Intro to Network Analysis with R

# Intro to Network Analysis with R
## R-Ladies St. Louis
### Maria C. Ramos
### 2020/11/11

---

# Intro & Overview
---

# Network Analysis

+ Map and understand complex structures & systems

+ Relational methods

+ Connections, structures & positions

--
.center[
##<br><br>_**Entities**_ and their _**relations**_
]

---
class: inverse, center, middle

# Some Applications
---
COVID-19
![img_covid](images/covid.png)
Goodreau SM, Pollock ED, Birnbaum JK, Hamilton DT, Morris M, on behalf of the Statnet Development Team. 2020. Can’t I please just visit one friend?: Visualizing social distancing networks in the era of COVID-19. http://statnet.org/COVID-JustOneFriend/]

---
Political Polarization

![img_polarization](images/polarization.png)
<br>Moody, J., & Mucha, P. J. (2013). Portrait of political party polarization. Network Science, 1(1), 119-121.

---
Connectome<br><br>

![img_food](images/connectome.png)

<br><br>Wu, G. R., Stramaglia, S., Chen, H., Liao, W., & Marinazzo, D. (2013). Mapping the voxel-wise effective connectome in resting state fMRI. PloS one, 8(9), e73670.
---
Food Web<br><br>
![img_food](images/food.png)

<br><br>Ahn, Y. Y., Ahnert, S. E., Bagrow, J. P., & Barabasi, A. L. (2011). Flavor network and the principles of food pairing. Sci Rep, 1, 196.
---

# Today's Workshop

<img src="Intro_Nets_slides_files/figure-html/unnamed-chunk-4-1.png" width="504" />
]

---

# Network Elements

---
# Basic Network Elements

- Vertices (nodes)

.center[
<img src="Intro_Nets_slides_files/figure-html/unnamed-chunk-6-1.png" width="504" />
]
---
# Basic Network Elements

- Edges (ties)

---
# Basic Network Elements

## Direction
.pull-left[
- Directed 
<img src="Intro_Nets_slides_files/figure-html/unnamed-chunk-8-1.png" width="504" />
]

.pull-right[
- Undirected 
<img src="Intro_Nets_slides_files/figure-html/unnamed-chunk-9-1.png" width="504" />
]

---

# Basic Network Elements

## Weights

.pull-left[
- Unweighted 
<img src="Intro_Nets_slides_files/figure-html/unnamed-chunk-10-1.png" width="504" />
]

.pull-right[
- Weighted 
<img src="Intro_Nets_slides_files/figure-html/unnamed-chunk-11-1.png" width="504" />
]

---

# Let's take a look at our network

---
class: inverse, center, top

# Your turn!

.left[
+ Explore the karate network 
+ How many nodes does the network have? 
+ Is the network directed or indirected? 
+ What vertex and edge attributes does the network have?
]

---

```r
data(karate)
karate
```

```
*## IGRAPH 4b458a1 UNW- 34 78 -- Zachary's karate club network
*## + attr: name (g/c), Citation (g/c), Author (g/c), Faction (v/n), name
*## | (v/c), label (v/c), color (v/n), weight (e/n)
## + edges from 4b458a1 (vertex names):
##  [1] Mr Hi  --Actor 2  Mr Hi  --Actor 3  Mr Hi  --Actor 4  Mr Hi  --Actor 5 
##  [5] Mr Hi  --Actor 6  Mr Hi  --Actor 7  Mr Hi  --Actor 8  Mr Hi  --Actor 9 
##  [9] Mr Hi  --Actor 11 Mr Hi  --Actor 12 Mr Hi  --Actor 13 Mr Hi  --Actor 14
## [13] Mr Hi  --Actor 18 Mr Hi  --Actor 20 Mr Hi  --Actor 22 Mr Hi  --Actor 32
## [17] Actor 2--Actor 3  Actor 2--Actor 4  Actor 2--Actor 8  Actor 2--Actor 14
## [21] Actor 2--Actor 18 Actor 2--Actor 20 Actor 2--Actor 22 Actor 2--Actor 31
## [25] Actor 3--Actor 4  Actor 3--Actor 8  Actor 3--Actor 9  Actor 3--Actor 10
## + ... omitted several edges
```

---
class: center, middle

# Closer inspection

---

# Your turn!

+ How many factions does the karate network have?
+ How many nodes belong to each faction?
]

---

# Network Visualization

---
# Basics

+ Via algorithms

+ Reduce the crossing of edges

+ Keep the edge length as constant as possible

---
# Plotting Parameters

**Nodes**

vertex.[parameter] (e.g., vertex.color =)

<table>
 <thead>
  <tr>
   <th style="text-align:left;"> node_parameter </th>
   <th style="text-align:left;"> purpose_options </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;"> color </td>
   <td style="text-align:left;"> node color </td>
  </tr>
  <tr>
   <td style="text-align:left;"> shape </td>
   <td style="text-align:left;"> circle, square, rectangle, sphere, pie, raster, etc. </td>
  </tr>
  <tr>
   <td style="text-align:left;"> size </td>
   <td style="text-align:left;"> default = 15 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> label </td>
   <td style="text-align:left;"> vector with labels </td>
  </tr>
  <tr>
   <td style="text-align:left;"> label family </td>
   <td style="text-align:left;"> font family of the label: Helvetica, Times </td>
  </tr>
  <tr>
   <td style="text-align:left;"> label font </td>
   <td style="text-align:left;"> 1= plain, 2= bold, 3= italic, 4 = bold italic </td>
  </tr>
  <tr>
   <td style="text-align:left;"> label cex </td>
   <td style="text-align:left;"> font size </td>
  </tr>
  <tr>
   <td style="text-align:left;"> label distance </td>
   <td style="text-align:left;"> distance between node and label </td>
  </tr>
  <tr>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;">  </td>
  </tr>
</tbody>
</table>

---
# Plotting Parameters

**Edges**

edge.[parameter] (e.g., edge.color =)

<table>
 <thead>
  <tr>
   <th style="text-align:left;"> edge_parameter </th>
   <th style="text-align:left;"> purpose_options </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;"> color </td>
   <td style="text-align:left;"> edge color </td>
  </tr>
  <tr>
   <td style="text-align:left;"> lty </td>
   <td style="text-align:left;"> type of line: 0='blank', 1= 'solid', 2= 'dashed', 3= 'dotted', 4 = 'dotdash', 5= 'longdash', 6= 'twodash' </td>
  </tr>
  <tr>
   <td style="text-align:left;"> width </td>
   <td style="text-align:left;"> default = 1 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> label </td>
   <td style="text-align:left;"> vector with labels </td>
  </tr>
  <tr>
   <td style="text-align:left;"> label family </td>
   <td style="text-align:left;"> font family of the label: Helvetica, Times </td>
  </tr>
  <tr>
   <td style="text-align:left;"> label font </td>
   <td style="text-align:left;"> 1= plain, 2= bold, 3= italic, 4 = bold italic </td>
  </tr>
  <tr>
   <td style="text-align:left;"> label cex </td>
   <td style="text-align:left;"> font size </td>
  </tr>
  <tr>
   <td style="text-align:left;"> curvature </td>
   <td style="text-align:left;"> edge curvature - range [0,1] </td>
  </tr>
  <tr>
   <td style="text-align:left;"> arrow size </td>
   <td style="text-align:left;"> default = 1 </td>
  </tr>
</tbody>
</table>

---
# Two Options

+ 1. Set vertex/edge attributes
+ 2. Plot the net

```r
# vertex properties 
*V(UKfaculty)$color <- "dodgerblue"

# vertex label properties
V(UKfaculty)$label.color <- "white"
V(UKfaculty)$label.cex <- 0.5

# edge properties
E(UKfaculty)$color <- "gray"

*plot(UKfaculty)
```

]

```r
*plot(UKfaculty,
     # === vertex properties 
*    vertex.color = "dodgerblue",
     vertex.frame.color = "dodgerblue",
     vertex.size = 9,
     # === vertex label properties
     vertex.label.cex = 0.5,
     vertex.label.color = "white",
     vertex.label.family = "Helvetica",
     # === edge properties
     edge.color = "gray",
     edge.width = 0.5,
     edge.arrow.size = 0.2)
```

]
---
#Which option to choose?

+ 1. Set vertex/edge attributes
+ 2. Plot the net

<br><br>_**Use for assigning local visual properties to different subsets**_

]

<br><br><br>_**Use for assigning global visual properties**_ 
]
--

---

# Let's try these!

---

# Your turn!

+ Use the parameter cheatsheet and color cheatsheet

Reach goal: color different subsets of vertices and edges in a different way using the selection tools we learned in the previous section.

]

---
class: center, middle

# Descriptive Network Statistics
---

# Descriptive Network Statistics

## Density

Proportion of actual edges out of possible edges.

--
## Reciprocity

Two types

+ Number of reciprocal edges over the total number of edges

+ Number of reciprocal edges over the number of dyads with only one, unreciprocated edge

# Descriptive Network Statistics

## Dyad Census

Dyads are pairs of vertices. In directed graphs they can be:

+ Null: no edge between the pair.

+ Asymmetric: one directed edge.

+ Mutual: two directed edges.

---
# Descriptive Network Statistics

## Transitivity

Also known as clustering coefficient

Fraction of transitive triplets

.pull-left[
**Transitive triplet**
<img src="Intro_Nets_slides_files/figure-html/unnamed-chunk-20-1.png" width="504" />
]

.pull-right[
**Intransitive triplet**
<img src="Intro_Nets_slides_files/figure-html/unnamed-chunk-21-1.png" width="504" />
]
---

# Descriptive Network Statistics

## Reachability - Average path length
.center[
<img src="Intro_Nets_slides_files/figure-html/unnamed-chunk-22-1.png" width="504" />
]
---
# Descriptive Network Statistics

### Diameter

Distance (number of steps) between farthest vertices

---
# Descriptive Network Statistics

### Connected components

.pull-left[
**Strongly connected**
<img src="Intro_Nets_slides_files/figure-html/unnamed-chunk-24-1.png" width="504" />
]
.pull-right[
**Weakly connected**
<img src="Intro_Nets_slides_files/figure-html/unnamed-chunk-25-1.png" width="504" />
]
---
# Descriptive Network Statistics

### Articulation points

Nodes that if removed would break the network into more components.

<img src="Intro_Nets_slides_files/figure-html/unnamed-chunk-26-1.png" width="504" />
---
class: inverse, center, middle

# Let's try these!

---
class: center, top

# Your turn!

<table>
 <thead>
  <tr>
   <th style="text-align:left;"> measures </th>
   <th style="text-align:left;"> functions </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;"> density </td>
   <td style="text-align:left;"> graph.density(net) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> reciprocity </td>
   <td style="text-align:left;"> reciprocity(net) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> dyad census </td>
   <td style="text-align:left;"> dyad_census(net) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> transitivity </td>
   <td style="text-align:left;"> transiticity(net) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> average path length </td>
   <td style="text-align:left;"> average.path.length(net) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> diameter </td>
   <td style="text-align:left;"> diameter(net) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> articulation points </td>
   <td style="text-align:left;"> articulation.points(net) </td>
  </tr>
</tbody>
</table>

.center[What can you say about this network?]
<div class="countdown" id="timer_5fa97d05" style="bottom:0;left:0;margin:1%;padding:5px;font-size:4em;" data-warnwhen="0">
<code class="countdown-time"><span class="countdown-digits minutes">05</span><span class="countdown-digits colon">:</span><span class="countdown-digits seconds">00</span></code>
</div>

---
class: center, middle

# Centrality

---
# Centrality

### Degree Centrality 
.pull-left[
**Indegree**
<img src="Intro_Nets_slides_files/figure-html/unnamed-chunk-29-1.png" width="504" />
]

.pull-right[
**Outdegree**
<img src="Intro_Nets_slides_files/figure-html/unnamed-chunk-30-1.png" width="504" />
]
---
# Centrality

### Closeness Centrality

+ Based on the distance to all other nodes.

+ Inverse of the node’s average geodesic distance to others in the network.

### Betweenness Centrality

+ Based on its brokerage position.

+ Number of shortest that pass through the node.

---
# Centrality 
.center[
<img src="Intro_Nets_slides_files/figure-html/unnamed-chunk-31-1.png" width="504" />
]

---
class: inverse, center, middle

# Let's try these!

---

# Your turn!

Calculate degree, closeness, and betweenness centrality for the karate network.

What are the most central nodes according to different measures?
]

---
class: center, middle

# Community Detection
---
# Community Detection

+ Different ways of doing this

+ Modularity: more intra-community edges than one would expect at random

+ Algorithms try to maximize modularity

+ Most of these procedures are done with undirected  & unweighted data

<br><br>.center[**Always check substantively**]

---
class: inverse, center, middle

# Let's try these!

---

# Your turn!

Conduct a community detection procedure for the karate data?

What are the communities you find?

Plot your results
]

<div class="countdown" id="timer_5fa97f77" style="right:0;bottom:0;left:0;margin:5%;padding:50px;font-size:6em;" data-warnwhen="0">
<code class="countdown-time"><span class="countdown-digits minutes">05</span><span class="countdown-digits colon">:</span><span class="countdown-digits seconds">00</span></code>
</div>
---
class: center, middle

# Where to go from here?
---
# Key Questions

## Networks as independent variables

Non-network outcome:

- Are people whose friends suffer from some disease more likely to have the disease themselves?

- Do central actors have access to more resources?

## Networks as dependent variables

Network outcome

- How structurally cohesive is a given network?

- What processes generate certain network structures?

---
# Mechanism of Action

## Connectionist

Networks as pipes

Outcome results from what flows in the network:

- Spread of a virus

- Sharing of information

## Positional

Outcome results from the positions & roles that nodes occupy:

- Popularity effects

- Network embeddedness

---
# More Resources

+ Kolaczyk, E. D., & Csárdi, G. (2014). Statistical analysis of network data with R (Vol. 65): Springer.

+ Luke, D. (2015). A User’s Guide to Network Analysis in R. Cham: Springer International Publishing : Imprint: Springer.

+ [Duke Network Analysis Center Tutorials](https://https://https://dnac.ssri.duke.edu/)

+ [Katya Ognyanova Tutorials](https://https://kateto.net/)
---
class: center, middle
# Thank you!

.center[<br><br><br>[mariacramos.com](https://https://mariacramos.com/)
<br><br>.large[@mariacramosf]
]