intro-sna.qmd

---
title: "Introduction to Network Analysis Methodologies and Tools"
author: "<b>Ryan Horne</b> <br/> UCLA OARC <br/> rmhorne@ucla.edu <br/>Twitter: @RyanMHorne"
format:
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  logo: images/CC_BY-SA_icon.svg
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---

## Overview {auto-animate="true" background-color="#005c96"}


![](images/presentation-code.svg){.absolute top="0" right="0" width="100" height="100"}

::: {.incremental}

-   Data practices
-   Discussion of network terms and concepts
    - Software deomnstration (Gephi, Cytoscape, and Python oh my!)
    - Python is live!
:::

## Basic Idea {auto-animate="true" background-color="#005c96"}


::: {.incremental}
-   Networks are a collection of entities
-   At least some are *linked*
-   All kinds of subject domains
-   Very flexible definition
:::

## What is SNA? {auto-animate="true" background-color="#005c96"}

::: {.incremental}

- Method to perform visual and mathematical analysis of relationships
- Analysis has to be visually interesting / useful and mathematically rigorous
- Fundamental point: We are looking at networks
-  Connections, connections, connections
-  Networks are all over the place

:::


## What is SNA Used For? {auto-animate="true" background-color="#005c96"}


::: {.incremental}


-   People
-   Concepts
-   Literature
-   Biological Systems
-   Electronic Systems

:::


##  {auto-animate="true" background-color="#005c96"}


![](images/comp-net.png)

##  {auto-animate="true" background-color="#005c96"}


![](images/facebook.png)

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![](images/thrones.png)

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::: columns
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![](images/counter-2.png)
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![](images/counter-1.png)
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## Basic Terms {auto-animate="true" background-color="#005c96"}

::: {data-id="box" style="background: #2780e3; padding: 10px;"}
Nodes
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<br/>

::: {data-id="box" style="background: #3fb618; padding: 10px;"}
Edges
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<br/>

::: {data-id="box" style="background: #e83e8c; padding: 10px;"}
Graph
:::

##  {auto-animate="true" background-color="#005c96"}

<h3>

::: {data-id="box" style="background: #2780e3; padding: 10px;"}
Nodes
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</h3>

::: {.incremental}

-   The "stuff" you are looking at
-   Any attributes you want!
-   Traditionally represented by circles on a graph
-   May see "actors" used

:::

##  {auto-animate="true" background-color="#005c96"}

<h3>

::: {data-id="box" style="background: #3fb618; padding: 10px;"}
Edges
:::

</h3>

::: {.incremental}


-   What links your *nodes*
    -   Sometimes called links
    -   Up to us to define what this means
-   Think of this workshop
-   Can have *weight*
-   Lines on a *graph*

:::

##  {auto-animate="true" background-color="#005c96"}

<h3>

::: {data-id="box" style="background: #e83e8c; padding: 10px;"}
Graph
:::

</h3>

::: columns
::: {.column width="50%"}
-   Mathematical models of network structures
-   There are rules!
:::

::: {.column width="50%"}
![](images/walter.png)
:::
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## Undirected Graph {auto-animate="true" background-color="#005c96"}

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::: {.column width="50%"}

::: {.incremental}

-   Direction of the relationship does not matter
-   No arrows are needed
-   “Default” for many SNA discussions

:::
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![](images/a-b.png)
:::
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##  {auto-animate="true" background-color="#005c96"}

![](images/thrones.png)

## Symmetrical and Asymmetrical Edges {auto-animate="true" background-color="#005c96"}

::: {.incremental}

-   Sometimes not enough to simply show a connection
-   A → B but not the other way around
-   Directed graph: Directed nodes and directed edges

:::

##  {auto-animate="true" background-color="#005c96"}

![](images/thrones-2.png)

## What About Data? {auto-animate="true" background-color="#005c96"}

![](images/data.png)

## Some Things to Consider {auto-animate="true" background-color="#005c96"}

::: {.incremental}

-   What is your data?
-   What are you trying to show?
-   How are you going to organize your data?
    -   Are there standards in your field?
-   In short: Think a lot about database design!

:::


## Data Tools: The Basics {auto-animate="true" background-color="#005c96"}


![](images/data-tools.png)

## Basics {auto-animate="true" background-color="#005c96"}

::: {.incremental}

- Most basic level: Spreadsheet with two columns
- Entries need to be in the same format AND have the same spellings, etc
- AT MOST two different *types* of entities
- More information is good!

:::

## Some Best Practices {auto-animate="true" background-color="#005c96"}


::: {.incremental}


-   Create a unique identifier
-   Each column contains the same category of data in every row in the column
-   Each row in the spreadsheet contains all of the fields of data for one entity
-   The first row of the spreadsheet must contain a unique name at the top of each column
-   No blank rows
-   Think about attributes!

:::


## More Best Practices {auto-animate="true" background-color="#005c96"}


::: {.incremental}

-   Do not be afraid to make multiple spreadsheets!
    -   These can translate into multiple tables in a database
-   Think about the minimum work needed to maintain and update your data
-   Document!

:::


## Modes vs Types {auto-animate="true" background-color="#005c96"}


::: {.incremental}

-   Modes tell you what is in the graph
    -   People, people and things, etc
-   Types tell you what kind of graph it is
    -   Are we looking at an individual? Group? Text?

:::


## One Mode / Unipartite Networks {auto-animate="true" background-color="#005c96"}

::: {.incremental}

-   Relationships among a single set of similar nodes
-   Same type of nodes
-   Same type of edges
    -   Some differentiation allowed; i.e. parent / child relationships

::: 

##  {auto-animate="true" background-color="#005c96"}

![](images/thrones.png)

## Two Mode / Multipartite Networks {auto-animate="true" background-color="#005c96"}

::: {.incremental}

-   Relations among two (or more!) different sets of nodes
    -   Can be two different sets of people
-   Also used between nodes of different conceptual type
    -   People vs. interests / events
    -   Important for the analysis of weak ties – we will get into this shortly

:::


##  {auto-animate="true" background-color="#005c96"}

![](images/bipartite.png)

## Making a Graph: Two Basic Ways {auto-animate="true" background-color="#005c96"}

::: {data-id="box" style="background: #2780e3; padding: 10px;"}
Edges Only
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<br/>

::: {data-id="box" style="background: #3fb618; padding: 10px;"}
Edges + Nodes
:::

<br/>


##  {auto-animate="true" background-color="#005c96"}

<h3>

::: {data-id="box" style="background: #2780e3; padding: 10px;"}
Edges Only
:::

</h3>

::: columns
::: {.column width="50%"}
Pros

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-   Quick and dirty
-   Can get network stats fast
-   Less data overhead to deal with
- Can specify connections

:::
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Cons

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-   No information about nodes
- Hard to filter / query
- Stuck with one data relationship

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##  {auto-animate="true" background-color="#005c96"}

<h3>

::: {data-id="box" style="background: #3fb618; padding: 10px;"}
Edges + Nodes
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</h3>

::: columns
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Pros

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-   Can include far more information
- Can specify connections
-   Data can be used elsewhere

:::
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::: {.column width="50%"}

Cons

::: {.incremental}


- More information overhead
- Separation of network data
- Longer process to make a network

:::
:::
:::


## First Networks {auto-animate="true" background-color="#005c96"}

Start with just edges in:
<br />
<br />

::: {data-id="box" style="background: #2780e3; padding: 10px;"}
Gephi
:::

<br/>

::: {data-id="box" style="background: #3fb618; padding: 10px;"}
Cytoscape
:::

<br/>

::: {data-id="box" style="background: #e83e8c; padding: 10px;"}
Python
:::

##  {auto-animate="true" background-color="#005c96"}

<h3>

::: {data-id="box" style="background: #2780e3; padding: 10px;"}
Gephi
:::

</h3>

![](images/gephi-intro.png)

##  {auto-animate="true" background-color="#005c96"}

<h3>

::: {data-id="box" style="background: #2780e3; padding: 10px;"}
Gephi
:::

</h3>

![](images/gephi-menu.png)

##  {auto-animate="true" background-color="#005c96"}

<h3>

::: {data-id="box" style="background: #2780e3; padding: 10px;"}
Gephi
:::

</h3>

![](images/gephi-select.png)

##  {auto-animate="true" background-color="#005c96"}

<h3>

::: {data-id="box" style="background: #2780e3; padding: 10px;"}
Gephi
:::

</h3>

![](images/gephi-settings.png)

##  {auto-animate="true" background-color="#005c96"}

<h3>

::: {data-id="box" style="background: #2780e3; padding: 10px;"}
Gephi
:::

</h3>

![](images/gephi-first-net.png)



## {auto-animate="true" background-color="#005c96"}

<h3>

::: {data-id="box" style="background: #3fb618; padding: 10px;"}
Cytoscape
:::

</h3>

![](images/get-your-edge-list-into-cytoscape.png)

## {auto-animate="true" background-color="#005c96"}

<h3>

::: {data-id="box" style="background: #3fb618; padding: 10px;"}
Cytoscape: Add Edges the Hard Way
:::

</h3>

Import Network from File button (circled below) and select your edge list.

![](images/if-you-don-t-see-that-welcome-screen.png)

## {auto-animate="true" background-color="#005c96"}

<h3>

::: {data-id="box" style="background: #3fb618; padding: 10px;"}
Cytoscape: What's What
:::

</h3>

::: {.incremental}


- We need to tell Cytoscape that the edge list we’ve provided contains *sources* in one column and *targets* in another.
- This is an *undirected graph*
    - Does order matter?
- Green and Red icons

:::

## {auto-animate="true" background-color="#005c96"}

<h3>

::: {data-id="box" style="background: #3fb618; padding: 10px;"}
Cytoscape: What's What
:::

</h3>

![](images/got-edge-import.png)

## {auto-animate="true" background-color="#005c96"}

<h3>

::: {data-id="box" style="background: #3fb618; padding: 10px;"}
Cytoscape Graph
:::

</h3>
![](images/cyto-got-edges.png)

## {auto-animate="true" background-color="#005c96" .smaller}

<h3>

::: {data-id="box" style="background: #e83e8c; padding: 10px;"}
Python
:::

</h3>

::: panel-tabset
### Python Code
```{python}
#| eval: false
#| echo: true
import networkx as nx
import csv
import pandas as pd
from community import community_louvain
import matplotlib.cm as cm
import matplotlib.pyplot as plt

# First, get the edge data
url = 'https://raw.githubusercontent.com/mathbeveridge/gameofthrones/master/data/got-s1-edges.csv'
dfedges = pd.read_csv(url)
dfedges
```
### Result  {.smaller} 
```{python}
import networkx as nx
import csv
import pandas as pd
from community import community_louvain
import matplotlib.cm as cm
import matplotlib.pyplot as plt

# First, get the edge data
url = 'https://raw.githubusercontent.com/mathbeveridge/gameofthrones/master/data/got-s1-edges.csv'
dfedges = pd.read_csv(url)
dfedges
```
:::


##  {auto-animate="true" background-color="#005c96" .smaller}

<h3>

::: {data-id="box" style="background: #e83e8c; padding: 10px;"}
Python Graphs
:::

</h3>

::: panel-tabset
### Python Code

```{python}
#| eval: false
#| echo: true

import networkx as nx
import csv
import pandas as pd
from community import community_louvain
import matplotlib.cm as cm
import matplotlib.pyplot as plt

# First, get the edge data
url = 'https://raw.githubusercontent.com/mathbeveridge/gameofthrones/master/data/got-s1-edges.csv'
dfedges = pd.read_csv(url)
# Dataset is now stored in a Pandas Dataframe

# Now we create the graph from the edge list. We need to specify the column names as they are in mixed case
G = nx.from_pandas_edgelist(dfedges, source="Source", target = "Target", edge_attr=True)
# Draw the graph!
pos = nx.spring_layout(G, k=1, iterations=20)
nx.draw(G, pos, with_labels=True)
```

### Result

```{python}
import networkx as nx
import csv
import pandas as pd
from community import community_louvain
import matplotlib.cm as cm
import matplotlib.pyplot as plt

# First, get the edge data
url = 'https://raw.githubusercontent.com/mathbeveridge/gameofthrones/master/data/got-s1-edges.csv'
dfedges = pd.read_csv(url)
# Dataset is now stored in a Pandas Dataframe

# Now we create the graph from the edge list. We need to specify the column names as they are in mixed case
G = nx.from_pandas_edgelist(dfedges, source="Source", target = "Target", edge_attr=True)
# Draw the graph!
pos = nx.spring_layout(G, k=1, iterations=20)
nx.draw(G, pos, with_labels=True)

```

:::

## Edges Only: Only Node Information {auto-animate="true" background-color="#005c96"}

- No information about nodes
- Our data set does not have much, but you will see how to add it


##  {auto-animate="true" background-color="#005c96"}

<h3>

::: {data-id="box" style="background: #2780e3; padding: 10px;"}
Gephi: Add Nodes
:::

</h3>


![](images/gephi-nodes-added.png)

##  {auto-animate="true" background-color="#005c96"}

<h3>

::: {data-id="box" style="background: #2780e3; padding: 10px;"}
Gephi: Node Settings
:::

</h3>


![](images/gephi-settings2.png)

##  {auto-animate="true" background-color="#005c96"}

<h3>

::: {data-id="box" style="background: #2780e3; padding: 10px;"}
Gephi: Node Information
:::

</h3>

![](images/gephi-first-lab.png)


## {auto-animate="true" background-color="#005c96"}

<h3>

::: {data-id="box" style="background: #3fb618; padding: 10px;"}
Cytoscape: Add Nodes
:::

</h3>


![](images/add-your-node-list-to-your-cytoscape-graph.png)

## {auto-animate="true" background-color="#005c96"}

<h3>

::: {data-id="box" style="background: #3fb618; padding: 10px;"}
Cytoscape: Node Settings
:::

</h3>

![](images/cyto-nodes-1.png)

## {auto-animate="true" background-color="#005c96"}

<h3>

::: {data-id="box" style="background: #3fb618; padding: 10px;"}
Cytoscape: Results
:::

</h3>

![](images/cyto-with-nodes.png)


## {auto-animate="true" background-color="#005c96" .smaller}

<h3>

::: {data-id="box" style="background: #e83e8c; padding: 10px;"}
Python: Nodes
:::

</h3>

::: panel-tabset
### Python Code

```{python}
#| eval: false
#| echo: true

import networkx as nx
import csv
import pandas as pd
from community import community_louvain
import matplotlib.cm as cm
import matplotlib.pyplot as plt

# First, get the edge data
url = 'https://raw.githubusercontent.com/mathbeveridge/gameofthrones/master/data/got-s1-edges.csv'
dfedges = pd.read_csv(url)

# Now get the node data
urlNode = 'https://raw.githubusercontent.com/mathbeveridge/gameofthrones/master/data/got-s1-nodes.csv'
dfnodes = pd.read_csv(urlNode)

# Dataset is now stored in a Pandas Dataframe

# Now we create the graph from the edge list. We need to specify the column names as they are in mixed case
G = nx.from_pandas_edgelist(dfedges, source="Source", target = "Target", edge_attr=True)
data = dfnodes.set_index('Id').to_dict('index').items()
G.add_nodes_from(data)

print(G.nodes(data=True))

```

### Result

```{python}
import networkx as nx
import csv
import pandas as pd
from community import community_louvain
import matplotlib.cm as cm
import matplotlib.pyplot as plt

# First, get the edge data
url = 'https://raw.githubusercontent.com/mathbeveridge/gameofthrones/master/data/got-s1-edges.csv'
dfedges = pd.read_csv(url)

# Now get the node data
urlNode = 'https://raw.githubusercontent.com/mathbeveridge/gameofthrones/master/data/got-s1-nodes.csv'
dfnodes = pd.read_csv(urlNode)

# Dataset is now stored in a Pandas Dataframe

# Now we create the graph from the edge list. We need to specify the column names as they are in mixed case
G = nx.from_pandas_edgelist(dfedges, source="Source", target = "Target", edge_attr=True)
data = dfnodes.set_index('Id').to_dict('index').items()
G.add_nodes_from(data)

print(G.nodes(data=True))


```

:::


## Why Not Just Combine the Lists Later? {auto-animate="true" background-color="#005c96"}

::: {.incremental}

- You *can*, but...
    - You can use node attributes for styling
    - You can use node attrbutes for filtering
    - Many other uses

:::


## Exploring our Graph: Paths {auto-animate="true" background-color="#005c96"}


::: {.incremental}


-   Movement in a graph via edges
-   Sequence of nodes connected via edges
-   *Simple path*: A path that does not repeat nodes

:::


## Connectivity {auto-animate="true" background-color="#005c96"}


::: {.incremental}


-   Path between every pair of nodes
-   Goal of most designed networks
-   NOT a necessary feature of graphs though!
-   There are social networks with disconnected features

:::


## Example – Anyone know what this is? {auto-animate="true" background-color="#005c96"}

![](images/darpanet.png)


## Graph Distance {auto-animate="true" background-color="#005c96"}

::: {.incremental}


-   Not geographic (mostly!)
-   Distance = length of the shortest path between two nodes
    -   Number of edges
    -   Sometimes we can simply look at this
    -   Other times...we need computers!

:::


##  {auto-animate="true" background-color="#005c96"}

<h3>

::: {data-id="box" style="background: #2780e3; padding: 10px;"}
Gephi: Path
:::

</h3>

![](images/gephi-path-final.png)


## {auto-animate="true" background-color="#005c96"}

<h3>

::: {data-id="box" style="background: #3fb618; padding: 10px;"}
Cytoscape: Paths
:::


</h3>

![](images/cyto-path.png)

## {auto-animate="true" background-color="#005c96"}

<h3>

::: {data-id="box" style="background: #3fb618; padding: 10px;"}
Cytoscape: Paths
:::

</h3>

I....can't get these to work right. 
<br />
<br />
There is javascript code though!


## {auto-animate="true" background-color="#005c96" .smaller}

<h3>

::: {data-id="box" style="background: #e83e8c; padding: 10px;"}
Python: Graph Distance
:::

</h3>

::: panel-tabset
### Python Code {data-background="#005c96"}

```         
path = dict(nx.all_pairs_shortest_path(G))
path
```

### Result {data-background="#005c96"}

```{python}
path = dict(nx.all_pairs_shortest_path(G))
path

```
:::

## {auto-animate="true" background-color="#005c96" .smaller}

<h3>

::: {data-id="box" style="background: #e83e8c; padding: 10px;"}
Python: Paths
:::

</h3>

::: panel-tabset
### Python Code

```{python}
#| eval: false
#| echo: true

import networkx as nx
import csv
import pandas as pd
from community import community_louvain
import matplotlib.cm as cm
import matplotlib.pyplot as plt

# First, get the edge data
url = 'https://raw.githubusercontent.com/mathbeveridge/gameofthrones/master/data/got-s1-edges.csv'
dfedges = pd.read_csv(url)
# Dataset is now stored in a Pandas Dataframe

# Now we create the graph from the edge list. We need to specify the column names as they are in mixed case
G = nx.from_pandas_edgelist(dfedges, source="Source", target = "Target", edge_attr=True)
# Draw the graph!
pos = nx.spring_layout(G, k=4, iterations=20)
nx.draw(G, pos, with_labels=True, node_size=5, font_size=5, width=.2)
# draw path in red
path = nx.shortest_path(G,source='HUGH_OF_THE_VALE',target='MIRRI_MAZ_DUUR')
path_edges = list(zip(path,path[1:]))
nx.draw_networkx_nodes(G,pos,nodelist=path,node_color='r')
nx.draw_networkx_edges(G,pos,edgelist=path_edges,edge_color='r',width=10)
plt.axis('equal')
plt.show()
```

### Result

```{python}
import networkx as nx
import csv
import pandas as pd
from community import community_louvain
import matplotlib.cm as cm
import matplotlib.pyplot as plt

# First, get the edge data
url = 'https://raw.githubusercontent.com/mathbeveridge/gameofthrones/master/data/got-s1-edges.csv'
dfedges = pd.read_csv(url)
# Dataset is now stored in a Pandas Dataframe

# Now we create the graph from the edge list. We need to specify the column names as they are in mixed case
G = nx.from_pandas_edgelist(dfedges, source="Source", target = "Target", edge_attr=True)
# Draw the graph!
pos = nx.spring_layout(G, k=4, iterations=20)
nx.draw(G, pos, with_labels=True, node_size=5, font_size=5, width=.2)
# draw path in red
path = nx.shortest_path(G,source='HUGH_OF_THE_VALE',target='MIRRI_MAZ_DUUR')
path_edges = list(zip(path,path[1:]))
nx.draw_networkx_nodes(G,pos,nodelist=path,node_color='r')
nx.draw_networkx_edges(G,pos,edgelist=path_edges,edge_color='r',width=10)
plt.axis('equal')
plt.show()
```

:::

## Small-world phenomenon {auto-animate="true" background-color="#005c96"}


::: columns
::: {.column width="50%"}

::: {.incremental}


-   Shorter path then you would think to get from one node to another
-   Origin of the term “six degrees of separation”
-   Practical terms: Who has a friend from another country?

:::
:::

::: {.column width="50%"}
![](images/kevin.png)
:::
:::


## Components {auto-animate="true" background-color="#005c96"}


::: {.incremental}

-   Natural breaks for connected portions of a graph
-   Connected component of a graph
    -   Every node in the subset has a path to each other

::: 

## Giant Component {auto-animate="true" background-color="#005c96"}


::: columns
::: {.column width="50%"}
Informal definition: Connected component that contains a significant fraction of all the nodes

-   Return to Game of Thrones: People who want Joffrey dead. Not **everybody**, but close!
-   Most networks only have one giant component
:::

::: {.column width="50%"}
![](images/joff.png)
:::
:::

## {auto-animate="true" background-color="#005c96" .smaller}

<h3>

::: {data-id="box" style="background: #e83e8c; padding: 10px;"}
Python: Giant Component
:::

</h3>

::: panel-tabset
### Python Code {data-background="#005c96"}

```{python}
#| eval: false
#| echo: true         
# Draw the graph!
pos = nx.spring_layout(G, k=1, iterations=20)
Gcc = sorted(nx.connected_components(G), key=len, reverse=True)
G0 = G.subgraph(Gcc[0])
nx.draw(G0, pos, with_labels=True)
```

### Result {data-background="#005c96"}

```{python}
# Draw the graph!
pos = nx.spring_layout(G, k=1, iterations=20)
Gcc = sorted(nx.connected_components(G), key=len, reverse=True)
G0 = G.subgraph(Gcc[0])
nx.draw(G0, pos, with_labels=True)

```
:::

## Merger of Giant Components {auto-animate="true" background-color="#005c96"}

::: {.incremental}


-   Only one connection merges giant components into one
    -   In history: Sudden, often catastrophic change
    -   Think of 1492 C.E.
        -   Disease
        -   Political change
        -   Previous contacts were not sustained
-   Issue of time

:::


## Beyond Visualization {auto-animate="true" background-color="#005c96"}


::: {.incremental}


-   You know about *nodes*, *edges*, *paths*, *distance*, *components*, *directed* and *undirected* graphs
-   Time to move on from description of graphs to some operations
-   These are some of the most common measurements

::: 

## Network Density {auto-animate="true" background-color="#005c96"}


::: {.incremental}


-   Number of actual edges divided by total number of possible edges
    -   Actual vs. potential connections
-   One of the most basic measurements in SNA
-   Especially interesting in epidemiology
    -   Or any analysis of how something spreads in a network

:::


##  {auto-animate="true" background-color="#005c96"}

<h3>

::: {data-id="box" style="background: #2780e3; padding: 10px;"}
Gephi: Network Statistics
:::

</h3>

![](images/gephi-run.png)

##  {auto-animate="true" background-color="#005c96"}

<h3>

::: {data-id="box" style="background: #2780e3; padding: 10px;"}
Gephi: Graph Density
:::

</h3>

![](images/graph-density1.png)

##  {auto-animate="true" background-color="#005c96"}

<h3>

::: {data-id="box" style="background: #2780e3; padding: 10px;"}
Gephi: Graph Density
:::

</h3>

![](images/graph-density2.png)

## {auto-animate="true" background-color="#005c96"}

<h3>

::: {data-id="box" style="background: #3fb618; padding: 10px;"}
Cytoscape: Tools
:::

</h3>

![](images/cytoscape-tools.png)

## {auto-animate="true" background-color="#005c96"}

<h3>

::: {data-id="box" style="background: #3fb618; padding: 10px;"}
Cytoscape: Density
:::

</h3>

![](images/cyto-density.png)




## {auto-animate="true" background-color="#005c96" .smaller}

<h3>

::: {data-id="box" style="background: #e83e8c; padding: 10px;"}
Python: Network Density
:::

</h3>

::: panel-tabset
### Python Code {data-background="#005c96"}

```         
nx.density(G)
```

### Result {data-background="#005c96"}

```{python}
nx.density(G)

```
:::

## Degree Measurements {auto-animate="true" background-color="#005c96"}


::: {.incremental}

-   Sum of all other nodes with a direct *path* to a node
-   Signifies activity or popularity
-   Very good for looking at nodes in a local context
-   In, Out
    -   Weighted and unweighted
- In Gephi and Cytoscape we already ran these
    - I will point them out then move on to python

:::



## {auto-animate="true" background-color="#005c96" .smaller}

<h3>

::: {data-id="box" style="background: #e83e8c; padding: 10px;"}
Python: Degree Measurements
:::

</h3>

::: panel-tabset
### Python Code {data-background="#005c96"}

```         
G.degree
```

### Result {data-background="#005c96"}

```{python}
G.degree

```
:::

## Size by Degree {auto-animate="true" background-color="#005c96"}

- Now we will visualize this on our graph
- Same techniques can be used for all other measurements / attributes

##  {auto-animate="true" background-color="#005c96"}

<h3>

::: {data-id="box" style="background: #2780e3; padding: 10px;"}
Gephi: Size by Degree
:::

</h3> 
![](images/gephi-size1.png)


##  {auto-animate="true" background-color="#005c96"}

<h3>

::: {data-id="box" style="background: #2780e3; padding: 10px;"}
Gephi: Size by Degree
:::

</h3> 
![](images/gephi-size2.png)

##  {auto-animate="true" background-color="#005c96"}

<h3>

::: {data-id="box" style="background: #2780e3; padding: 10px;"}
Gephi: Size by Degree
:::

</h3> 
![](images/gephi-size3.png)

## {auto-animate="true" background-color="#005c96"}

<h3>

::: {data-id="box" style="background: #3fb618; padding: 10px;"}
Cytoscape: Size by Degree
:::

</h3>

![](images/cyto-vis1.png)


## {auto-animate="true" background-color="#005c96"}


<h3>

::: {data-id="box" style="background: #3fb618; padding: 10px;"}
Cytoscape: Size by Degree
:::

</h3>

![](images/cyto-map-1.png)


## {auto-animate="true" background-color="#005c96" .smaller}

<h3>

::: {data-id="box" style="background: #e83e8c; padding: 10px;"}
Python: Degree graph
:::

</h3>

::: panel-tabset
### Python Code {data-background="#005c96"}

```{python}
#| eval: false
#| echo: true

d = dict(G.degree)

nx.draw(G, nodelist=d.keys(), node_size=[v * 10 for v in d.values()])
plt.show()

```

### Result {data-background="#005c96"}

```{python}
d = dict(G.degree)

nx.draw(G, nodelist=d.keys(), node_size=[v * 10 for v in d.values()])
plt.show()

```
:::

## Centrality {auto-animate="true" background-color="#005c96"}


::: {.incremental}

-   ***VERY*** important concept!
-   What many people want to see in networks: the most prominent nodes
-   These are often the “key” players in a network
-   Idea of social power
    -   Assertion: Power is inherently relational

:::


## Betweeness Centrality {auto-animate="true" background-color="#005c96"}


::: {.incremental}

-   Measures how often a node appears on shortest paths between nodes in the network
-   Often better to change visualization to identify them
-   A node with a high measure here could be important...or at the periphery of multiple networks

:::


## {auto-animate="true" background-color="#005c96" .smaller}

<h3>

::: {data-id="box" style="background: #e83e8c; padding: 10px;"}
Python: Betweeness Centrality
:::

</h3>

::: panel-tabset
### Python Code {data-background="#005c96"}

```{python}
#| eval: false
#| echo: true         
nx.betweenness_centrality(G)
```

### Result {data-background="#005c96"}

```{python}
nx.betweenness_centrality(G)

```
:::

## Closeness Centrality {auto-animate="true" background-color="#005c96"}


-   A sum of the shortest path between all nodes from a node
-   Useful to find out who spreads information quickly; might not be useful in a highly connected network


## {auto-animate="true" background-color="#005c96" .smaller}

<h3>

::: {data-id="box" style="background: #e83e8c; padding: 10px;"}
Python: Closeness Centrality
:::

</h3>

::: panel-tabset

### Python Code {auto-animate="true" background-color="#005c96"}


```         
nx.closeness_centrality(G)
```

### Result {data-background="#005c96"}

```{python}
nx.closeness_centrality(G)
```
:::

## Eigenvector Centrality {.smaller auto-animate="true" background-color="#005c96"}

::: {.incremental}

-   Basic idea: A node is important if it is linked to by other important nodes
    - I have almost no friends - but my friends are
        - The President
        - The Pope
        - Santa Claus
        - *Insert influencer / Reality TV star here*

-   Global vs. local importance
-   Mathematical modeling of this stretches back to the 1940s
    -   Software does this for us!

:::

## {auto-animate="true" background-color="#005c96" .smaller}

<h3>

::: {data-id="box" style="background: #e83e8c; padding: 10px;"}
Python: Eigenvector Centrality
:::

</h3>


::: panel-tabset
### Python Code {data-background="#005c96"}

```         
nx.eigenvector_centrality(G)
```

### Result {data-background="#005c96"}

```{python}
nx.eigenvector_centrality(G)
```
:::

## Page Rank {auto-animate="true" background-color="#005c96"}

-   Similar to Eigenvector, but takes into account the direction and weight of connections
-   Famously used by Google

## {auto-animate="true" background-color="#005c96" .smaller}

<h3>

::: {data-id="box" style="background: #e83e8c; padding: 10px;"}
Python: Page Rank
:::

</h3>

::: panel-tabset
### Python Code {data-background="#005c96"}

```         
nx.pagerank(G)
```

### Result {data-background="#005c96"}

```{python}
nx.pagerank (G)
```
:::

## Bridges {auto-animate="true" background-color="#005c96"}

::: {.incremental}

-   Edge joining two nodes is a bridge if deleting that edge would cause the nodes to be in two different components of the graph
    -   Very rare in social networks – think of the small world principle
-   Local bridge if the endpoints have no friends in common
    -   There can still be a path between the nodes if the bridge is deleted
-   Best statistical approximation: Betweenness Centrality

:::

## Bridges {auto-animate="true" background-color="#005c96"}

::: panel-tabset

### Python Code {data-background="#005c96"}

```         
nx.has_bridges(G)
```

### Result {data-background="#005c96"}

```{python}
nx.has_bridges(G)
```
:::

## {auto-animate="true" background-color="#005c96" .smaller}

<h3>

::: {data-id="box" style="background: #e83e8c; padding: 10px;"}
Python: Bridges
:::

</h3>


::: panel-tabset
### Python Code {data-background="#005c96"}

```         
list(nx.bridges(G))
```

### Result {data-background="#005c96"}

```{python}
list(nx.bridges(G))
```
:::

## {auto-animate="true" background-color="#005c96" .smaller}

<h3>

::: {data-id="box" style="background: #e83e8c; padding: 10px;"}
Python: Highlight Bridges
:::

</h3>

::: panel-tabset
### Python Code

```{python}
#| eval: false
#| echo: true

# Identify the bridges
bridges = list(nx.bridges(G))

# Set positions for nodes using a layout algorithm
pos = nx.spring_layout(G, k=.01, iterations=20)

# Draw entire network
nx.draw(G, pos, with_labels=False, node_size=5, width=.2)

# Draw bridges in red
for bridge in bridges:
    nx.draw_networkx_edges(G, pos, edgelist=[bridge], edge_color='red', width=2)
    nx.draw_networkx_nodes(G, pos, nodelist=bridge, node_color='red', node_size=700)

# Create a dictionary of labels for nodes involved in bridges
bridge_labels = {node: node for bridge in bridges for node in bridge}

# Draw labels for nodes involved in bridges
nx.draw_networkx_labels(G, pos, labels=bridge_labels, font_size=8, font_weight='bold')

plt.show()
```

### Result

```{python}

# Identify the bridges
bridges = list(nx.bridges(G))

# Set positions for nodes using a layout algorithm
pos = nx.spring_layout(G, k=.01, iterations=20)

# Draw entire network
nx.draw(G, pos, with_labels=False, node_size=5, width=.2)

# Draw bridges in red
for bridge in bridges:
    nx.draw_networkx_edges(G, pos, edgelist=[bridge], edge_color='red', width=2)
    nx.draw_networkx_nodes(G, pos, nodelist=bridge, node_color='red', node_size=700)

# Create a dictionary of labels for nodes involved in bridges
bridge_labels = {node: node for bridge in bridges for node in bridge}

# Draw labels for nodes involved in bridges
nx.draw_networkx_labels(G, pos, labels=bridge_labels, font_size=8, font_weight='bold')

plt.show()


```

:::


## Connection Strength {auto-animate="true" background-color="#005c96"}

::: {.incremental}


-   No real formal, strict definition
-   Stronger links represent closer friendship / greater degrees of interaction
-   Largely up to you!

:::

## Strong Ties and Weak Ties {auto-animate="true" background-color="#005c96"}

-   Strong ties = close friendship, etc
-   Weak ties = acquaintances, etc

## Network Evolution: Triadic Closure {auto-animate="true" background-color="#005c96"}

::: {.incremental}

-   Concept: If two people in a social network have a friend in common, then there is an increased likelihood that they will become friends themselves at some point in the future
-   Example: If Jaime and Pod are friends, and Jaime and Brienne of Tarth are friends, then it is likely that Brienne and Pod will become friends

:::


## Triadic Closure {auto-animate="true" background-color="#005c96"}

::: {.incremental}

-   This forms a triangle in the graph
-   Generally form in social networks given enough time
-   Think facebook friends feature
-   Basic functionality of a social network

:::


##  {auto-animate="true" background-color="#005c96"}

![](images/tri1.png)

##  {auto-animate="true" background-color="#005c96"}


![](images/tri2.png)


## {auto-animate="true" background-color="#005c96" .smaller}

<h3>

::: {data-id="box" style="background: #e83e8c; padding: 10px;"}
Python: Find All Potential Triads
:::

</h3>

::: panel-tabset
### Python Code

```{python}
#| eval: false
#| echo: true

plt.savefig('graph1.png') 

```

### Result

```{python}

plt.savefig('graph1.png') 


```

:::


## Position at Structural Holes {auto-animate="true" background-color="#005c96"}


::: {.incremental}

-   Structural hole
    -   Empty space between sets of nodes that do not otherwise interact closely
-   Position is advantageous
    -   Access to information that other components might not have
    -   Energy in reaching out to different groups rather than the same one

:::

## Other Issues {auto-animate="true" background-color="#005c96"}


::: {.incremental}

-   Synthesis from multiple ideas
-   Social gatekeeping
    -   A source of power as the position regulates communications
    -   Some people might try to keep triangles from forming!
-   Interests of a node and an organization may not be aligned
    -   Connection may not be in the node's best interests
    -   Unknown amount of time before triadic closure happens

:::

## Community Detection {auto-animate="true" background-color="#005c96"}

::: {.incremental}

-   The number of connections between nodes is more dense in a certain grouping than outside it
-   In Gephi, this is the modularity measurement
-   GOOD IDEA / common practice to make this the color of your nodes!

:::


## {auto-animate="true" background-color="#005c96" .smaller}

<h3>

::: {data-id="box" style="background: #e83e8c; padding: 10px;"}
Python: Community Detection
:::

</h3>

::: panel-tabset
### Python Code {data-background="#005c96"}

```         
partition = community_louvain.best_partition(G)
print(partition)
```

### Result {data-background="#005c96"}

```{python}
partition = community_louvain.best_partition(G)
print(partition)
```
:::

## {auto-animate="true" background-color="#005c96" .smaller}

<h3>

::: {data-id="box" style="background: #e83e8c; padding: 10px;"}
Python: Community Detection
:::

</h3>

::: panel-tabset
### Python Code {data-background="#005c96"}

```         
partition = community_louvain.best_partition(G)
pos = nx.spring_layout(G)
# color the nodes according to their partition
cmap = cm.get_cmap('viridis', max(partition.values()) + 1)
nx.draw_networkx_nodes(G, pos, partition.keys(), node_size=40,
                       cmap=cmap, node_color=list(partition.values()))
nx.draw_networkx_edges(G, pos, alpha=0.5)
plt.show()
```

### Result {data-background="#005c96"}

```{python}
partition = community_louvain.best_partition(G)
pos = nx.spring_layout(G)
# color the nodes according to their partition
cmap = cm.get_cmap('viridis', max(partition.values()) + 1)
nx.draw_networkx_nodes(G, pos, partition.keys(), node_size=40,
                       cmap=cmap, node_color=list(partition.values()))
nx.draw_networkx_edges(G, pos, alpha=0.5)
plt.show()
```
:::

## Export Graphs {auto-animate="true" background-color="#005c96"}

- We have a graph....now what?
- Play around with different visulizations
- Export as an image

##  {auto-animate="true" background-color="#005c96"}

<h3>

::: {data-id="box" style="background: #2780e3; padding: 10px;"}
Gephi: Export
:::

</h3>

![](images/gephi-preview.png)

## {auto-animate="true" background-color="#005c96"}

<h3>

::: {data-id="box" style="background: #3fb618; padding: 10px;"}
Cytoscape: Export
:::

</h3>

![](images/cyto-ex-1.png)

## {auto-animate="true" background-color="#005c96"}

<h3>

::: {data-id="box" style="background: #3fb618; padding: 10px;"}
Cytoscape: Export
:::

</h3>

![](images/cyto-ex-2.png)

## {auto-animate="true" background-color="#005c96" .smaller}

<h3>

::: {data-id="box" style="background: #e83e8c; padding: 10px;"}
Python: Export
:::

</h3>

::: panel-tabset
### Python Code

```{python}
#| eval: false
#| echo: true

partition = community_louvain.best_partition(G)
pos = nx.spring_layout(G)
# color the nodes according to their partition
cmap = cm.get_cmap('viridis', max(partition.values()) + 1)
nx.draw_networkx_nodes(G, pos, partition.keys(), node_size=40,
                       cmap=cmap, node_color=list(partition.values()))
nx.draw_networkx_edges(G, pos, alpha=0.5)
plt.savefig('graph1.png') 

```

### Result

```{python}

partition = community_louvain.best_partition(G)
pos = nx.spring_layout(G)
# color the nodes according to their partition
cmap = cm.get_cmap('viridis', max(partition.values()) + 1)
nx.draw_networkx_nodes(G, pos, partition.keys(), node_size=40,
                       cmap=cmap, node_color=list(partition.values()))
nx.draw_networkx_edges(G, pos, alpha=0.5)
plt.savefig('graph1.png') 

```

:::

## {auto-animate="true" background-color="#005c96" .smaller}

<h3>

::: {data-id="box" style="background: #e83e8c; padding: 10px;"}
Python: Export
:::

</h3>

![](graph1.png)

## Thank You! {auto-animate="true" background-color="#005c96"}
<br />
<br />
Any Questions?