---
title: "Marvel Comics Network Assignment"
author: "Alice Wu"
date: "19 April 2022"
output:
  html_document:
    code_folding: hide
---

Marvel Comics Network

This week we talked about network data: where it comes from, what it describes, and how to work with it in R. In this short “mini-lab” you’ll work with network data from Marvel Comics, and you’ll answer one simple question: is this co-occurrence network similar to a real social network?

About the Data

Characters from the Marvel Universe are everywhere. Since getting bought by Disney, Marvel has grown into one of the largest and most financially successful franchises in film history. There are dozens of movies, spin-off TV shows, toys, theme park rides, you name it. Iron Man and Black Widow have become household names! But it all started with one thing: comic books.

In 2002, years before the first Marvel Studios film hit theaters, a group of data analysts and network researchers in Spain set out to study the social network of Marvel characters. To do this, they collected data from an incredible (and very retro) website, The Marvel Chronology Project. The site records every single Marvel character, no matter how small. (Yes, Spider-Ham is included, too.) And it shows which comic books those characters appeared in.

As we learned in class, from data like this you can make a simple co-occurrence network, and that’s exactly what our researchers did. If two characters appeared together in the same comics issue, an edge was made between them. This is the edge table marvel_unimodal_edges.csv that you’ll find on Notebowl. Weight, as you might have guessed, represents the total number of issues in which the two characters appeared together.

library(tidyverse)

## ── Attaching packages ─────────────────────────────────────── tidyverse 1.3.1 ──

## ✓ ggplot2 3.3.5     ✓ purrr   0.3.4
## ✓ tibble  3.1.6     ✓ dplyr   1.0.8
## ✓ tidyr   1.2.0     ✓ stringr 1.4.0
## ✓ readr   2.1.2     ✓ forcats 0.5.1

## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## x dplyr::filter() masks stats::filter()
## x dplyr::lag()    masks stats::lag()

library(igraph)

## 
## Attaching package: 'igraph'

## The following objects are masked from 'package:dplyr':
## 
##     as_data_frame, groups, union

## The following objects are masked from 'package:purrr':
## 
##     compose, simplify

## The following object is masked from 'package:tidyr':
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## The following object is masked from 'package:tibble':
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##     as_data_frame

## The following objects are masked from 'package:stats':
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##     decompose, spectrum

## The following object is masked from 'package:base':
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##     union

library(networkD3)
marvel <- read_csv("marvel-unimodal-edges.csv")

## Rows: 9891 Columns: 3

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

Excelsior! Time for your Analysis

Your mission is to answer one question: is the Marvel network a small world network? Remember our discussion about Kevin Bacon and the small world principle? How would you know if a network has small world features?

If it has a high clustering coefficient and low average shortest path length between distant nodes, it is a small-world network.

Since we’d like to know whether the Marvel co-occurrence network is like a real-life social network, knowing whether it’s a small world can help us to draw a tentative conclusion.

To complete this assignment, follow these steps:

1. Create a new RMarkdown file. Make sure it has your name, a title, section headings, code folding: the works! It should have all the sections that the rest of our labs have, and organizing the lab report is up to you. You’ll turn in the knitted HTML output of this file.

2. Load the necessary libraries. Which libraries do you need for network analysis? Do you need any others? (In this and all other steps, the slides and your notes from class should be very helpful.)

3. Read in the CSV. Once you’ve got it, create an iGraph network object of your network. Call this MG for “Marvel Graph,” and remember that in iGraph “graph” is a synonym for network.

4. Calculate the degree, betweenness, and betweenness over degree for each node in the network. When you’re done, convert the nodes into a dataframe that you can view. Which nodes are the hubs (highest degree)? Which nodes are the bridges (highest betweenness over degree)? Were these the characters you expected? Why or why not?

MG = graph_from_data_frame(d=marvel, directed=F)

plot(MG)

lc <- largest.cliques(MG)
lc

## [[1]]
## + 46/327 vertices, named, from 8e8eed7:
##  [1] Thanos Doppelganger            Storm / Ororo Munroe S        
##  [3] Hudson, Heather                Strong Guy / Guido Car        
##  [5] Nova / Richard Rider           Magus                         
##  [7] Sasquatch / Walter Lan         Rogue  /                      
##  [9] Wolverine / Logan              Psylocke / Elisabeth B        
## [11] Havok / Alex Summers           She-hulk / Jennifer Wa        
## [13] Vision                         Colossus Ii / Peter Ra        
## [15] Human Torch / Johnny S         Angel / Warren Kenneth        
## [17] Living Lightning / Mig         Marvel Girl / Jean Grey       
## [19] Iceman / Robert Bobby          Cyclops / Scott Summer        
## + ... omitted several vertices
## 
## [[2]]
## + 46/327 vertices, named, from 8e8eed7:
##  [1] Thanos Doppelganger            Storm / Ororo Munroe S        
##  [3] Hudson, Heather                Strong Guy / Guido Car        
##  [5] Nova / Richard Rider           Magus                         
##  [7] Sasquatch / Walter Lan         Rogue  /                      
##  [9] Wolverine / Logan              Psylocke / Elisabeth B        
## [11] Havok / Alex Summers           She-hulk / Jennifer Wa        
## [13] Vision                         Colossus Ii / Peter Ra        
## [15] Human Torch / Johnny S         Angel / Warren Kenneth        
## [17] Living Lightning / Mig         Marvel Girl / Jean Grey       
## [19] Iceman / Robert Bobby          Cyclops / Scott Summer        
## + ... omitted several vertices
## 
## [[3]]
## + 46/327 vertices, named, from 8e8eed7:
##  [1] Thanos Doppelganger            Storm / Ororo Munroe S        
##  [3] Hudson, Heather                Strong Guy / Guido Car        
##  [5] Nova / Richard Rider           Magus                         
##  [7] Sasquatch / Walter Lan         Rogue  /                      
##  [9] Wolverine / Logan              Psylocke / Elisabeth B        
## [11] Havok / Alex Summers           She-hulk / Jennifer Wa        
## [13] Vision                         Colossus Ii / Peter Ra        
## [15] Human Torch / Johnny S         Angel / Warren Kenneth        
## [17] Living Lightning / Mig         Marvel Girl / Jean Grey       
## [19] Iceman / Robert Bobby          Cyclops / Scott Summer        
## + ... omitted several vertices
## 
## [[4]]
## + 46/327 vertices, named, from 8e8eed7:
##  [1] Thanos Doppelganger            Storm / Ororo Munroe S        
##  [3] Hudson, Heather                Strong Guy / Guido Car        
##  [5] Nova / Richard Rider           Magus                         
##  [7] Sasquatch / Walter Lan         Rogue  /                      
##  [9] Wolverine / Logan              Psylocke / Elisabeth B        
## [11] Havok / Alex Summers           She-hulk / Jennifer Wa        
## [13] Vision                         Colossus Ii / Peter Ra        
## [15] Human Torch / Johnny S         Angel / Warren Kenneth        
## [17] Living Lightning / Mig         Marvel Girl / Jean Grey       
## [19] Iceman / Robert Bobby          Cyclops / Scott Summer        
## + ... omitted several vertices
## 
## [[5]]
## + 46/327 vertices, named, from 8e8eed7:
##  [1] Thanos Doppelganger            Storm / Ororo Munroe S        
##  [3] Hudson, Heather                Strong Guy / Guido Car        
##  [5] Nova / Richard Rider           Magus                         
##  [7] Sasquatch / Walter Lan         Rogue  /                      
##  [9] Wolverine / Logan              Psylocke / Elisabeth B        
## [11] Havok / Alex Summers           She-hulk / Jennifer Wa        
## [13] Vision                         Colossus Ii / Peter Ra        
## [15] Human Torch / Johnny S         Angel / Warren Kenneth        
## [17] Living Lightning / Mig         Marvel Girl / Jean Grey       
## [19] Iceman / Robert Bobby          Cyclops / Scott Summer        
## + ... omitted several vertices
## 
## [[6]]
## + 46/327 vertices, named, from 8e8eed7:
##  [1] Thanos Doppelganger            Storm / Ororo Munroe S        
##  [3] Hudson, Heather                Strong Guy / Guido Car        
##  [5] Nova / Richard Rider           Magus                         
##  [7] Sasquatch / Walter Lan         Rogue  /                      
##  [9] Wolverine / Logan              Psylocke / Elisabeth B        
## [11] Havok / Alex Summers           She-hulk / Jennifer Wa        
## [13] Vision                         Colossus Ii / Peter Ra        
## [15] Human Torch / Johnny S         Angel / Warren Kenneth        
## [17] Living Lightning / Mig         Marvel Girl / Jean Grey       
## [19] Iceman / Robert Bobby          Cyclops / Scott Summer        
## + ... omitted several vertices
## 
## [[7]]
## + 46/327 vertices, named, from 8e8eed7:
##  [1] Thanos Doppelganger            Storm / Ororo Munroe S        
##  [3] Hudson, Heather                Strong Guy / Guido Car        
##  [5] Nova / Richard Rider           Magus                         
##  [7] Sasquatch / Walter Lan         Rogue  /                      
##  [9] Wolverine / Logan              Psylocke / Elisabeth B        
## [11] Havok / Alex Summers           She-hulk / Jennifer Wa        
## [13] Vision                         Colossus Ii / Peter Ra        
## [15] Human Torch / Johnny S         Angel / Warren Kenneth        
## [17] Living Lightning / Mig         Marvel Girl / Jean Grey       
## [19] Iceman / Robert Bobby          Cyclops / Scott Summer        
## + ... omitted several vertices
## 
## [[8]]
## + 46/327 vertices, named, from 8e8eed7:
##  [1] Thanos Doppelganger            Storm / Ororo Munroe S        
##  [3] Hudson, Heather                Strong Guy / Guido Car        
##  [5] Nova / Richard Rider           Magus                         
##  [7] Sasquatch / Walter Lan         Rogue  /                      
##  [9] Wolverine / Logan              Psylocke / Elisabeth B        
## [11] Havok / Alex Summers           She-hulk / Jennifer Wa        
## [13] Vision                         Colossus Ii / Peter Ra        
## [15] Human Torch / Johnny S         Angel / Warren Kenneth        
## [17] Living Lightning / Mig         Marvel Girl / Jean Grey       
## [19] Iceman / Robert Bobby          Cyclops / Scott Summer        
## + ... omitted several vertices
## 
## [[9]]
## + 46/327 vertices, named, from 8e8eed7:
##  [1] Thanos Doppelganger            Storm / Ororo Munroe S        
##  [3] Hudson, Heather                Strong Guy / Guido Car        
##  [5] Nova / Richard Rider           Magus                         
##  [7] Sasquatch / Walter Lan         Rogue  /                      
##  [9] Wolverine / Logan              Psylocke / Elisabeth B        
## [11] Havok / Alex Summers           She-hulk / Jennifer Wa        
## [13] Vision                         Colossus Ii / Peter Ra        
## [15] Human Torch / Johnny S         Angel / Warren Kenneth        
## [17] Living Lightning / Mig         Marvel Girl / Jean Grey       
## [19] Iceman / Robert Bobby          Cyclops / Scott Summer        
## + ... omitted several vertices
## 
## [[10]]
## + 46/327 vertices, named, from 8e8eed7:
##  [1] Thanos Doppelganger            Storm / Ororo Munroe S        
##  [3] Hudson, Heather                Strong Guy / Guido Car        
##  [5] Nova / Richard Rider           Magus                         
##  [7] Sasquatch / Walter Lan         Rogue  /                      
##  [9] Wolverine / Logan              Psylocke / Elisabeth B        
## [11] Havok / Alex Summers           She-hulk / Jennifer Wa        
## [13] Vision                         Colossus Ii / Peter Ra        
## [15] Human Torch / Johnny S         Angel / Warren Kenneth        
## [17] Living Lightning / Mig         Marvel Girl / Jean Grey       
## [19] Iceman / Robert Bobby          Cyclops / Scott Summer        
## + ... omitted several vertices
## 
## [[11]]
## + 46/327 vertices, named, from 8e8eed7:
##  [1] Thanos Doppelganger            Storm / Ororo Munroe S        
##  [3] Hudson, Heather                Strong Guy / Guido Car        
##  [5] Nova / Richard Rider           Magus                         
##  [7] Sasquatch / Walter Lan         Rogue  /                      
##  [9] Wolverine / Logan              Psylocke / Elisabeth B        
## [11] Havok / Alex Summers           She-hulk / Jennifer Wa        
## [13] Vision                         Colossus Ii / Peter Ra        
## [15] Human Torch / Johnny S         Angel / Warren Kenneth        
## [17] Living Lightning / Mig         Marvel Girl / Jean Grey       
## [19] Iceman / Robert Bobby          Cyclops / Scott Summer        
## + ... omitted several vertices
## 
## [[12]]
## + 46/327 vertices, named, from 8e8eed7:
##  [1] Thanos Doppelganger            Storm / Ororo Munroe S        
##  [3] Hudson, Heather                Strong Guy / Guido Car        
##  [5] Nova / Richard Rider           Magus                         
##  [7] Sasquatch / Walter Lan         Rogue  /                      
##  [9] Wolverine / Logan              Psylocke / Elisabeth B        
## [11] Havok / Alex Summers           She-hulk / Jennifer Wa        
## [13] Vision                         Colossus Ii / Peter Ra        
## [15] Human Torch / Johnny S         Angel / Warren Kenneth        
## [17] Living Lightning / Mig         Marvel Girl / Jean Grey       
## [19] Iceman / Robert Bobby          Cyclops / Scott Summer        
## + ... omitted several vertices
## 
## [[13]]
## + 46/327 vertices, named, from 8e8eed7:
##  [1] Thanos Doppelganger            Storm / Ororo Munroe S        
##  [3] Hudson, Heather                Strong Guy / Guido Car        
##  [5] Nova / Richard Rider           Magus                         
##  [7] Sasquatch / Walter Lan         Rogue  /                      
##  [9] Wolverine / Logan              Psylocke / Elisabeth B        
## [11] Havok / Alex Summers           She-hulk / Jennifer Wa        
## [13] Vision                         Colossus Ii / Peter Ra        
## [15] Human Torch / Johnny S         Angel / Warren Kenneth        
## [17] Living Lightning / Mig         Marvel Girl / Jean Grey       
## [19] Iceman / Robert Bobby          Cyclops / Scott Summer        
## + ... omitted several vertices
## 
## [[14]]
## + 46/327 vertices, named, from 8e8eed7:
##  [1] Thanos Doppelganger            Storm / Ororo Munroe S        
##  [3] Hudson, Heather                Strong Guy / Guido Car        
##  [5] Nova / Richard Rider           Magus                         
##  [7] Sasquatch / Walter Lan         Rogue  /                      
##  [9] Wolverine / Logan              Psylocke / Elisabeth B        
## [11] Havok / Alex Summers           She-hulk / Jennifer Wa        
## [13] Vision                         Colossus Ii / Peter Ra        
## [15] Human Torch / Johnny S         Angel / Warren Kenneth        
## [17] Living Lightning / Mig         Marvel Girl / Jean Grey       
## [19] Iceman / Robert Bobby          Cyclops / Scott Summer        
## + ... omitted several vertices
## 
## [[15]]
## + 46/327 vertices, named, from 8e8eed7:
##  [1] Warlock Ii / Adam Warl         Storm / Ororo Munroe S        
##  [3] Nova / Richard Rider           Sasquatch / Walter Lan        
##  [5] Rogue  /                       Wolverine / Logan             
##  [7] She-hulk / Jennifer Wa         Vision                        
##  [9] Colossus Ii / Peter Ra         Human Torch / Johnny S        
## [11] Angel / Warren Kenneth         Dr. Strange / Stephen         
## [13] Marvel Girl / Jean Grey        Iceman / Robert Bobby         
## [15] Cyclops / Scott Summer         Thunderstrike / Eric K        
## [17] Beast / Henry &hank& P         Thing / Benjamin J. Gr        
## [19] Hercules [greek God]           Professor X / Charles         
## + ... omitted several vertices
## 
## [[16]]
## + 46/327 vertices, named, from 8e8eed7:
##  [1] Warlock Ii / Adam Warl         Storm / Ororo Munroe S        
##  [3] Nova / Richard Rider           Sasquatch / Walter Lan        
##  [5] Rogue  /                       Wolverine / Logan             
##  [7] She-hulk / Jennifer Wa         Vision                        
##  [9] Colossus Ii / Peter Ra         Human Torch / Johnny S        
## [11] Angel / Warren Kenneth         Dr. Strange / Stephen         
## [13] Marvel Girl / Jean Grey        Iceman / Robert Bobby         
## [15] Cyclops / Scott Summer         Thunderstrike / Eric K        
## [17] Beast / Henry &hank& P         Thing / Benjamin J. Gr        
## [19] Hercules [greek God]           Professor X / Charles         
## + ... omitted several vertices
## 
## [[17]]
## + 46/327 vertices, named, from 8e8eed7:
##  [1] Warlock Ii / Adam Warl         Storm / Ororo Munroe S        
##  [3] Nova / Richard Rider           Sasquatch / Walter Lan        
##  [5] Rogue  /                       Wolverine / Logan             
##  [7] She-hulk / Jennifer Wa         Vision                        
##  [9] Colossus Ii / Peter Ra         Human Torch / Johnny S        
## [11] Angel / Warren Kenneth         Dr. Strange / Stephen         
## [13] Marvel Girl / Jean Grey        Iceman / Robert Bobby         
## [15] Cyclops / Scott Summer         Thunderstrike / Eric K        
## [17] Beast / Henry &hank& P         Thing / Benjamin J. Gr        
## [19] Hercules [greek God]           Professor X / Charles         
## + ... omitted several vertices
## 
## [[18]]
## + 46/327 vertices, named, from 8e8eed7:
##  [1] Warlock Ii / Adam Warl         Storm / Ororo Munroe S        
##  [3] Nova / Richard Rider           Sasquatch / Walter Lan        
##  [5] Rogue  /                       Wolverine / Logan             
##  [7] She-hulk / Jennifer Wa         Vision                        
##  [9] Colossus Ii / Peter Ra         Human Torch / Johnny S        
## [11] Angel / Warren Kenneth         Dr. Strange / Stephen         
## [13] Marvel Girl / Jean Grey        Iceman / Robert Bobby         
## [15] Cyclops / Scott Summer         Thunderstrike / Eric K        
## [17] Beast / Henry &hank& P         Thing / Benjamin J. Gr        
## [19] Hercules [greek God]           Professor X / Charles         
## + ... omitted several vertices

degree(MG)

##         Black Panther / T'chal                Ghaur [deviant] 
##                            101                             20 
##          Dr. Doom / Victor Von         Storm / Ororo Munroe S 
##                            126                            190 
##          Scarlet Witch / Wanda         Toad / Mortimer Toynbe 
##                            194                             38 
## Hulk / Dr. Robert Bruce Banner         Firestar / Angelica Jo 
##                            182                             91 
##         Wonder Man / Simon Wil          Drax / Arthur Douglas 
##                            161                             75 
##           Dugan, Timothy Aloyi                 Carter, Sharon 
##                             48                             20 
##          Black Knight V / Dane         Sunfire / Shiro Yoshid 
##                            141                             51 
##                         Triton                         Ultron 
##                             38                             52 
##           Jones, Richard Milho          Iron Man / Tony Stark 
##                             67                            203 
##           Nelson, Franklin Fog                Captain America 
##                             40                            258 
##                  Jarvis, Edwin         Quasar Iii / Wendell V 
##                            130                            125 
##              Jameson, J. Jonah           Masters, Alicia Reis 
##                             84                             58 
##        Magneto / Magnus / Eric          Invisible Woman / Sue 
##                            119                            195 
##          Professor X / Charles         Iron Fist / Daniel Ran 
##                            185                             56 
##         Black Bolt / Blackanto                           Hawk 
##                             44                            170 
##         Sandman / William Bake            Falcon / Sam Wilson 
##                             56                             84 
##          Stingray / Dr. Walter         Justice Ii / Vance Ast 
##                             38                             49 
##           Hercules [greek God]         Usagent / Captain John 
##                            171                             93 
##         Captain Marvel Ii / Mo              Crystal [inhuman] 
##                             98                            114 
##           Tigra / Greer Nelson         Spider-woman Ii / Juli 
##                             78                             90 
##             Machine Man / X-51         Mockingbird / Dr. Barb 
##                             43                             62 
##         Captain Marvel / Capta          Wasp / Janet Van Dyne 
##                             37                            188 
##            Fury, Col. Nicholas         Thor / Dr. Donald Blak 
##                            107                            205 
##         Quicksilver / Pietro M         Captain Britain / Bria 
##                            159                             44 
##          Shadowcat / Katherine          Black Widow / Natasha 
##                            113                            147 
##         Ant-man / Dr. Henry J.         Moon Knight / Marc Spe 
##                            163                             69 
##                        Jocasta         Moondragon / Heather D 
##                             27                            103 
##         Thing / Benjamin J. Gr         Beast / Henry &hank& P 
##                            214                            205 
##         Triathlon / Delroy Gar         Cage, Luke / Carl Luca 
##                             28                             62 
##          Beetle / Abner Ronald           Lilandra Neramani [s 
##                             45                             64 
##               Odin [asgardian]           Hogan, Virginia Pepp 
##                             56                             16 
##         Mad Dog / Colonel Buzz           Kincaid, Dr. Jane Fo 
##                             21                             28 
##         Wizard / Bentley Wittm         Nighthawk Ii / Kyle Ri 
##                             29                             32 
##              Mantis / ? Brandt         Swordsman / Jacques Du 
##                             25                             28 
##         Charcoal / Charlie Bur           Blob / Fred J. Dukes 
##                             21                             62 
##         Cloak / Tyrone Johnson         Thunderstrike / Eric K 
##                             24                            104 
##         Power Man / Erik Joste          Human Torch Android / 
##                             42                             36 
##         Juggernaut / Cain Mark         Cyclops / Scott Summer 
##                             30                            197 
##          Iceman / Robert Bobby               Pharaoh Rama-tut 
##                            162                             85 
##        Marvel Girl / Jean Grey               Karnak [inhuman] 
##                            155                             45 
##          Dr. Strange / Stephen         Absorbing Man / Carl C 
##                            141                             52 
##                        Redwing                       Volstagg 
##                             25                             41 
##         Shaman / Michael Twoyo        Snowbird / Narya / Anne 
##                             75                             30 
##           Dagger / Tandy Bowen         Phoenix Iii / Rachel S 
##                             29                             54 
##                       Mandarin            Fandral [asgardian] 
##                             22                             45 
##         Ms. Marvel Ii / Sharon            Pip / Prince Gofern 
##                             26                             60 
##       Enchantress / Amora / He             Jameson, Col. John 
##                             69                             36 
##            Cooper, Dr. Valerie         Nova Ii / Frankie Raye 
##                             70                             68 
##         Darkhawk / Chris Powel         Medusa / Medusalith Am 
##                             70                             50 
##         Nomad Iii / Jack Monro                 Robertson, Joe 
##                             26                             49 
##               Gorgon [inhuman]         Gargoyle Ii / Isaac Ch 
##                             44                             37 
##         Namorita / Nita Prenti         Iron Man Iv / James R. 
##                             93                             65 
##            Ross, Gen. Thaddeus               Harkness, Agatha 
##                             29                             77 
##                  Carter, Peggy           Richards, Franklin B 
##                             35                             92 
##         Firebird / Bonita Juar                 Sersi / Sylvia 
##                             38                             82 
##                       Hyperion         Living Lightning / Mig 
##                             20                             86 
##                    Jones, Gabe              Osborn, Liz Allan 
##                             28                             38 
##             Leeds, Betty Brant               Loki [asgardian] 
##                             41                             62 
##                            Sif         Dazzler Ii / Allison B 
##                             38                             52 
##         Molecule Man / Owen Re         Speedball / Robbie Bal 
##                             40                             77 
##      Spider-man / Peter Parker         Lizard / Dr. Curtis Co 
##                            218                             48 
##         Volcana / Marsha Rosen                       Lockheed 
##                             36                             50 
##            Klaw / Ulysses Klaw         Wrecker Iii / Dirk Gar 
##                             54                             54 
##         Titania Ii / Mary Skee          Piledriver Ii / Brian 
##                             43                             49 
##         Nightcrawler / Kurt Wa         Bulldozer / Henry Camp 
##                            142                             49 
##         Angel / Warren Kenneth         Thunderball / Dr. Elio 
##                            169                             55 
##         Mr. Fantastic / Reed R         Human Torch / Johnny S 
##                            198                            193 
##         Colossus Ii / Peter Ra                         Vision 
##                            188                            213 
##                 Starfox / Eros         She-hulk / Jennifer Wa 
##                             73                            178 
##         Mystique / Raven Darkh            Gyrich, Henry Peter 
##                             58                             55 
##         Banshee / Sean Cassidy         Legion Ii / David Hall 
##                             69                             29 
##           Havok / Alex Summers         Psylocke / Elisabeth B 
##                            124                            132 
##                       Longshot              Wolverine / Logan 
##                             33                            220 
##                          Forge         Sabretooth / Victor Cr 
##                             73                             40 
##           Maddicks, Arthur Art                    Warlock Iii 
##                             26                             59 
##         Rictor / Julio Esteban         Sunspot / Roberto Daco 
##                             53                             82 
##         Firefist / Rusty Colli                      Bishop  / 
##                             32                             68 
##         Daytripper / Amanda Se           Polaris / Lorna Dane 
##                             25                            111 
##         Wild Child / Kyle Gibn         Sauron / Dr. Karl Lyko 
##                             56                             25 
##                         Spiral           Summers, Madelyne Ma 
##                             29                             37 
##         Pyro / Allerdyce Johnn                          Leech 
##                             46                             28 
##         Siryn / Theresa Rourke         Shatterstar Ii / Gavee 
##                             53                             42 
##         Boomer / Tabitha Smith         Mirage Ii / Danielle M 
##                             66                             58 
##         Avalanche / Dominic Pe                 Marrow / Sarah 
##                             39                             33 
##                       Rogue  /           Mactaggert, Moira Ki 
##                            169                             78 
##         Feral / Maria Callasan         Destiny Ii / Irene Adl 
##                             36                             33 
##         Cannonball Ii / Sam Gu                           Zabu 
##                            110                             25 
##        Domino Iii / Beatrice /                           Uatu 
##                             24                             82 
##                      Caliban /               Galactus / Galan 
##                             41                             98 
##         Dr. Octopus / Otto Oct         Silver Surfer / Norrin 
##                             57                            119 
##         Binary / Carol Danvers          Apocalypse / En Sabah 
##                             86                             56 
##           Gambit / Remy Lebeau                 Hunter, Stevie 
##                            121                             38 
##                        Corsair                          Ch'od 
##                             35                             30 
##             Mam'selle Hepzibah                           Zero 
##                             30                             31 
##         Darkstar / Laynia Serg            X-man / Nathan Grey 
##                             32                             31 
##         Karma / Xi'an Coy Manh         Daredevil / Matt Murdo 
##                             29                            145 
##                         Thanos          Aurora / Jeanne-marie 
##                             78                             60 
##           Mr. Fantastic Doppel                       Beyonder 
##                             49                             36 
##         Multiple Man / James A           Colossus Ii Doppelga 
##                             76                             26 
##                     Scanner Ii         Ka-zar / Kevin Plunder 
##                             19                             33 
##         White Queen / Emma Fro         Sasquatch / Walter Lan 
##                             40                             94 
##          Northstar / Jean-paul        Magma / Amara Aquilla / 
##                             74                             28 
##                         Gamora         Dr. Druid / Anthony Lu 
##                             59                             71 
##         Warlock Ii / Adam Warl            Thanos Doppelganger 
##                             75                             61 
##                          Magus           Nova / Richard Rider 
##                             72                            103 
##         Wolfsbane / Rahne Sinc          Skids / Sally Blevins 
##                            116                             32 
##         Sub-mariner / Namor Ma         Punisher Ii / Frank Ca 
##                            143                             38 
##                           Zeus                           Wong 
##                             24                             31 
##              Hogun [asgardian]         Box Iv / Madison Jeffr 
##                             44                             20 
##         Guardian / James Macdo         Doc Samson / Dr. Leona 
##                             33                             40 
##         Vanguard / Nicolai Kry         Firelord / Pyreus Kril 
##                             25                             36 
##           Lyja Lazerfist [skru                          Thena 
##                             32                             22 
##             Stankowicz, Fabian                          Death 
##                             25                             43 
##                           Clea                         Attuma 
##                             20                             24 
##                 Le Fey, Morgan         Rage / Elvin Daryl Hal 
##                             18                             47 
##                    Parker, May               Gee / Alex Power 
##                             43                             22 
##         Strong Guy / Guido Car         Puck / Eugene Milton J 
##                             93                             79 
##                Hudson, Heather           Iron Man Doppelgange 
##                             82                             46 
##            Watson-parker, Mary                     Silhouette 
##                             58                             35 
##         Mister Hyde / Calvin Z         Night Thrasher / Duane 
##                             24                             26 
##                  Knight, Misty            Leader / Sam Sterns 
##                             27                             17 
##           Summers, Nathan Chri         Spider-woman / Jessica 
##                             83                             30 
##         Hobgoblin V / Jason Ph         Collector / Taneleer T 
##                             26                             30 
##         Ghost Rider Ii / Johnn           Banner, Betty Ross T 
##                             27                             37 
##          Ghost Rider Iii / Dan                     Arranger / 
##                             19                             20 
##                  Osborn, Harry          Green Goblin / Norman 
##                             28                             23 
##          Cobra / Klaus Vorhees               O'brien, Michael 
##                             16                             34 
##         Black Cat / Felicia Ha         Mole Man / Harvey Rupe 
##                             29                             35 
##           Cypher / Doug Ramsey          Citizen V Ii / Helmut 
##                             41                             31 
##         Fixer Ii / Paul Norber          Kingpin / Wilson Fisk 
##                             34                             48 
##                     Leeds, Ned                   Watson, Anna 
##                             24                             26 
##         Screaming Mimi / Melis                     Urich, Ben 
##                             30                             37 
##         Ant-man Ii / Scott Har               Robertson, Randy 
##                             51                             22 
##                    Page, Karen            Grant, Gloria Glory 
##                             16                             28 
##                 Lubenski, Nate           Thompson, Eugene Fla 
##                             19                             42 
##         Spider-man Clone / Ben         Forgotten One / Gilgam 
##                             19                             28 
##          Jack Of Hearts / Jack         Red Skull / Johann Sch 
##                             39                             38 
##         Eternity / Adam Qadmon              Rosenthal, Bernie 
##                             61                             21 
##         Puppet Master / Philli         High Evolutionary / He 
##                             25                             41 
##         Hellstorm / Daimon Hel         Hellcat / Patsy Walker 
##                             28                             62 
##              Maximus [inhuman]              Lockjaw [inhuman] 
##                             20                             45 
##                       Mephisto         Moonstone Ii / Karla S 
##                             56                             40 
##         Ikaris / Ike Harris [e         Luna / Luna Maximoff [ 
##                             17                             29 
##         Demolition Man / Denni                 Cortez, Fabian 
##                             30                             21 
##         Jubilee / Jubilation L         Thunderbird Ii / James 
##                             59                             59 
##         Whizzer Ii / Stanley S                  Austin, Susan 
##                             15                             17 
##               Hela [asgardian]           De La Fontaine, Cont 
##                             33                             22 
##         Diamondback Ii / Rache       Makkari / Mike Khary / I 
##                             20                             26 
##                         Vizier             Balder [asgardian] 
##                             23                             33 
##           Heimdall [asgardian]                   Gladiator Ii 
##                             22                             23 
##                         Meggan          Mr. Sinister / Nathan 
##                             21                             30 
##         Black King / Sebastian                 Raza Longknife 
##                             31                             28 
##         Tilby, Trish / Patrici                  Wing, Colleen 
##                             33                             12 
##                 Hodge, Cameron                       Callisto 
##                             27                             27 
##             Deathbird [shi'ar]         Magik / Illyana Rasput 
##                             28                             41 
##           Husk / Paige Guthrie           Norriss, Sister Barb 
##                             16                             61 
##                     Hammerhead         Tombstone / Lonnie Tho 
##                             19                             21 
##          Dr. Spectrum / Joseph                           Ulik 
##                             15                             19 
##                  Beta Ray Bill       Deadpool / Jack / Wade W 
##                             24                             13 
##               Katzenberg, Nick                  Cushing, Kate 
##                             20                             23 
##                   Mercado, Joy                  Asp Ii / Cleo 
##                             21                              8 
##         Black Mamba / Tanya Se                         Stryfe 
##                              8                             34 
##         Skin / Angelo Espinosa           Bridge, George Washi 
##                             14                             22 
##          Diamond Lil / Lillian 
##                             14

degree <- betweenness(MG)/degree(MG)

5. Using the dataframe from the last step, create a histogram of the network’s degree distribution. Make it polished with labels, titles, and colors. Write a short explanation of this plot: does this distribution suggest we have a small world network?

nodes <- igraph::as_data_frame(MG, what = "vertices")
ggplot(nodes, aes(degree, fill = "red")) + geom_histogram() + labs(title = "Distribution of degree in the Marvel Comics universe network") + theme(legend.position = "none")

## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

I would say it is a small world network because the vast majority of the nodes have a degree under 5.

6. In addition to degree distribution, we know a couple other measures that can help us assess whether the Marvel network is a small world: the average shortest path length and the diameter. Run those two functions and report the results! Do these match the expectations of a small world network?

diameter(MG)

## [1] 3

farthest.nodes(MG)

## $vertices
## + 2/327 vertices, named, from 8e8eed7:
## [1] Ghaur [deviant]        Hobgoblin V / Jason Ph
## 
## $distance
## [1] 3

Yes, it does, because the greatest distance between nodes is 3. Its diameter is also 3.

• iGraph gives us functions for both of these, but we haven’t discussed them yet. Find the two functions you need in the iGraph documentation. (Hint: average shortest path length is also called the “mean distance.”)

7. As a bonus question, create a D3 network visualization of the Marvel graph. You can follow the code we used in our in-class example, replacing the example graph with your Marvel network. But beware: this is a big network and the visualization might slow down RStudio quite a bit!

marveld3 <- igraph_to_networkD3(MG, membership(cluster_fast_greedy(MG)))
marveld3$nodes$degree <- V(MG)$degree
marveld3$links$weight <- E(MG)$weight

simpleNetwork(marvel, opacity = 1, zoom = TRUE)

This is a hairball, but the better version that was in the slides didn’t work when I tried to use it.

8. What’s your overall assessment? Is the Marvel network a small world network or not? What evidence do you have to back up your claim?

The Marvel network is a small world network due to its low farthest node distance, low diameter, and high largest clique size.

Good work! Turn in the knitted HTML on Github, and remember that you’re also working on the Code Glossary this week.