Today's Class

Network Analysis: an introduction

1. Definitions. What is network analysis?

2. Network features and measurements

3. Collecting/managing network data

4. Applications to Political Science

5. Network Visualization

What is a network (i.e., a graph)?

A set of nodes and relation(s) defined on them

Defining Network Features & Measurements: What's a node?

• A node can be defined as an entity that can form relations with other entities.

Synonyms:

• actor: from sociometry, common terminology in sociology and psychology
• vertex: from graph theory (i.e., math), common terminology in mathematics and physics

Term node is common in statistics and applied sciences outside of soc and psych.

Examples of Nodes

• Individuals (Mad Men characters, legislators, terrorists)

• Families

• Organizations, Human Rights NGOs

• Countries

Defining Network Features & Measurements: What's a relation?

• A relation/tie defines the existence of an attribute relating nodes.

Synonyms:

• link: common in computer science (e.g., huge lit on “Link Prediction”) and social sciences
• edge: graph theoretic terminology common in physics and math, but also elsewhere

Ties can have characteristics:

• Weight
• Qualitative attributes
• Direction

Exampesl of Ties

• Romantic relationship, marriage, friendship

• Business relationship

• Cooperation/conflict

Network graphs can reveal important structures

Adolescent romantic and sexual networks

Bearman, Moody and Stovel

Adolescent Social Structure by Jim Moody

Adolescent Social Structure by Jim Moody

Managing Network Data

You might begin with either a matrix or information stored separately about edges and nodes. This depends on your data collection strategy.

Useful terminology for working in $R$:

• Matrices: the adjacency matrix
• Edges: linkages between actors or nodes
• Vertices: nodes (or actors) in your system

Example: International Alliances 1914

Download the data here

• Countries are nodes

• Alliances are ties

defMat<-read.csv("https://raw.githubusercontent.com/ochyzh/POLS478/master/defmat1914.csv" , header=T)
head(defMat)

##   name1 name2 ally
## 1   AUH   GUA    0
## 2   AUH   HON    0
## 3   AUH   SAL    0
## 4   AUH   NIC    0
## 5   AUH   ECU    0
## 6   AUH   UKG    0

Your Turn (5 min)

Can you transform defAlly into a matrix form as shown below?

as.matrix(defMat)[1:20,1:20]

##       AUH BOL BUL COS ECU FRN GMY GRC GUA HON ITA JPN MNG NIC POR ROM RUS SAL
##  [1,]  NA   0   1   0   0   0   1   0   0   0   1   0   0   0   0   1   0   0
##  [2,]   0  NA   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##  [3,]   1   0  NA   0   0   0   1   0   0   0   0   0   0   0   0   0   0   0
##  [4,]   0   0   0  NA   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##  [5,]   0   0   0   0  NA   0   0   0   0   0   0   0   0   0   0   0   0   0
##  [6,]   0   0   0   0   0  NA   0   0   0   0   0   0   0   0   0   0   1   0
##  [7,]   1   0   1   0   0   0  NA   0   0   0   1   0   0   0   0   1   0   0
##  [8,]   0   0   0   0   0   0   0  NA   0   0   0   0   0   0   0   0   0   0
##  [9,]   0   0   0   0   0   0   0   0  NA   0   0   0   0   0   0   0   0   0
## [10,]   0   0   0   0   0   0   0   0   0  NA   0   0   0   0   0   0   0   0
## [11,]   1   0   0   0   0   0   1   0   0   0  NA   0   0   0   0   0   0   0
## [12,]   0   0   0   0   0   0   0   0   0   0   0  NA   0   0   0   0   0   0
## [13,]   0   0   0   0   0   0   0   0   0   0   0   0  NA   0   0   0   0   0
## [14,]   0   0   0   0   0   0   0   0   0   0   0   0   0  NA   0   0   0   0
## [15,]   0   0   0   0   0   0   0   0   0   0   0   0   0   0  NA   0   0   0
## [16,]   1   0   0   0   0   0   1   0   0   0   0   0   0   0   0  NA   1   0
## [17,]   0   0   0   0   0   1   0   0   0   0   0   0   0   0   0   1  NA   0
## [18,]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0  NA
## [19,]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
## [20,]   0   0   1   0   0   0   1   0   0   0   0   0   0   0   0   0   0   0
##       SPN TUR
##  [1,]   0   0
##  [2,]   0   0
##  [3,]   0   1
##  [4,]   0   0
##  [5,]   0   0
##  [6,]   0   0
##  [7,]   0   1
##  [8,]   0   0
##  [9,]   0   0
## [10,]   0   0
## [11,]   0   0
## [12,]   0   0
## [13,]   0   0
## [14,]   0   0
## [15,]   0   0
## [16,]   0   0
## [17,]   0   0
## [18,]   0   0
## [19,]  NA   0
## [20,]   0  NA

Make a Network Graph

library(igraph)
pGraph <- graph_from_adjacency_matrix(as.matrix(defMat), weighted=NULL, mode="undirected", 
                                      diag=FALSE) #convert to an igraph object
pGraph <- delete.vertices(pGraph , which(degree(pGraph)==0)) #remove isolates
V(pGraph)$color <- "turquoise"
AllyPlot<- plot(pGraph, 
     edge.arrow.size=.2, 
     edge.color="black",
     vertex.frame.color="black",
     vertex.label=V(pGraph)$names, 
     vertex.label.color="black", layout=layout_with_fr,
     edge.width=E(pGraph)$weight/5, edge.curved=.08, vertex.size=30)

Make a Network Graph