.width=(E(ipcc_net)$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.
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:
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 usegraph_from_data_frame()
). Then plot the network.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?
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).
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?
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).