Network Analysis Tutorial

title	date	output
PolNet 2018 Workshop	06/06/2018	html_document

Network Analysis Tutorial

With Applications in `R`

Bruce A. Desmarais

Pennsylvania State University

1 Introduction

Provide a broad introduction to many concepts/methods (nothing in depth)
Present technical intuition and some essential math (no derivations)
Comments describing functions generally (see help for explanations of all options)

2 Introduction to R

2.1 Programming in R: First Steps

R is a Command-line interpreted programming language
Commands executed sequentially by return (i.e., `enter') or separated by ';'
Script files are formatted in plain text files (e.g. UTF-8) with extension ".R"
Comment heavily using '#'

# In R, functions are executed as '<function.name>(<input>)'
# <input> is a comma-separated list of arguments
# The exception is the 'print()' function, which can 
# be executed by typing the name of the object to 
# print and hitting enter
# Try
print(x='Hello World')

## [1] "Hello World"

# x is the only argument

2.2 Objects: Vectors and Matrices

In R everything is an object.
R environment - collection of objects accessible to R in RAM
Vector - column of nubmers, characters, logicals (T/F)

# Vectors contain data of the same type
# Create a character vector
char_vec <- c('a','b','c')
# Look at it
char_vec

## [1] "a" "b" "c"

# Create a numeric vector
num_vec <- numeric(5)
num_vec

## [1] 0 0 0 0 0

# Change Values
num_vec[1] <- 4
num_vec[2:4] <- c(3,2,1) 
num_vec

## [1] 4 3 2 1 0

num_vec[5] <- '5'
num_vec

## [1] "4" "3" "2" "1" "5"

# Reference all but 3
num_vec[-3]

## [1] "4" "3" "1" "5"

num_vec

## [1] "4" "3" "2" "1" "5"

Matrix

# Create a matrix
MyMat <- matrix(1:25,nrow=5,ncol=5)
MyMat

##      [,1] [,2] [,3] [,4] [,5]
## [1,]    1    6   11   16   21
## [2,]    2    7   12   17   22
## [3,]    3    8   13   18   23
## [4,]    4    9   14   19   24
## [5,]    5   10   15   20   25

# Access (or change) a cell
MyMat[1,3]

## [1] 11

MyMat[2,4] <- 200 
MyMat[2,4]

## [1] 200

# Rows then columns
MyMat[1,]

## [1]  1  6 11 16 21

MyMat[,3] <- c(1,1,1,1,1)
MyMat[,3]

## [1] 1 1 1 1 1

MyMat

##      [,1] [,2] [,3] [,4] [,5]
## [1,]    1    6    1   16   21
## [2,]    2    7    1  200   22
## [3,]    3    8    1   18   23
## [4,]    4    9    1   19   24
## [5,]    5   10    1   20   25

# Multiple rows/columns and negation
MyMat[1:3,-c(1:3)]

##      [,1] [,2]
## [1,]   16   21
## [2,]  200   22
## [3,]   18   23

# The matrix (shortcut for network objects)
MyMat[,]

##      [,1] [,2] [,3] [,4] [,5]
## [1,]    1    6    1   16   21
## [2,]    2    7    1  200   22
## [3,]    3    8    1   18   23
## [4,]    4    9    1   19   24
## [5,]    5   10    1   20   25

2.3 Objects: Data Frames

Data Frames can hold columns of different types

# A Data Frame is the conventional object type for a dataset
## Create a data frame containing numbers and a character vector
## Construct a letter vector
let_vec <- c('a','b','c','d','e')

## Combine various objects into a data frame
dat <- data.frame(MyMat, num_vec,let_vec, stringsAsFactors=F)

## Create/override variable names
names(dat) <- c("mm1","mm2","mm3","mm4","mm5","nv","lv")

# Variables can be accessed with '/pre>
dat$lv

## [1] "a" "b" "c" "d" "e"

# Or with matrix-type column indexing
dat[,7]

## [1] "a" "b" "c" "d" "e"

2.4 R Packages

# Use install.packages() to install
# library() or require() to use the package
# install.packages('statnet') 
# install.packages('igraph') 
# install.packages('GGally') 
library(statnet,quietly=T)

# R is OPEN SOURCE,  SO LOOK AT THE CODE !!!
network.size

## function (x) 
## {
##     if (!is.network(x)) 
##         stop("network.size requires an argument of class network.\\n")
##     else get.network.attribute(x, "n")
## }
## <environment: namespace:network>

# And give credit to the authors
citation('statnet')

## 
## `statnet` is part of the Statnet suite of packages.  If you are
## using the `statnet` package for research that will be published,
## we request that you acknowledge this by citing the following. For
## BibTeX format, use toBibtex(citation("statnet")).
## 
## Handcock M, Hunter D, Butts C, Goodreau S, Krivitsky P,
## Bender-deMoll S and Morris M (2016). _statnet: Software Tools for
## the Statistical Analysis of Network Data_. The Statnet Project
## (<URL: http://www.statnet.org>). R package version 2016.9, <URL:
## CRAN.R-project.org/package=statnet>.
## 
## Handcock M, Hunter D, Butts C, Goodreau S and Morris M (2008).
## "statnet: Software Tools for the Representation, Visualization,
## Analysis and Simulation of Network Data." _Journal of Statistical
## Software_, *24*(1), pp. 1-11. <URL:
## http://www.jstatsoft.org/v24/i01>.
## 
## We have invested a lot of time and effort in creating the Statnet
## suite of packages for use by other researchers. Please cite it in
## all papers where it is used. The package statnet is made
## distributed under the terms of the license: GPL-3 + file LICENSE
## To see these entries in BibTeX format, use 'print(<citation>,
## bibtex=TRUE)', 'toBibtex(.)', or set
## 'options(citation.bibtex.max=999)'.

# BibTeX Users
toBibtex(citation("statnet"))

## @Manual{,
##   author = {Mark S. Handcock and David R. Hunter and Carter T. Butts and Steven M. Goodreau and Pavel N. Krivitsky and Skye Bender-deMoll and Martina Morris},
##   title = {statnet: Software Tools for the Statistical Analysis of Network Data},
##   organization = {The Statnet Project (\url{http://www.statnet.org})},
##   year = {2016},
##   note = {R package version 2016.9},
##   url = {CRAN.R-project.org/package=statnet},
## }
## 
## @Article{,
##   title = {statnet: Software Tools for the Representation, Visualization, Analysis and Simulation of Network Data},
##   author = {Mark S. Handcock and David R. Hunter and Carter T. Butts and Steven M. Goodreau and Martina Morris},
##   journal = {Journal of Statistical Software},
##   year = {2008},
##   volume = {24},
##   number = {1},
##   pages = {1--11},
##   url = {http://www.jstatsoft.org/v24/i01},
## }

2.5 Interactions with the Hard Drive

# Saving dat as a .csv
write.csv(dat,'dat.csv', row.names=F)

# Loading it as such
dat2 <- read.csv('dat.csv',stringsAsFactors=F)

# Save to RData file and load
save(list=c("dat2","dat"),file="dat_and_dat2.RData")
load("dat_and_dat2.RData")
# understand that objects in the loaded objects will overwrite

2.6 R can help

# When you know the function name exactly
help("evcent")
# or
?evcent

# Find help files containing a word
help.search("eigenvector")

R help files contain

function usage arguments
detailed description
values (objects) returned
links to related functions
references on the methods
error-free examples

3 Introduction to Networks

3.1 Network Terminology and the Basics

Units in the network: Nodes, actors, or vertices
Relationships between nodes: edges, links, or ties
Pairs of actors: Dyads
Direction: Directed vs. Undirected (digraph vs. graph)
Tie value: Dichotomous/Binary, Valued/Weighted
Ties to Self: Loops

3.2 Network and Network Data Types

Many Modes with unconnected nodes: Bi/Multipartite
- Affiliation Networks
- Association/correlation Networks
- Beware of Collapsed Modes!
Many relations among nodes: Multiplex
Data types
- Have all the data: Network Census
- Have links data from a sample of nodes: Ego Network
- Sample along links starting with Ego: link tracing, snowball, respondent-driven

3.3 Network Data

Vertex-level Data: Vertex attributes (n rows and k columns)
Adjacency Matrix Data for each relation (n by n) matrix
Edgelist Data for each edge (e by p) matrix. p typically two---sender & receiver

# Read in adjacency matrices
## read.csv creates a data frame object from a CSV file
## Need to indicate that there's no header row in the CSV
advice <- read.csv("Advice.csv", header=F)

reportsto <- read.csv("ReportsTo.csv", header = F)

# Read in vertex attribute data
attributes <- read.csv("KrackhardtVLD.csv")

3.4.1 Creating Network Objects: Managers in a "Hi-Tech" Firm

# Read in the library for network analysis
library(network,quietly=T)

# Use the advice network dataset to create network object
adviceNet <- network(advice)

# Add the vertex attributes into the network
set.vertex.attribute(adviceNet,names(attributes),attributes)

# Add the organizational chart as a network variable
set.network.attribute(adviceNet,"reportsto",reportsto)

# Simple plot
## Set random number seed so the plot is replicable
set.seed(5)
## create vertex labels
vertex.labels <- get.vertex.attribute(adviceNet,"Level")
## create edge colors
edge.colors <- rgb(150,150,150,100,maxColorValue=255)
## Now plot
## Plot the network
plot(adviceNet,              # network object
     displaylabels=T,        # label nodes
     label=vertex.labels,    # label vector
     label.cex=1,            # size of the vertex lables
     vertex.cex=3,           # vertex size
     edge.col=edge.colors,   # edge color vector
     label.pos=5,            # position labels in the center
     vertex.col="lightblue") # set the vertex color

# check out all the options with ?plot.network

# gg-verse alternative based on plot.network/sna:::gplot
library(GGally)
set.seed(5)
ggnet(adviceNet,
      size = 11,
      color="white",
      segment.color=edge.colors,
      label=vertex.labels)

3.4.2 Creating Network Objects: Defense Pacts (edgelist) (2000)

# Read in vertex dataset
allyV <- read.csv("allyVLD.csv",stringsAsFactors=F)

# Read in edgelist
allyEL <- read.csv("allyEL.csv", stringsAsFactors=F)

# Read in contiguity
contig <- read.csv("contiguity.csv",stringsAsFactors=F,row.names=1)

require(network)
# (1) Initialize network
# store number of vertices
n <- nrow(allyV)
AllyNet <- network.initialize(n,dir=F)

# (2) Set vertex labels
network.vertex.names(AllyNet)  <- allyV$stateabb

# (3) Add in the edges
# Note, edgelist must match vertex labels
AllyNet[as.matrix(allyEL)]  <- 1

# (4) Store country code attribute
set.vertex.attribute(x=AllyNet, 			# Network in which to store
			"ccode",			# What to name the attribute
			allyV$ccode)			# Values to put in

# (5) Store year attribute
set.vertex.attribute(AllyNet,"created",allyV$styear)

# (6) Store network attribute
set.network.attribute(AllyNet,"contiguous",as.matrix(contig))

# Simple plot
plot(AllyNet,displaylabels=T,label.cex=.5,edge.col=rgb(150,150,150,100,maxColorValue=255))

# check out all the options with ?plot.network

4 The Individual Level: Actor Position Analysis

4.1 Connectedness: Degree Centrality

require(sna)
# (in-) Degree Centrality is the number of in-connections by node
dc <- degree(adviceNet, cmode="indegree")

# Store in vertex level data frame
attributes$dc <- dc

# Plot degree centrality against age
## Make a simple scatter plot
par(cex=2,las=1)
plot(attributes$Tenure,attributes$dc)
## Add a trend (i.e., regression) line
abline(lm(attributes$dc ~ attributes$Tenure))

# Plot network with node size proportional to Degree Centrality
## First normalize degree 
ndc <- dc/max(dc)
## Set random number seed so the plot is replicable
set.seed(5)
## create vertex labels
vertex.labels <- get.vertex.attribute(adviceNet,"Level")
## create edge colors
edge.colors <- rgb(150,150,150,100,maxColorValue=255)
## Now plot
plot(adviceNet,              # network object
     displaylabels=T,        # label nodes
     label=vertex.labels,    # label vector
     vertex.cex=3*ndc,       # vertex size vector
     label.cex=1,            # size of the vertex lables
     edge.col=edge.colors,   # edge color vector
     label.pos=5,            # position labels in the center
     vertex.col="lightblue") # set the vertex color

4.2 Connectedness: Eigenvector Centrality

**x** = λ^-1A**x**

# Eigenvector Centrality Recursively Considers Neighbors' Centrality
ec <- evcent(adviceNet)

# Store in vertex level data frame
attributes$ec <- ec

# Plot eigenvector centrality against age
## Make a simple scatter plot
par(cex=2,las=1)
plot(attributes$Tenure,attributes$ec)
## Add a trend (i.e., regression) line
abline(lm(attributes$ec ~ attributes$Tenure))

# Plot network with node size proportional to eigenvector centrality
## First normalize
nec <- ec/max(ec)
## Set random number seed so the plot is replicable
set.seed(5)
## Now plot
plot(adviceNet,displaylabels=T,label=get.vertex.attribute(adviceNet,"Level"),vertex.cex=3*nec,label.cex=1,edge.col=rgb(150,150,150,100,maxColorValue=255),label.pos=5,vertex.col="lightblue")

4.3 Connectedness: Betweenness Centrality

knitr::include_graphics("betweenness.png")

![](betcent.jpg)

# Betweenness Centrality Considers unlikely connections
# Proportion of shortest paths that pass through a vertex
bc <- betweenness(adviceNet,rescale=T)

# Store in vertex level data frame
attributes$bc <- bc

# Plot eigenvector centrality against age
## Make a simple scatter plot
par(cex=2,las=1)
plot(attributes$Tenure,attributes$bc)
## Add a trend (i.e., regression) line
abline(lm(attributes$bc ~ attributes$Tenure))

# Plot network with node size proportional to betweenness centrality
## First normalize
nbc <- bc/max(bc)
## Set random number seed so the plot is replicable
set.seed(5)
## Now plot
plot(adviceNet,displaylabels=T,label=get.vertex.attribute(adviceNet,"Level"),vertex.cex=3*nbc,label.cex=1,edge.col=rgb(150,150,150,100,maxColorValue=255),label.pos=5,vertex.col="lightblue")

4.4 Comparing Centrality Measures

# DC vs. EC
par(cex=2,las=1)
plot(dc,ec)

# DC vs. BC
par(cex=2,las=1)
plot(dc,bc)

# BC vs. EC
par(cex=2,las=1)
plot(bc,ec)

# Correlations among all of them
cor(cbind(ec,bc,dc))

##           ec        bc         dc
## ec  1.000000 0.4320920 -0.3164510
## bc  0.432092 1.0000000  0.5436799
## dc -0.316451 0.5436799  1.0000000

4.5 Embeddedness: Clustering Coefficient

Clustering coefficient is the proportion of potential ties among a node's neightbors that exist.

# Read in library for clustering coefficient
require(igraph,quietly=T)

## Warning: package 'igraph' was built under R version 3.4.4

## 
## Attaching package: 'igraph'

## The following objects are masked from 'package:sna':
## 
##     betweenness, bonpow, closeness, components, degree,
##     dyad.census, evcent, hierarchy, is.connected, neighborhood,
##     triad.census

## The following objects are masked from 'package:network':
## 
##     %c%, %s%, add.edges, add.vertices, delete.edges,
##     delete.vertices, get.edge.attribute, get.edges,
##     get.vertex.attribute, is.bipartite, is.directed,
##     list.edge.attributes, list.vertex.attributes,
##     set.edge.attribute, set.vertex.attribute

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

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

# Compute local transitivity, i.e., the clustering clef
anet <- graph.adjacency(adviceNet[,])
cc <- transitivity(anet,type="local")

# Store in data frame
attributes$cc <- cc
attributes

##    Age Tenure Level Department dc         ec           bc        cc
## 1   33      9     3          4 13 0.13887187 0.0511034401 0.5263158
## 2   42     20     2          4 18 0.04122224 0.0220658524 0.5666667
## 3   40     13     3          2  5 0.28317710 0.0245530182 0.5105263
## 4   33      8     3          4  8 0.21911327 0.0509618222 0.3473684
## 5   32      3     3          2  5 0.29140287 0.0188794477 0.4210526
## 6   59     28     3          1 10 0.02466730 0.0000000000 0.6909091
## 7   55     30     1          0 13 0.11196954 0.1026936921 0.3047619
## 8   34     11     3          1 10 0.16751801 0.0147754765 0.4967320
## 9   62      5     3          2  4 0.21796754 0.0146987667 0.5514706
## 10  37      9     3          3  9 0.34421295 0.0680179383 0.3162055
## 11  46     27     3          3 11 0.03538648 0.0044550658 0.7252747
## 12  34      9     3          1  7 0.03823355 0.0009441199 0.4722222
## 13  48      0     3          2  4 0.14344220 0.0033191715 0.5555556
## 14  43     10     2          2 10 0.09198919 0.0021891780 0.4835165
## 15  40      8     3          2  4 0.41860823 0.0227975453 0.4528986
## 16  27      5     3          4  8 0.11228627 0.0026022305 0.4848485
## 17  30     12     3          1  9 0.08660158 0.0094116953 0.4945055
## 18  33      9     2          3 15 0.40245199 0.3305452292 0.2016129
## 19  32      5     3          2  4 0.28747761 0.0028028560 0.4571429
## 20  38     12     3          2  8 0.21341504 0.0296630672 0.4842105
## 21  36     13     2          1 15 0.20359254 0.2235203871 0.2430769

# Remove igraph before using statnet functions
detach(package:igraph)

# Plot network with node size proportional to clustering clef
## First normalize
ncc <- cc/max(cc)
## Set random number seed so the plot is replicable
set.seed(5)
## Now plot
plot(adviceNet,displaylabels=T,label=get.vertex.attribute(adviceNet,"Level"),vertex.cex=3*ncc,label.cex=1,edge.col=rgb(150,150,150,100,maxColorValue=255),label.pos=5,vertex.col="lightblue")

# Correlations among all of them
cor(cbind(ec,bc,dc,cc))

##            ec         bc         dc         cc
## ec  1.0000000  0.4320920 -0.3164510 -0.5872217
## bc  0.4320920  1.0000000  0.5436799 -0.7536546
## dc -0.3164510  0.5436799  1.0000000 -0.2204078
## cc -0.5872217 -0.7536546 -0.2204078  1.0000000

5 Group-Level Analysis: Communities and Clusters

5.1 Clustering by Structural Equivalence

# Blockmodeling is the Classical SNA Approach
# Goal is to group nodes based on structural equivalence

## Create clusters based on structural equivalence
eclusts <- equiv.clust(adviceNet)

## First check out a dendrogram to eyeball the number of clusters
plot(eclusts,hang=-1)

# Run a block model identifying six groups
adviceBlockM <- blockmodel(adviceNet, eclusts, k=6)

# Create block membership vector and colors
## Extract block memberships
bmems <- adviceBlockM$block.membership[adviceBlockM$order.vec]
## Create group colors
colVec <- c("black","white","red","blue","yellow","gray60")
## Assign colors to individual nodes based on block membership
bcols <- colVec[bmems]

set.seed(5)
## Now plot
plot(adviceNet,displaylabels=T,label=get.vertex.attribute(adviceNet,"Level"),vertex.cex=2,label.cex=1,edge.col=rgb(150,150,150,100,maxColorValue=255),label.pos=5,vertex.col=bcols)

5.2 Clustering Based on Modularity: Community Detection

Modularity = 1/(2m)Σ_ij[A_ij-k_ik_j/(2m)]**1**(c_i=c_j)

k is the degree
m is the number of edges in the network
c is the group index
1 is the indicator function (i.e., are the groups of i and j equal)

# Modularity-based community detection popular in physics
# Modularity = Dense within communities, sparse across 
library(igraph,quietly=T)

## Warning: package 'igraph' was built under R version 3.4.4

## 
## Attaching package: 'igraph'

## The following objects are masked from 'package:sna':
## 
##     betweenness, bonpow, closeness, components, degree,
##     dyad.census, evcent, hierarchy, is.connected, neighborhood,
##     triad.census

## The following objects are masked from 'package:network':
## 
##     %c%, %s%, add.edges, add.vertices, delete.edges,
##     delete.vertices, get.edge.attribute, get.edges,
##     get.vertex.attribute, is.bipartite, is.directed,
##     list.edge.attributes, list.vertex.attributes,
##     set.edge.attribute, set.vertex.attribute

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

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

# Convert into a graph
anet <- graph.adjacency(adviceNet[,])

## Use semi-greedy splitting and merging
mem <- spinglass.community(anet)$membership

# Check number of communities
max(mem)

## [1] 2

# Get memberships and plot
detach("package:igraph")
bcols <- c("lightblue","yellow")
set.seed(5)
## Now plot
plot(adviceNet,displaylabels=T,label=get.vertex.attribute(adviceNet,"Department"),vertex.cex=2,label.cex=1,edge.col=rgb(150,150,150,100,maxColorValue=255),label.pos=5,vertex.col=bcols)

6 Network-Level: Testing Structural Hypotheses

6.1 Introduction

Now assume the network is stochastic
We might have hypotheses about the stochastic process
- Nodes that are similar are likely to form ties: Homophily
- Directed edges are likely to be reciprocated: Reciprocity
- A friend of a friend is a friend: Transitivity

6.3 μ=0, the z-test

Suppose x is a large univariate sample of size n, and T(x) is the z-statistic.

Our null is that X has finite positive variance and a mean of zero.

![](zstat.jpg)

-->

6.3 H₀ for a network...

**Maximum Entropy Null Distribution** ![](net3.jpg) **Uniform/Equal Probability of Every Network**

6.5 Conditional Uniform Graph Testing: Comparing Observed to Null

# Conditional Uniform Graph Tests
# "CUG" tests allow you to control for features of the observed network in the null
# We should test for transitivity
# gtrans function in sna package measures graph transitivity

# control for the number of edges
cug_gtrans_edges <- cug.test(adviceNet,gtrans,cmode=c("edges"),reps=500)

# Check results
cug_gtrans_edges

## 
## Univariate Conditional Uniform Graph Test
## 
## Conditioning Method: edges 
## Graph Type: digraph 
## Diagonal Used: FALSE 
## Replications: 500 
## 
## Observed Value: 0.6639785 
## Pr(X>=Obs): 0 
## Pr(X<=Obs): 1

# what if we consider the dyad census null?
dyad.census(adviceNet)

##      Mut Asym Null
## [1,]  45  100   65

# control for the number of edges
cug_gtrans_dcensus <- cug.test(adviceNet,gtrans,cmode=c("dyad.census"),reps=500)

cug_gtrans_dcensus

## 
## Univariate Conditional Uniform Graph Test
## 
## Conditioning Method: dyad.census 
## Graph Type: digraph 
## Diagonal Used: FALSE 
## Replications: 500 
## 
## Observed Value: 0.6639785 
## Pr(X>=Obs): 0 
## Pr(X<=Obs): 1

# Now lets look at something else
# Do more experienced managers have higher in-degree centrality?

# function to estimate correlation between in-degree and node attribute
indegCor <-  function(net,attr){
	require(sna)
	cor(degree(net,cmode="indegree"),attr)
}

# See the additional argument in cmode, now controlling for dyad census
cug_indcor_dcensus <- cug.test(adviceNet,indegCor,cmode=c("dyad.census"),reps=500, FUN.args=list(attr = attributes$Tenure))

# Check results
cug_indcor_dcensus

## 
## Univariate Conditional Uniform Graph Test
## 
## Conditioning Method: dyad.census 
## Graph Type: digraph 
## Diagonal Used: FALSE 
## Replications: 500 
## 
## Observed Value: 0.5493177 
## Pr(X>=Obs): 0.004 
## Pr(X<=Obs): 0.996

## Can we incorporate both? 
## Need ERGM for that!

7 Independent exercise with the allliance network

What are the 5 most central states, according to each centrality measure?
Do community detection and blockmodeling result in substantially different partitions?
Is the age of the state significantly correlated with the number of alliance ties?

Name		Name	Last commit message	Last commit date
Latest commit History 6 Commits
figure		figure
.DS_Store		.DS_Store
ALL.RData		ALL.RData
Advice.csv		Advice.csv
KrackhardtVLD.csv		KrackhardtVLD.csv
README.md		README.md
ReportsTo.csv		ReportsTo.csv
Tutorial.html		Tutorial.html
allyEL.csv		allyEL.csv
allyVLD.csv		allyVLD.csv
betcent.jpg		betcent.jpg
betweenness.png		betweenness.png
centralityEVpng.png		centralityEVpng.png
clustCoef.jpg		clustCoef.jpg
communities.png		communities.png
contiguity.csv		contiguity.csv
dat.csv		dat.csv
dat_and_dat2.RData		dat_and_dat2.RData
degcent.jpg		degcent.jpg
degcentEV.jpg		degcentEV.jpg
degcentEVpng.png		degcentEVpng.png
evcent.jpg		evcent.jpg
myfirstplot.pdf		myfirstplot.pdf
net3.jpg		net3.jpg
tutorial.rmd		tutorial.rmd
zstat.jpg		zstat.jpg

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Network Analysis Tutorial

With Applications in R

Bruce A. Desmarais

Pennsylvania State University

1 Introduction

2 Introduction to R

2.1 Programming in R: First Steps

2.2 Objects: Vectors and Matrices

2.3 Objects: Data Frames

2.4 R Packages

2.5 Interactions with the Hard Drive

2.6 R can help

3 Introduction to Networks

3.1 Network Terminology and the Basics

3.2 Network and Network Data Types

3.3 Network Data

3.4.1 Creating Network Objects: Managers in a "Hi-Tech" Firm

3.4.2 Creating Network Objects: Defense Pacts (edgelist) (2000)

4 The Individual Level: Actor Position Analysis

4.1 Connectedness: Degree Centrality

4.2 Connectedness: Eigenvector Centrality

4.3 Connectedness: Betweenness Centrality

4.4 Comparing Centrality Measures

4.5 Embeddedness: Clustering Coefficient

5 Group-Level Analysis: Communities and Clusters

5.1 Clustering by Structural Equivalence

5.2 Clustering Based on Modularity: Community Detection

6 Network-Level: Testing Structural Hypotheses

6.1 Introduction

6.3 μ=0, the z-test

6.3 H0 for a network...

6.5 Conditional Uniform Graph Testing: Comparing Observed to Null

7 Independent exercise with the allliance network

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With Applications in `R`

6.3 H₀ for a network...

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