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 argument2.2 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 0num_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] 11MyMat[2,4] <- 200
MyMat[2,4]## [1] 200# Rows then columns
MyMat[1,]## [1] 1 6 11 16 21MyMat[,3] <- c(1,1,1,1,1)
MyMat[,3]## [1] 1 1 1 1 1MyMat## [,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 20 252.3 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') # - suite of great network analysis packages
# install.packages('igraph') # - other great network analysis package
library(statnet,quietly=T)## network: Classes for Relational Data
## Version 1.13.0 created on 2015-08-31.
## copyright (c) 2005, Carter T. Butts, University of California-Irvine
## Mark S. Handcock, University of California -- Los Angeles
## David R. Hunter, Penn State University
## Martina Morris, University of Washington
## Skye Bender-deMoll, University of Washington
## For citation information, type citation("network").
## Type help("network-package") to get started.##
## ergm: version 3.7.1, created on 2017-03-20
## Copyright (c) 2017, Mark S. Handcock, University of California -- Los Angeles
## David R. Hunter, Penn State University
## Carter T. Butts, University of California -- Irvine
## Steven M. Goodreau, University of Washington
## Pavel N. Krivitsky, University of Wollongong
## Martina Morris, University of Washington
## with contributions from
## Li Wang
## Kirk Li, University of Washington
## Skye Bender-deMoll, University of Washington
## Based on "statnet" project software (statnet.org).
## For license and citation information see statnet.org/attribution
## or type citation("ergm").## NOTE: Versions before 3.6.1 had a bug in the implementation of the
## bd() constriant which distorted the sampled distribution somewhat.
## In addition, Sampson's Monks datasets had mislabeled verteces. See
## the NEWS and the documentation for more details.##
## networkDynamic: version 0.9.0, created on 2016-01-12
## Copyright (c) 2016, Carter T. Butts, University of California -- Irvine
## Ayn Leslie-Cook, University of Washington
## Pavel N. Krivitsky, University of Wollongong
## Skye Bender-deMoll, University of Washington
## with contributions from
## Zack Almquist, University of California -- Irvine
## David R. Hunter, Penn State University
## Li Wang
## Kirk Li, University of Washington
## Steven M. Goodreau, University of Washington
## Jeffrey Horner
## Martina Morris, University of Washington
## Based on "statnet" project software (statnet.org).
## For license and citation information see statnet.org/attribution
## or type citation("networkDynamic").##
## tergm: version 3.4.0, created on 2016-03-28
## Copyright (c) 2016, Pavel N. Krivitsky, University of Wollongong
## Mark S. Handcock, University of California -- Los Angeles
## with contributions from
## David R. Hunter, Penn State University
## Steven M. Goodreau, University of Washington
## Martina Morris, University of Washington
## Nicole Bohme Carnegie, New York University
## Carter T. Butts, University of California -- Irvine
## Ayn Leslie-Cook, University of Washington
## Skye Bender-deMoll
## Li Wang
## Kirk Li, University of Washington
## Based on "statnet" project software (statnet.org).
## For license and citation information see statnet.org/attribution
## or type citation("tergm").##
## ergm.count: version 3.2.2, created on 2016-03-29
## Copyright (c) 2016, Pavel N. Krivitsky, University of Wollongong
## with contributions from
## Mark S. Handcock, University of California -- Los Angeles
## David R. Hunter, Penn State University
## Based on "statnet" project software (statnet.org).
## For license and citation information see statnet.org/attribution
## or type citation("ergm.count").## NOTE: The form of the term 'CMP' has been changed in version 3.2
## of 'ergm.count'. See the news or help('CMP') for more information.## sna: Tools for Social Network Analysis
## Version 2.4 created on 2016-07-23.
## copyright (c) 2005, Carter T. Butts, University of California-Irvine
## For citation information, type citation("sna").
## Type help(package="sna") to get started.##
## statnet: version 2016.9, created on 2016-08-29
## Copyright (c) 2016, Mark S. Handcock, University of California -- Los Angeles
## David R. Hunter, Penn State University
## Carter T. Butts, University of California -- Irvine
## Steven M. Goodreau, University of Washington
## Pavel N. Krivitsky, University of Wollongong
## Skye Bender-deMoll
## Martina Morris, University of Washington
## Based on "statnet" project software (statnet.org).
## For license and citation information see statnet.org/attribution
## or type citation("statnet").## unable to reach CRAN# 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# 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
# Save and load it all
save.image('ALL.RData')
load('ALL.RData')
# Beware of memory aggregation with save.image()!!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
2.7 Use R for graphics
# Initialize the plot
# first column of MyMat on x-axis
# second on y-axis
plot(MyMat[,1],MyMat[,2],pch=1:5,cex=3,col=1:5)
# Draw a line
lines(MyMat[,1],MyMat[,2], lty =2, col="grey45",lwd=3)
# Re-write the points
points(MyMat[,1],MyMat[,2],pch=1:5,cex=3, col=1:5)
# add a legend
legend("topleft", legend = c("Circle", "Triangle", "Plus", "Times", "Diamond"), col=1:5,pch=1:5)
# Check out all the other options
?par
# Save it this time (as a PDF)
pdf('myfirstplot.pdf')
plot(MyMat[,1],MyMat[,2],pch=1:5,cex=3,col=1:5)
lines(MyMat[,1],MyMat[,2], lty =2, ,col="grey45",lwd=3)
points(MyMat[,1],MyMat[,2],pch=1:5,cex=3,col=1:5)
legend("topleft", legend = c("Circle", "Triangle", "Plus", "Times", "Diamond"), col=1:5,pch=1:5)
dev.off()## quartz_off_screen
## 23 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("http://brucedesmarais.com/Advice.csv", header=F)
reportsto <- read.csv("http://brucedesmarais.com/ReportsTo.csv", header = F)
# Read in vertex attribute data
attributes <- read.csv("http://brucedesmarais.com/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)
## Plot the network
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="lightblue")