POL 478H1 F

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# POL 478H1 F
## Intro to Network Analysis
### Olga Chyzh [www.olgachyzh.com]

---

## Today's Class
 **Network Analysis: an introduction**

1. Definitions. What is network analysis?
 
 3. Network features and measurements 
 
 4. Collecting/managing network data
 
 5. Applications to Political Science
 
 6. Network Visualization
---

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

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

<img src="images/madmen.png" width="400px" style="display: block; margin: auto;" />
---

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

- A <span style="color:DarkCyan">**node**</span> 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 <span style="color:DarkCyan">**relation/tie**</span> 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

<div class="figure" style="text-align: center">
<img src="images/p1.png" alt=" " width="49%" height="10%" /><img src="images/p2.png" alt=" " width="49%" height="10%" />
<p class="caption"> </p>
</div>
---
## Adolescent romantic and sexual networks

<img src="images/jefferson.jpg" width="600px" style="display: block; margin: auto;" />
**Bearman, Moody and Stovel**
---
## Adolescent Social Structure by **Jim Moody**
<img src="images/schoolGrade.png" width="600px" style="display: block; margin: auto;" />

---
## Adolescent Social Structure by **Jim Moody**
<img src="images/schoolRace.png" width="600px" style="display: block; margin: auto;" />
---
## 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](https://raw.githubusercontent.com/ochyzh/POLS478/master/defmat1914.csv)  
  - Countries are nodes
  
  - Alliances are ties

```r
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?

```r
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

```r
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