knitr::opts_chunk$set(echo = TRUE, warning = FALSE)
########################################
# For General Data Manipulation
library(tidyverse)
########################################
# Network Analysis Library (Handle data and Viz)
library(igraph)
library(netrankr)
########################################
# For Network "Manipulation"
library(tidygraph)
# For Network Visualization
library(ggraph)
library(graphlayouts)
library(visNetwork)
# For "Network" Datasets
library(igraphdata)
The Grammar of Networks
Visualizing and Manipulating Network data in R
Setting up R Packages
Introduction
This Quarto document is part of my workshop course on R . The material is based on A Layered Grammar of Graphics by Hadley Wickham. The intent of this Course is to build Skill in coding in R, and also appreciate R as a way to metaphorically visualize information of various kinds, using predominantly geometric figures and structures.
All Quarto document files combine code, text, web-images, and figures developed using code. Everything is text; code chunks are enclosed in fences (```)
Goals
At the end of this Lab session, we should:
- know the types and structures of
network data
and be able to work with them - understand the basics of modern network packages in R
- be able to create network visualizations using
tidygraph
,ggraph
( static visualizations ) andvisNetwork
(interactive visualizations) - see directions for how the network metaphor applies in a variety of domains (e.g. biology/ecology, ideas/influence, technology, transportation, to name a few)
Pedagogical Note
The method followed will be based on PRIMM:
- PREDICT Inspect the code and guess at what the code might do, write predictions
- RUN the code provided and check what happens
-
INFER what the
parameters
of the code do and write comments to explain. What bells and whistles can you see? -
MODIFY the
parameters
code provided to understand theoptions
available. Write comments to show what you have aimed for and achieved. - MAKE : take an idea/concept of your own, and graph it.
Graph Metaphors
Network graphs are characterized by two key terms: nodes and edges
-
Nodes
: Entities- Metaphors: Individual People? Things? Ideas? Places? to be connected in the network.
- Synonyms:
vertices
. Nodes haveIDs
.
-
Edges
: Connections- Metaphors: Interactions? Relationships? Influence? Letters sent and received? Dependence? between the entities.
- Synonyms:
links
,ties
.
In R, we create network representations using node and edge information. One way in which these could be organized are:
-
Node list
: a data frame with a single column listing the node IDs found in the edge list. You can also add attribute columns to the data frame such as the names of the nodes or grouping variables. ( Type? Class? Family? Country? Subject? Race? )
ID | Node Name | Attribute? Qualities?Categories? Family? Country?Planet? |
1 | Ned | Nursery School Teacher |
2 | Jaguar Paw | Main Character, Apocalypto |
3 | John Snow | Epidemiologist |
-
Edge list
: data frame containing two columns: source node and destination node of anedge
. Source and Destination havenode IDs
. -
Weighted network graph
: An edge list can also contain additional columns describing attributes of the edges such as a magnitude aspect for an edge. If the edges have a magnitude attribute the graph is considered weighted.
From | To | Relationship | Weightage |
---|---|---|---|
1 | 3 | Financial Dealings | 6 |
2 | 1 | History Lessons | 2 |
2 | 3 | Vaccination | 15 |
-
Layout
: A geometric arrangement ofnodes
andedges
.- Metaphors: Location? Spacing? Distance? Coordinates? Colour? Shape? Size? Provides visual insight due to the
arrangement
.
- Metaphors: Location? Spacing? Distance? Coordinates? Colour? Shape? Size? Provides visual insight due to the
-
Layout Algorithms
:Method
to arrangesnodes
andedges
with the aim of optimizing somemetric
.- Metaphors: Nodes are
masses
and edges aresprings
. The Layout algorithm minimizes the stretching and compressing of all springs.(BTW, are the Spring Constants K the same for all springs?…)
- Metaphors: Nodes are
Directed and undirected network graph
: If the distinction between source and target is meaningful, the network is directed. If the distinction is not meaningful, the network is undirected. Directed edges represent an ordering of nodes, like a relationship extending from one node to another, where switching the direction would change the structure of the network. Undirected edges are simply links between nodes where order does not matter.
Examples:
- The World Wide Web is an example of a directed network because
hyperlinks connect one Web page to another, but not necessarily
the other way around.
- Co-authorship networks represent examples of un-directed networks,
where nodes are authors and they are connected by an edge if they
have written a publication together
- When people send e-mail to each other, the distinction between the
sender (source) and the recipient (target) is clearly meaningful,
therefore the network is directed.
-
Connected
andDisconnected
graphs: If there is some path from any node to any other node, the Networks is said to be Connected. Else, Disconnected.
Predict/Run/Infer -1
Using tidygraph
and ggraph
tidygraph
and ggraph
are modern R packages for network data. Graph Data setup and manipulation is done in tidygraph and graph visualization with ggraph.
-
tidygraph
Data -> “Network Object” in R. -
ggraph
Network Object -> Plots using a chosen layout/algo.
Both leverage the power of igraph
, which is the Big Daddy of all network packages. We will be using the Grey’s Anatomy dataset in our first foray into networks.
Step1. Read the data
Download these two datasets into your current project-> data folder.
grey_nodes <- read_csv("../../../materials/data/networks/grey_nodes.csv")
grey_edges <- read_csv("../../../materials/data/networks/grey_edges.csv")
grey_nodes
grey_edges
Questions and Inferences #1:
Look at the console output thumbnail. What does for example name = col_character
mean? What attributes (i.e. extra information) are seen for Nodes and Edges? Understand the data in both nodes and edges as shown in the second and third thumbnails. Write some comments and inferences here.
Step 2.Create a network object using tidygraph:
Key function:
-
tbl_graph()
: (aka “tibble graph”). Key arguments:nodes
,edges
anddirected
. Note this is a very versatile command and can take many input forms, such as data structures that result from other packages. Type?tbl_graph
in the Console and see theUsage
section.
ga <- tbl_graph(nodes = grey_nodes,
edges = grey_edges,
directed = FALSE)
ga
# A tbl_graph: 54 nodes and 57 edges
#
# An undirected simple graph with 4 components
#
# Node Data: 54 × 7 (active)
name sex race birthyear position season sign
<chr> <chr> <chr> <dbl> <chr> <dbl> <chr>
1 Addison Montgomery F White 1967 Attending 1 Libra
2 Adele Webber F Black 1949 Non-Staff 2 Leo
3 Teddy Altman F White 1969 Attending 6 Pisces
4 Amelia Shepherd F White 1981 Attending 7 Libra
5 Arizona Robbins F White 1976 Attending 5 Leo
6 Rebecca Pope F White 1975 Non-Staff 3 Gemini
7 Jackson Avery M Black 1981 Resident 6 Leo
8 Miranda Bailey F Black 1969 Attending 1 Virgo
9 Ben Warren M Black 1972 Other 6 Aquarius
10 Henry Burton M White 1972 Non-Staff 7 Cancer
# ℹ 44 more rows
#
# Edge Data: 57 × 4
from to weight type
<int> <int> <dbl> <chr>
1 5 47 2 friends
2 21 47 4 benefits
3 5 46 1 friends
# ℹ 54 more rows
Questions and Inferences #2:
Questions and Inferences: What information does the graph object contain? What attributes do the nodes have? What about the edges?
Step 3. Plot using ggraph
3a. Quick Plot: autograph()
This is to check quickly is the data is imported properly and to decide upon going on to a more elaborate plotting.
autograph(ga)
Questions and Inferences #3:
Questions and Inferences: Describe this graph, in simple words here. Try to use some of the new domain words we have just acquired: nodes/edges, connected/disconnected, directed/undirected.
3b. More elaborate plot
Key functions:
-
ggraph(layout = "......")
: Create classic node-edge diagrams; i.e. Sets up the graph. Rather likeggplot
for networks!
Two kinds of geom
: one set for nodes, and another for edges
geom_node_point(aes(.....))
: Draws node as “points”. Alternatives arecircle / arc_bar / tile / voronoi
. Remember thegeom
s that we have seen before in Grammar of Graphics!geom_edge_link(aes(.....))
: Draws edges as “links”. Alternatives arearc / bend / elbow / hive / loop / parallel / diagonal / point / span /tile
.geom_node_text(aes(label = ......), repel = TRUE)
: Adds text labels (non-overlapping). Alternatives arelabel /...
labs(title = "....", subtitle = "....", caption = "....")
: Change main titles, axis labels and legend titles. We know this from our work withggplot
.
# Write Comments next to each line
# About what that line does for the overall graph
ggraph(graph = ga, layout = "kk") +
#
geom_edge_link(width = 2, color = "pink") +
#
geom_node_point(
shape = 21,
size = 8,
fill = "blue",
color = "green",
stroke = 2
) +
#
labs(title = "Whoo Hoo! My first silly Grey's Anatomy graph in R!",
subtitle = "Why did I ever get in this course...",
caption = "Bro, they are doing **cool** things in the other
classes...")
Questions and Inferences #3:
Questions and Inferences: What parameters have been changed here, compared to the earlier graph? Where do you see these changes in the code above?
Let us Play with this graph and see if we can make some small changes. Colour? Fill? Width? Size? Stroke? Labs? Of course!
# Change the parameters in each of the commands here to new ones
# Use fixed values for colours or sizes...etc.
ggraph(graph = ga, layout = "kk") +
geom_edge_link(width = 2) +
geom_node_point(shape = 21, size = 8,
fill = "blue",
color = "green",
stroke = 2) +
labs(title = "Whoo Hoo! My next silly Grey's Anatomy graph in R!",
subtitle = "Why did I ever get in this course...",
caption = "Bro, they are doing cool things in the other
classes...")
Questions and Inferences #4:
Questions and Inferences: What did the shape
parameter achieve? What are the possibilities with shape
? How about including alpha
?
3c. Aesthetic Mapping from Node and Edge attribute columns
Up to now, we have assigned specific numbers to geometric aesthetics such as shape and size. Now we are ready ( maybe ?) change the meaning and significance of the entire graph and each element within it, and use aesthetics / metaphoric mappings to achieve new meanings or insights. Let us try using aes()
inside each geom
to map a variable
to a geometric aspect.
Don’t try to use more than 2 aesthetic mappings simultaneously!!
The node elements we can tweak are:
- Types of Nodes:
geom_node_****()
- Node Parameters: inside
geom_node_****(aes(...............))
-aes(alpha = node-variable)
: opacity; a value between 0 and 1
-aes(shape = node-variable)
: node shape
-aes(colour = node-variable)
: node colour
-aes(fill = node-variable)
: fill colour for node
-aes(size = node-variable)
: size of node
The edge elements we can tweak are:
- Type of Edges”
geom_edge_****()
- Edge Parameters: inside
geom_edge_****(aes(...............))
-aes(colour = edge-variable)
: colour of the edge
-aes(width = edge-variable)
: width of the edge
-aes(label = some_variable)
: labels for the edge
Type ?geom_node_point
and ?geom-edge_link
in your Console for more information.
ggraph(graph = ga, layout = "fr") +
geom_edge_link0(aes(width = weight)) + # change variable here
geom_node_point(aes(color = race), size = 6) + # change variable here
labs(title = "Whoo Hoo! Yet another Grey's Anatomy graph in R!")
Questions and Inferences #5:
Questions and Inferences: Describe some of the changes here. What types of edges worked? Which variables were you able to use for nodes and edges and how? What did not work with either of the two?
Predict/Reuse/Infer-2
# Arc diagram
ggraph(ga, layout = "linear") +
geom_edge_arc(aes(width = weight), alpha = 0.8) +
scale_edge_width(range = c(0.2, 2)) +
geom_node_point(size = 2, colour = "red") +
labs(edge_width = "Weight")
Questions and Inferences #6:
Questions and Inferences: How does this graph look “metaphorically” different? Do you see a difference in the relationships between people here? Why?
# Coord diagram, circular
ggraph(ga, layout = "linear", circular = TRUE) +
geom_edge_arc(aes(width = weight), alpha = 0.8) +
scale_edge_width(range = c(0.2, 2)) +
geom_node_point(size = 4,colour = "red") +
geom_node_text(aes(label = name),repel = TRUE, size = 3,
max.overlaps = 20) +
labs(edge_width = "Weight") +
theme_graph()
Questions and Inferences #7:
Questions and Inferences: How does this graph look “metaphorically” different? Do you see a difference in the relationships between people here? Why?
Hierarchical layouts
These provide for some alternative metaphorical views of networks. Note that not all layouts are possible for all datasets!!
set_graph_style()
# This dataset contains the graph that describes the class
# hierarchy for the Flare visualization library.
# Type ?flare in your Console
head(flare$vertices)
head(flare$edges)
# flare class hierarchy
graph = tbl_graph(edges = flare$edges, nodes = flare$vertices)
# dendrogram
ggraph(graph, layout = "dendrogram") +
geom_edge_diagonal() +
labs(title = "Dendrogram")
# circular dendrogram
ggraph(graph, layout = "dendrogram", circular = TRUE) +
geom_edge_diagonal() +
geom_node_point(aes(filter = leaf)) +
coord_fixed()+
labs(title = "Circular Dendrogram")
# rectangular tree map
ggraph(graph, layout = "treemap", weight = size) +
geom_node_tile(aes(fill = depth), size = 0.25) +
labs(title = "Rectangular Tree Map")
# circular tree map
ggraph(graph, layout = "circlepack", weight = size) +
geom_node_circle(aes(fill = depth), size = 0.25, n = 50) +
coord_fixed() +
labs(title = "Circular Tree Map")
# icicle
ggraph(graph, layout = "partition") +
geom_node_tile(aes(y = -y, fill = depth))
# sunburst (circular icicle)
ggraph(graph, layout = "partition", circular = TRUE) +
geom_node_arc_bar(aes(fill = depth)) +
coord_fixed() +
labs(title = "Circular Icicle")
Questions and Inferences #8:
Questions and Inferences: How do graphs look “metaphorically” different? Do they reveal different aspects of the group? How?
Faceting
Faceting allows to create sub-plots according to the values of a qualitative attribute on nodes or edges.
# setting theme_graph
set_graph_style()
# facet edges by type
ggraph(ga,layout = "linear", circular = TRUE) +
geom_edge_link(aes(color = type)) +
geom_node_point() +
facet_edges(~ type) +
theme(aspect.ratio = 1)
# facet nodes by sex
ggraph(ga,layout = "linear", circular = TRUE) +
geom_edge_link() +
geom_node_point() +
facet_nodes(~race) +
theme(aspect.ratio = 1)
# facet both nodes and edges
ggraph(ga,layout = "linear", circular = TRUE) +
geom_edge_link(aes(color = type)) +
geom_node_point() +
facet_graph(type ~ race) +
th_foreground(border = TRUE) +
theme(aspect.ratio = 1, legend.position = "top")
Questions and Inferences #9:
Questions and Inferences: Does splitting up the main graph into subnetworks give you more insight? Describe some of these.
Network analysis with tidygraph
The data frame graph representation can be easily augmented with metrics or statistics computed on the graph. Remember how we computed counts
with the penguin dataset in Grammar of Graphics.
Before computing a metric on nodes or edges use the activate()
function to activate either node or edge data frames. Use dplyr
verbs (filter, arrange, mutate
) to achieve your computation in the proper way.
Network Centrality
Centrality is a an “ill-defined” metric of node and edge importance in a network. It is therefore calculated in many ways. Type ?centrality
in your Console.
Let’s add a few columns to the nodes and edges based on network centrality measures:
ga %>%
activate(nodes) %>%
# Node with the most connections?
mutate(degree = centrality_degree(mode = c("in"))) %>%
filter(degree > 0) %>%
activate(edges) %>%
# "Busiest" edge?
mutate(betweenness = centrality_edge_betweenness())
# A tbl_graph: 54 nodes and 57 edges
#
# An undirected simple graph with 4 components
#
# Edge Data: 57 × 5 (active)
from to weight type betweenness
<int> <int> <dbl> <chr> <dbl>
1 5 47 2 friends 20.3
2 21 47 4 benefits 44.7
3 5 46 1 friends 39
4 5 41 1 friends 66.3
5 18 41 6 friends 39
6 21 41 12 benefits 91.5
7 37 41 5 professional 164.
8 31 41 2 professional 98.8
9 20 31 3 professional 47.2
10 17 31 4 friends 102.
# ℹ 47 more rows
#
# Node Data: 54 × 8
name sex race birthyear position season sign degree
<chr> <chr> <chr> <dbl> <chr> <dbl> <chr> <dbl>
1 Addison Montgomery F White 1967 Attending 1 Libra 3
2 Adele Webber F Black 1949 Non-Staff 2 Leo 1
3 Teddy Altman F White 1969 Attending 6 Pisces 4
# ℹ 51 more rows
Packages tidygraph
and ggraph
can be pipe-lined to perform analysis and visualization tasks in one go.
# setting theme_graph
set_graph_style()
ga %>%
activate(nodes) %>%
# Who has the most connections?
mutate(degree = centrality_degree()) %>%
activate(edges) %>%
# Who is the go-through person?
mutate(betweenness = centrality_edge_betweenness()) %>%
# Now to continue with plotting
ggraph(layout = "nicely") +
geom_edge_link(aes(alpha = betweenness)) +
geom_node_point(aes(size = degree, colour = degree)) +
# discrete colour legend
scale_color_gradient(guide = "legend")
# or even less typing
ggraph(ga,layout = "nicely") +
geom_edge_link(aes(alpha = centrality_edge_betweenness())) +
geom_node_point(aes(colour = centrality_degree(),
size = centrality_degree())) +
scale_color_gradient(guide = "legend",
low = "green",
high = "red")
Questions and Inferences #10:
Questions and Inferences: How do the Centrality Measures show up in the graph? Would you “agree” with the way we have done it? Try to modify the aesthetics by copy-pasting this chunk below and see how you can make an alternative representation.
Analysis and visualizing Network Communities
Who is close to whom? Which are the groups you can see?
# setting theme_graph
set_graph_style()
# visualize communities of nodes
ga %>%
activate(nodes) %>%
mutate(community = as.factor(group_louvain())) %>%
ggraph(layout = "graphopt") +
geom_edge_link() +
geom_node_point(aes(color = community), size = 5)
Questions and Inferences #11:
Questions and Inferences: Is the Community depiction clear? How would you do it, with which aesthetic? Copy Paste this chunk below and try.
Interactive Graphs with visNetwork
Exploring the VisNetwork
package. Make graphs wiggle and shake using tidy
commands! The package implements interactivity using the physical metaphor of weights and springs we discussed earlier.
The visNetwork()
function uses a nodes list and edges list to create an interactive graph. The nodes list must include an “id” column, and the edge list must have “from” and “to” columns. The function also plots the labels for the nodes, using the names of the cities from the “label” column in the node list.
library(visNetwork)
# Prepare the data for plotting by visNetwork
grey_nodes
grey_edges
# Relabel greys anatomy nodes and edges for VisNetwork
grey_nodes_vis <- grey_nodes %>%
rowid_to_column(var = "id") %>%
rename("label" = name) %>%
mutate(sex = case_when(sex == "F" ~ "Female",
sex == "M" ~ "Male")) %>%
replace_na(., list(sex = "Transgender?")) %>%
rename("group" = sex)
grey_nodes_vis
grey_edges_vis <- grey_edges %>%
select(from, to) %>%
left_join(., grey_nodes_vis,
by = c("from" = "label")) %>%
left_join(., grey_nodes_vis,
by = c("to" = "label")) %>%
select("from"= id.x, "to" = id.y)
grey_edges_vis
Using fontawesome icons
grey_nodes_vis %>%
visNetwork(nodes = ., edges = grey_edges_vis) %>%
visNodes(font = list(size = 40)) %>%
# Colour and icons for each of the gender-groups
visGroups(groupname = "Female", shape = "icon",
icon = list(code = "f182", size = 75, color = "tomato"),
shadow = list(enabled = TRUE)) %>%
visGroups(groupname = "Male", shape = "icon",
icon = list(code = "f183", size = 75, color = "slateblue"),
shadow = list(enabled = TRUE)) %>%
visGroups(groupname = "Transgender?", shape = "icon",
icon = list(code = "f22c", size = 75, color = "fuchsia"),
shadow = list(enabled = TRUE)) %>%
#visLegend() %>%
#Add the fontawesome icons!!
addFontAwesome() %>%
# Add Interaction Controls
visInteraction(navigationButtons = TRUE,
hover = TRUE,
selectConnectedEdges = TRUE,
hoverConnectedEdges = TRUE,
zoomView = TRUE)
There is another family of icons available in visNetwork, called ionicons
. Let’s see how they look:
grey_nodes_vis %>%
visNetwork(nodes = ., edges = grey_edges_vis,) %>%
visLayout(randomSeed = 12345) %>%
visNodes(font = list(size = 50)) %>%
visEdges(color = "green") %>%
visGroups(
groupname = "Female",
shape = "icon",
icon = list(
face = 'Ionicons',
code = "f25d",
color = "fuchsia",
size = 125
)
) %>%
visGroups(
groupname = "Male",
shape = "icon",
icon = list(
face = 'Ionicons',
code = "f202",
color = "green",
size = 125
)
) %>%
visGroups(
groupname = "Transgender?",
shape = "icon",
icon = list(
face = 'Ionicons',
code = "f233",
color = "dodgerblue",
size = 125
)
) %>%
visLegend() %>%
addIonicons() %>%
visInteraction(
navigationButtons = TRUE,
hover = TRUE,
selectConnectedEdges = TRUE,
hoverConnectedEdges = TRUE,
zoomView = TRUE
)
Some idea of interactivity and controls with visNetwork
:
# We need to rename starwars nodes dataframe and edge dataframe columns for visNetwork
starwars_nodes_vis <-
starwars_nodes %>%
rename("label" = name)
# Convert from and to columns to **node ids**
starwars_edges_vis <-
starwars_edges %>%
# Matching Source <- Source Node id ("id.x")
left_join(., starwars_nodes_vis, by = c("source" = "label")) %>%
# Matching Target <- Target Node id ("id.y")
left_join(., starwars_nodes_vis, by = c("target" = "label")) %>%
# Select "id.x" and "id.y" ONLY
# Rename them as "from" and "to"
# keep "weight" column for aesthetics of edges
select("from" = id.x, "to" = id.y, "value" = weight)
# Check everything once
starwars_nodes_vis
starwars_edges_vis
Ok, let’s make things move and shake!!
visNetwork(nodes = starwars_nodes_vis,
edges = starwars_edges_vis) %>%
visNodes(font = list(size = 30), shape = "icon",
icon = list(code = "f1e3", size = 75)) %>%
addFontAwesome() %>%
visEdges(color = "red")
Your Assignments:
Make-1 : With a ready made dataset
Step 0. Fire up a New Project! Always!
Step 1. Fire up a new Quarto document. Fill in the YAML header.
Step 2. Take any one of the “Make1-Datasets” datasets described below.
Step 3. Document contents:
- Introduce / Inspect in R your data and describe
- Introduce your Purpose
- Create graph objects
- Try different layouts
- Write comments in the code
- Write narrative in text with sections, bold ,italic etc.
Step 4. Knit before you submit. Submit only your renderable .qmd
file.
Make1 - Datasets:
- Airline Data:
- Start with this bit of code in your second chunk, after
set up
- The Famous Zachary Karate Club dataset
-
Start with pulling this data into your Rmarkdown:
data(“karate”,package= “igraphdata”) karate
Try
?karate
in the consoleNote that this is not a set of nodes, nor edges, but already a graph-object!
So no need to create a graph object using
tbl_graph
.You will need to just go ahead and plot using
ggraph
.
- Game of Thrones:
- Start with pulling this data into your Rmarkdown:
GoT <- read_rds("../../../materials/data/networks/GoT.RDS")
- Note that this is a list of 7 graphs from Game of Thrones.
- Select one using
GoT[[index]]
where index = 1…7 and then plot directly. - Try to access the nodes and edges and modify them using any attribute data
- Any other graph dataset from
igraphdata
(type?igraphdata
in console)
- Ask me for help if you need any
Make-2: Literary Network with TV Show / Book / Story / Play
This is in groups. Groups of 4. To be announced
You need to create a Network Graph for your favourite Book, play, TV serial or Show. (E.g. Friends, BBT, or LB or HIMYM, B99, TGP, JTV…or Hamlet, Little Women , Pride and Prejudice, or LoTR)
Step 1. Go to: Literary Networks for instructions.
Step 2. Make your data using the instructions.
In the nodes excel, use
id
andnames
as your columns. Any other details in other columns to the right.In your
edges
excel, usefrom
andto
are your first columns. Entries in these columns can benames
orid
s but be consistent and don’t mix.
Step 3. Decide on 3 answers that you to seek and plan to make graphs for.
Step 4. Create graph objects. Say 3 visualizations.
Step 5. Write comments/answers in the code and narrative text. Add pictures from the web using Markdown syntax.
Step 6. Write Reflection ( ok, a short one!) inside your Quarto document. Make sure it renders !!
Step 7. Group Submission: Submit the render-able .qmd file AND the data. Quarto Markdown with joint authorship. Each person submits on their Assignments. All get the same grade on this one.
Ask me for clarifications on what to do after you have read the Instructions in your group.
Read more
Igraph: Network Analysis and Visualization. https://CRAN.R-project.org/package=igraph.
Pedersen, Thomas Lin. 2017a. Ggraph: An Implementation of Grammar of Graphics for Graphs and Networks. https://CRAN.R-project.org/package=ggraph.
———. 2017b. Tidygraph: A Tidy Api for Graph Manipulation. https://CRAN.R-project.org/package=tidygraph.
Tyner, Sam, François Briatte, and Heike Hofmann. 2017. “Network Visualization with ggplot2.” The R Journal 9 (1): 27–59. https://journal.r-project.org/archive/2017/RJ-2017-023/index.html.
Network Datasets https://icon.colorado.edu/#!/networks
Yunran Chen, Introduction to Network Analysis Using R