Introduction to social network analysis with R
Alex Hanna, Pablo Barbera, Dan Cervone
January 21, 2016
Importing network data into R
In this section we will be using a small network that indicates interactions in the movie Star Wars Episode IV. Here, each node is a character and each edge indicates whether they appeared together in a scene of the movie. Edges here are thus undirected and they also have weights attached, since they can appear in multiple scenes together.
The first step is to read the list of edges and nodes in this network:
edges <- read.csv("data/star-wars-network-edges.csv")
head(edges)## source target weight
## 1 C-3PO R2-D2 17
## 2 LUKE R2-D2 13
## 3 OBI-WAN R2-D2 6
## 4 LEIA R2-D2 5
## 5 HAN R2-D2 5
## 6 CHEWBACCA R2-D2 3nodes <- read.csv("data/star-wars-network-nodes.csv")
head(nodes)## name id
## 1 R2-D2 0
## 2 CHEWBACCA 1
## 3 C-3PO 2
## 4 LUKE 3
## 5 DARTH VADER 4
## 6 CAMIE 5For example, we learn that C-3PO and R2-D2 appeared in 17 scenes together.
How do we convert these two datasets into a network object in R? There are multiple packages to work with networks, but the most popular is igraph because it’s very flexible and easy to do, and in my experience it’s much faster and scales well to very large networks. Other packages that you may want to explore are sna and networks. We’ll see an example later in this class, because some network modeling packages are not compatible with igraph.
Now, how do we create the igraph object? We can use the graph_from_data_frame function, which takes two arguments: d, the data frame with the edge list in the first two columns; and vertices, a data frame with node data with the node label in the first column. (Note that igraph calls the nodes vertices, but it’s exactly the same thing.)
# install.packages("igraph")
library(igraph)
g <- graph_from_data_frame(d=edges, vertices=nodes, directed=FALSE)
g## IGRAPH UNW- 22 60 --
## + attr: name (v/c), id (v/n), weight (e/n)
## + edges (vertex names):
## [1] R2-D2 --C-3PO R2-D2 --LUKE
## [3] R2-D2 --OBI-WAN R2-D2 --LEIA
## [5] R2-D2 --HAN R2-D2 --CHEWBACCA
## [7] R2-D2 --DODONNA CHEWBACCA --OBI-WAN
## [9] CHEWBACCA --C-3PO CHEWBACCA --LUKE
## [11] CHEWBACCA --HAN CHEWBACCA --LEIA
## [13] CHEWBACCA --DARTH VADER CHEWBACCA --DODONNA
## [15] LUKE --CAMIE CAMIE --BIGGS
## + ... omitted several edgesWhat does it mean? - U means undirected
- N means named graph
- W means weighted graph
- 22 is the number of nodes
- 60 is the number of edges
- name (v/c) means name is a node attribute and it’s a character
- weight (e/n) means weight is an edge attribute and it’s numeric
This is how you access specific elements within the igraph object:
V(g) # nodes## + 22/22 vertices, named:
## [1] R2-D2 CHEWBACCA C-3PO LUKE DARTH VADER
## [6] CAMIE BIGGS LEIA BERU OWEN
## [11] OBI-WAN MOTTI TARKIN HAN GREEDO
## [16] JABBA DODONNA GOLD LEADER WEDGE RED LEADER
## [21] RED TEN GOLD FIVEV(g)$name # names of each node## [1] "R2-D2" "CHEWBACCA" "C-3PO" "LUKE" "DARTH VADER"
## [6] "CAMIE" "BIGGS" "LEIA" "BERU" "OWEN"
## [11] "OBI-WAN" "MOTTI" "TARKIN" "HAN" "GREEDO"
## [16] "JABBA" "DODONNA" "GOLD LEADER" "WEDGE" "RED LEADER"
## [21] "RED TEN" "GOLD FIVE"vertex_attr(g) # all attributes of the nodes## $name
## [1] "R2-D2" "CHEWBACCA" "C-3PO" "LUKE" "DARTH VADER"
## [6] "CAMIE" "BIGGS" "LEIA" "BERU" "OWEN"
## [11] "OBI-WAN" "MOTTI" "TARKIN" "HAN" "GREEDO"
## [16] "JABBA" "DODONNA" "GOLD LEADER" "WEDGE" "RED LEADER"
## [21] "RED TEN" "GOLD FIVE"
##
## $id
## [1] 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21E(g) # edges## + 60/60 edges (vertex names):
## [1] R2-D2 --C-3PO R2-D2 --LUKE
## [3] R2-D2 --OBI-WAN R2-D2 --LEIA
## [5] R2-D2 --HAN R2-D2 --CHEWBACCA
## [7] R2-D2 --DODONNA CHEWBACCA --OBI-WAN
## [9] CHEWBACCA --C-3PO CHEWBACCA --LUKE
## [11] CHEWBACCA --HAN CHEWBACCA --LEIA
## [13] CHEWBACCA --DARTH VADER CHEWBACCA --DODONNA
## [15] LUKE --CAMIE CAMIE --BIGGS
## [17] LUKE --BIGGS DARTH VADER--LEIA
## [19] LUKE --BERU BERU --OWEN
## + ... omitted several edgesE(g)$weight # weights for each edge## [1] 17 13 6 5 5 3 1 7 5 16 19 11 1 1 2 2 4 1 3 3 2 3 18
## [24] 2 6 17 1 19 6 1 2 1 7 9 26 1 1 6 1 1 13 1 1 1 1 1
## [47] 1 2 1 1 3 3 1 1 3 1 2 1 1 1edge_attr(g) # all attributes of the edges## $weight
## [1] 17 13 6 5 5 3 1 7 5 16 19 11 1 1 2 2 4 1 3 3 2 3 18
## [24] 2 6 17 1 19 6 1 2 1 7 9 26 1 1 6 1 1 13 1 1 1 1 1
## [47] 1 2 1 1 3 3 1 1 3 1 2 1 1 1g[] # adjacency matrix## 22 x 22 sparse Matrix of class "dgCMatrix"## [[ suppressing 22 column names 'R2-D2', 'CHEWBACCA', 'C-3PO' ... ]]##
## R2-D2 . 3 17 13 . . . 5 . . 6 . . 5 . . 1 . . . . .
## CHEWBACCA 3 . 5 16 1 . . 11 . . 7 . . 19 . . 1 . . . . .
## C-3PO 17 5 . 18 . . 1 6 2 2 6 . . 6 . . . . . 1 . .
## LUKE 13 16 18 . . 2 4 17 3 3 19 . . 26 . . 1 1 2 3 1 .
## DARTH VADER . 1 . . . . . 1 . . 1 1 7 . . . . . . . . .
## CAMIE . . . 2 . . 2 . . . . . . . . . . . . . . .
## BIGGS . . 1 4 . 2 . 1 . . . . . . . . . 1 2 3 . .
## LEIA 5 11 6 17 1 . 1 . 1 . 1 1 1 13 . . . . . 1 . .
## BERU . . 2 3 . . . 1 . 3 . . . . . . . . . . . .
## OWEN . . 2 3 . . . . 3 . . . . . . . . . . . . .
## OBI-WAN 6 7 6 19 1 . . 1 . . . . . 9 . . . . . . . .
## MOTTI . . . . 1 . . 1 . . . . 2 . . . . . . . . .
## TARKIN . . . . 7 . . 1 . . . 2 . . . . . . . . . .
## HAN 5 19 6 26 . . . 13 . . 9 . . . 1 1 . . . . . .
## GREEDO . . . . . . . . . . . . . 1 . . . . . . . .
## JABBA . . . . . . . . . . . . . 1 . . . . . . . .
## DODONNA 1 1 . 1 . . . . . . . . . . . . . 1 1 . . .
## GOLD LEADER . . . 1 . . 1 . . . . . . . . . 1 . 1 1 . .
## WEDGE . . . 2 . . 2 . . . . . . . . . 1 1 . 3 . .
## RED LEADER . . 1 3 . . 3 1 . . . . . . . . . 1 3 . 1 .
## RED TEN . . . 1 . . . . . . . . . . . . . . . 1 . .
## GOLD FIVE . . . . . . . . . . . . . . . . . . . . . .g[1,] # first row of adjacency matrix## R2-D2 CHEWBACCA C-3PO LUKE DARTH VADER CAMIE
## 0 3 17 13 0 0
## BIGGS LEIA BERU OWEN OBI-WAN MOTTI
## 0 5 0 0 6 0
## TARKIN HAN GREEDO JABBA DODONNA GOLD LEADER
## 0 5 0 0 1 0
## WEDGE RED LEADER RED TEN GOLD FIVE
## 0 0 0 0Network visualization
How can we visualize this network? The plot() function works out of the box, but the default options are often not ideal:
par(mar=c(0,0,0,0))
plot(g)
Let’s see how we can improve this figure. To see all the available plotting options, you can check ?igraph.plotting. Let’s start by fixing some of these.
par(mar=c(0,0,0,0))
plot(g,
vertex.color = "grey", # change color of nodes
vertex.label.color = "black", # change color of labels
vertex.label.cex = .75, # change size of labels to 75% of original size
edge.curved=.25, # add a 25% curve to the edges
edge.color="grey20") # change edge color to grey
Now imagine that we want to modify some of these plotting attributes so that they are function of network properties. For example, a common adjustment is to change the size of the nodes and node labels so that they match their importance (we’ll come back to how to measure that later). Here, strength will correspond to the number of scenes they appear in. And we’re only going to show the labels of character that appear in 10 or more scenes.
V(g)$size <- strength(g)
par(mar=c(0,0,0,0)); plot(g)
# taking the log to improve it
V(g)$size <- log(strength(g)) * 4 + 3
par(mar=c(0,0,0,0)); plot(g)
V(g)$label <- ifelse( strength(g)>=10, V(g)$name, NA )
par(mar=c(0,0,0,0)); plot(g)
# what does `ifelse` do?
nodes$name=="R2-D2"## [1] TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [12] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSEifelse(nodes$name=="R2-D2", "yes", "no")## [1] "yes" "no" "no" "no" "no" "no" "no" "no" "no" "no" "no"
## [12] "no" "no" "no" "no" "no" "no" "no" "no" "no" "no" "no"ifelse(grepl("R", nodes$name), "yes", "no")## [1] "yes" "no" "no" "no" "yes" "no" "no" "no" "yes" "no" "no"
## [12] "no" "yes" "no" "yes" "no" "no" "yes" "no" "yes" "yes" "no"We can also change the colors of each node based on what side they’re in (dark side or light side).
# create vectors with characters in each side
dark_side <- c("DARTH VADER", "MOTTI", "TARKIN")
light_side <- c("R2-D2", "CHEWBACCA", "C-3PO", "LUKE", "CAMIE", "BIGGS",
"LEIA", "BERU", "OWEN", "OBI-WAN", "HAN", "DODONNA",
"GOLD LEADER", "WEDGE", "RED LEADER", "RED TEN", "GOLD FIVE")
other <- c("GREEDO", "JABBA")
# node we'll create a new color variable as a node property
V(g)$color <- NA
V(g)$color[V(g)$name %in% dark_side] <- "red"
V(g)$color[V(g)$name %in% light_side] <- "gold"
V(g)$color[V(g)$name %in% other] <- "grey20"
vertex_attr(g)## $name
## [1] "R2-D2" "CHEWBACCA" "C-3PO" "LUKE" "DARTH VADER"
## [6] "CAMIE" "BIGGS" "LEIA" "BERU" "OWEN"
## [11] "OBI-WAN" "MOTTI" "TARKIN" "HAN" "GREEDO"
## [16] "JABBA" "DODONNA" "GOLD LEADER" "WEDGE" "RED LEADER"
## [21] "RED TEN" "GOLD FIVE"
##
## $id
## [1] 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
##
## $size
## [1] 18.648092 19.572539 19.635532 22.439250 12.591581 8.545177 13.556229
## [8] 19.310150 11.788898 11.317766 18.567281 8.545177 12.210340 20.528107
## [15] 3.000000 3.000000 9.437752 9.437752 11.788898 13.259797 5.772589
## [22] -Inf
##
## $label
## [1] "R2-D2" "CHEWBACCA" "C-3PO" "LUKE" "DARTH VADER"
## [6] NA "BIGGS" "LEIA" NA NA
## [11] "OBI-WAN" NA "TARKIN" "HAN" NA
## [16] NA NA NA NA "RED LEADER"
## [21] NA NA
##
## $color
## [1] "gold" "gold" "gold" "gold" "red" "gold" "gold"
## [8] "gold" "gold" "gold" "gold" "red" "red" "gold"
## [15] "grey20" "grey20" "gold" "gold" "gold" "gold" "gold"
## [22] "gold"par(mar=c(0,0,0,0)); plot(g)
# what does %in% do?
1 %in% c(1,2,3,4)## [1] TRUE1 %in% c(2,3,4)## [1] FALSEIf we want to indicate what the colors correspond to, we can add a legend.
par(mar=c(0,0,0,0)); plot(g)
legend(x=.75, y=.75, legend=c("Dark side", "Light side", "Other"),
pch=21, pt.bg=c("red", "gold", "grey20"), pt.cex=2, bty="n")
Edge properties can also be modified. For example, here the width of each edge is a function of the log number of scenes those two characters appear together.
E(g)$width <- log(E(g)$weight) + 1
edge_attr(g)## $weight
## [1] 17 13 6 5 5 3 1 7 5 16 19 11 1 1 2 2 4 1 3 3 2 3 18
## [24] 2 6 17 1 19 6 1 2 1 7 9 26 1 1 6 1 1 13 1 1 1 1 1
## [47] 1 2 1 1 3 3 1 1 3 1 2 1 1 1
##
## $width
## [1] 3.833213 3.564949 2.791759 2.609438 2.609438 2.098612 1.000000
## [8] 2.945910 2.609438 3.772589 3.944439 3.397895 1.000000 1.000000
## [15] 1.693147 1.693147 2.386294 1.000000 2.098612 2.098612 1.693147
## [22] 2.098612 3.890372 1.693147 2.791759 3.833213 1.000000 3.944439
## [29] 2.791759 1.000000 1.693147 1.000000 2.945910 3.197225 4.258097
## [36] 1.000000 1.000000 2.791759 1.000000 1.000000 3.564949 1.000000
## [43] 1.000000 1.000000 1.000000 1.000000 1.000000 1.693147 1.000000
## [50] 1.000000 2.098612 2.098612 1.000000 1.000000 2.098612 1.000000
## [57] 1.693147 1.000000 1.000000 1.000000par(mar=c(0,0,0,0)); plot(g)
Up to now, everytime we run the plot function, the nodes appear to be in a different location. Why? Because it’s running a probabilistic function trying to locate them in the optimal way possible.
However, we can also specify the layout for the plot; that is, the (x,y) coordinates where each node will be placed. igraph has a few different layouts built-in, that will use different algorithms to find an optimal distribution of nodes. The following code illustrates some of these:
par(mfrow=c(2, 3), mar=c(0,0,1,0))
plot(g, layout=layout_randomly, main="Random")
plot(g, layout=layout_in_circle, main="Circle")
plot(g, layout=layout_as_star, main="Star")
plot(g, layout=layout_as_tree, main="Tree")
plot(g, layout=layout_on_grid, main="Grid")
plot(g, layout=layout_with_fr, main="Force-directed")
Note that each of these is actually just a matrix of (x,y) locations for each node.
l <- layout_randomly(g)
str(l)## num [1:22, 1:2] 0.557 -0.949 -0.108 0.877 -0.882 ...The most popular layouts are force-directed. These algorithms, such as Fruchterman-Reingold, try to position the nodes so that the edges have similar length and there are as few crossing edges as possible. The idea is to generate “clean” layouts, where nodes that are closer to each other share more connections in common that those that are located further apart. Note that this is a non-deterministic algorithm: choosing a different seed will generate different layouts.
par(mfrow=c(1,2))
set.seed(777)
fr <- layout_with_fr(g, niter=1000)
par(mar=c(0,0,0,0)); plot(g, layout=fr)
set.seed(666)
fr <- layout_with_fr(g, niter=1000)
par(mar=c(0,0,0,0)); plot(g, layout=fr)