Introduction to SNA: Concepts and Data

Kevin Reuning

Who am I

  • I’m Kevin Reuning (ROY-ning).
  • I’m an Assistant Professor in Political Science.
  • Prior to grad school I had very little experience in coding.

Goals For this Bootcamp

  • Understand basic SNA terminology
  • Load a variety of SNA formats into R.
  • Calculate some basic network and nodal statistics.
  • Make network visualizations.
  • Know where to look for more.

Where We Are Going

Goals for Today

  • Go over some basic language of social network analysis.
  • Load some SNA data into R.
  • Start manipulating that

Social Network Concepts

Nodes/Vertices and Edges

SNA focuses on the relationships between different entities:

  • Nodes or Vertices: The entities that make-up your network.
    • Ex: individuals, animals, organizations, counties, …
  • Edges: The relationships that make-up your network.
    • Ex: Friendship, proximity, exchange of goods, …

Edges - Variation and Types

Edges comes in many flavors and can be divided between states and events.

  • States: The relationship is on-going (not forever necessarily but it exists overtime)
    • Types: Similarities, Roles, Cognition
  • Events: The relationship is captured by some discrete moment in time.
    • Types: Interactions and Flows.

How Events relate to States

Often we use events to identify a state:

  • Two students that are often seen together are likely to be friends.
  • Two students that text often are likely to be friends.

We also can think that events lead to a state:

  • Interacting with someone might lead to a friendship.

Edge Differences and Attributes

  • Edges can be directed or undirected:
    • Directed: Point from node A to node B.
    • Undirected: Are between node A and node B.
  • Edges can also be weighted. Examples:
    • The amount of trade flowing from country A to country B.
    • How long two individuals have known each other.
    • The valence of a feelings towards another node (negative to positive)

Adjacency Matrix

Networks can be written out as adjacency matrix:

\[ \mathbf{A} = \left[\begin{array} {rrr} 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 \\ 1 & 1 & 0 & 1 \\ 1 & 0 & 1 & 0 \\ \end{array}\right] \]

Adjacency matrices are written in row-to-column format. Undirected networks will always have a symmetric matrix

Edge Lists

The other common way to make write out a network is through an edge list format:

from to
a c
c a
c b
c d
d a
d c

R and SNA

There are two major sets of R libraries used for networking:

  • igraph: A lot of more basic analysis options, also has python and and C versions as well. Overall easier to manipulate your network objects.
  • statnet: Has access to more advanced analysis, but a lot of it is divided up into additional libraries.

Following along

You need to learn by doing. If you haven’t opened RStudio yet, do so now.

Network Data Formats

There are a variety of ways that networks are saved/shared:

  • As a csv:
    • Adjacency matrix or an edge list
    • Sometimes additional data is provided in a secondary csv
  • Graphml: Relatively common open format that is easily editable.
  • GML: Common open format that is less easy to edit (in my opinion)
  • Pajek: Weird old format that is not well documented but still appears

igraph Object

In each case we need to load in data and turn it into an igraph object.

As an igraph object we can easily apply a lot of network methods do it, plot it, etc.

Loading Network from an Adjacency Matrix

Start with a network of cocaine smugglers. Download the csv here, more info here

Need to do the following:

  1. Load the csv into R, treating the row names appropriately read.csv()
    • Set row.names=1 so that the first column is read in as row names.
  2. Convert it to a matrix as.matrix()
  3. Convert it to an igraph object graph_from_adjacency_matrix()
library(igraph)
mat <- read.csv("data/COCAINE_JAKE.csv", row.names=1)
mat <- as.matrix(mat)
net <- graph_from_adjacency_matrix(mat, mode="directed", 
                                   weighted=T)

graph_from_adjacency_matrix()

There are some options we can set:

  • mode=
    • "directed" directed network
    • "undirected" undirected, using upper triangle to make
  • weighted=
    • NULL (default) the numbers in matrix give the number of edges between.
    • TRUE creates edge weights.
    • NA creates edges if they are greater than 0, ignore the rest.
  • diag= where to include the diagonal, set to FALSE to ignore diagonals.
  • add.colnames=
    • NULL (default) use column names as the vertex names.
    • NA ignore the column names.

igraph Object

Calling the igraph object by itself provides some details about the network, including some example edges:

net 
IGRAPH ab1b6e0 DNW- 38 68 -- 
+ attr: name (v/c), weight (e/n)
+ edges from ab1b6e0 (vertex names):
 [1] ABFM ->AFM  ABFM ->FLMC ABFM ->JES  ABFM ->JHY  ABFM ->MCM  ABFM ->RBM 
 [7] ABFM ->VFH  AFM  ->JES  AIGC ->FFM  AIGC ->JES  CAR  ->FFM  DEJV ->CAR 
[13] DMN  ->ABFM FAERH->RBM  FFM  ->CAR  FFM  ->H5   FFM  ->JES  FFM  ->M2  
[19] FFM  ->MRQ  FFM  ->RJJ  FLMC ->ABFM FLMC ->DEJV FLMC ->EYVT FLMC ->H1  
[25] FLMC ->H2   FLMC ->H3   FLMC ->H9   FLMC ->JAGG FLMC ->JES  FLMC ->JFM 
[31] FLMC ->ROB  H10  ->FFM  H11  ->ABFM H6   ->JES  H7   ->JES  H8   ->JES 
[37] JAGG ->FLMC JES  ->ABFM JES  ->AFM  JES  ->AIGC JES  ->CHA  JES  ->FFM 
[43] JES  ->FLMC JES  ->JFM  JES  ->M3   JES  ->RBM  JFM  ->ABFM JFM  ->AFM 
+ ... omitted several edges

Basic Functions

vcount(net) # Number of vertices/nodes
[1] 38
ecount(net) # Number of edges 
[1] 68

Basic Plot

We will make better plots later, but this gives us a quick idea of what our network looks like

plot(net)

Network Components

Dividing Up a Network

  • We can group vertices by who they can reach:
    • A component is the maximal (largest) group of vertices where every vertex within it can reach every other vertex.
    • Every network can be broken into 1 or more component(s).
  • A vertex that cannot reach any other vertices is an isolate

Some Components

This network has 6 components, the largest has 10 vertices in it.

Components with Directed Graphs

When a network is directed, then we need to think about direction.

  • Weak Component: Is a component if we disregard direction of edges.
  • Strong Component: Is a component if we follow direction of edges

Strong/Weak Components:

Broken into Weak Components

Broken into Strong Components

Calculating Components

comps <- components(net, mode="strong")
comps$no ## Number of components
[1] 22
comps$csize ## Size of each component
 [1]  1  1  1  1  1  1  1  1  1 17  1  1  1  1  1  1  1  1  1  1  1  1
comps$membership ## Membership for each node
 ABFM   AFM  AIGC   AMG   CAR   CHA  DEJV   DMN  EYVT FAERH   FFM  FLMC    H1 
   10    10    10    13    10    19    10     9    18    10    10    10    17 
  H10   H11    H2    H3    H5    H6    H7    H8    H9  JAGG   JES   JFM   JHY 
    8     7    16    15    22     6     5     4    14    10    10    10    10 
 JMBM    M1    M2    M3   MCM   MRQ    PR   PRS   RBM   RJJ   ROB   VFH 
   12     3    21    10    10    10     2     1    10    20    10    11

Loading Network from an Edge List

Process

Now we are going to use a network of political donors in Ohio. Download the edgelist data here and the nodal data here. More info is here.

Need to do the following:

  1. Load the edge list and nodal data into R as two different objects read.csv()
  2. Combine them into an igraph object graph_from_data_frame()
edge_df <- read.csv("data/edge_OH.csv")
node_df <- read.csv("data/meta_OH.csv")
net <- graph_from_data_frame(edge_df, vertices=node_df, directed=F)

graph_from_data_frame

There are some options we can set:

  • directed=
    • Directed or not? TRUE or FALSE
  • vertices=
    • Adding data to the vertices. The first column needs to match the identifiers used in the ede list.

Warning

You can only directly include isolates in edge lists if you have a vertex data frame.

igraph Object for Ohio Network

net
IGRAPH 6ae6587 UN-- 336 14183 -- 
+ attr: name (v/c), ContributorName (v/c), CatCodeIndustry (v/c),
| CatCodeGroup (v/c), CatCodeBusiness (v/c), PerDem (v/n), PerRep
| (v/n), DemCol (v/c), RepCol (v/c), Total (v/n), edge (e/c)
+ edges from 6ae6587 (vertex names):
 [1] 10041   --1039     1025    --1039     10041   --1055     1025    --1055    
 [5] 1039    --1055     10041   --10680063 1055    --10688628 10680063--10701104
 [9] 1025    --10770383 1039    --10770383 1025    --10812576 1039    --10812576
[13] 10770383--10812576 10041   --10986    1025    --10986    1039    --10986   
[17] 1055    --10986    10680063--10986    10041   --1116     1039    --1116    
[21] 1055    --1116     10680063--1116     10688628--1116     10986   --1116    
+ ... omitted several edges

Vertex and Edge Attributes

Accessing Them

You can access vertex and edges in your Igraph object using V() or E(). This is useful to access attributes using $variable

V(net)$variable_1 ## Accesses the `variable_1` vertex attribute
E(net)$variable_1 ## Accesses the `variable_1` edge attribute

Example

There is a Total vertex attribute which is the total amount donated:

V(net)$Total[1:10] ## Access the first 10 
 [1] 25000.00 10500.00 26500.00  4350.00  8433.31 11200.00  1500.00  3000.00
 [9]  1050.00  2250.00

Deleting Vertices

This can be helpful in deleting vertices with the delete_vertices() function. Lets remove all vertices where they donated less than $2,000:

verts_delete <- V(net)[V(net)$Total < 2000]
sub_net <- delete_vertices(net, verts_delete)
vcount(sub_net)
[1] 261

Deleting Edges

We can do the same thing with edges, lets keep just the edges that are marked "Strong" in the edge edge attribute:

components(net)$no ## Everything in 1 component
[1] 1
edges_delete <- E(net)[ E(net)$edge!= "Strong"]
trimmed_net <- delete_edges(net, edges_delete)
components(trimmed_net)$no ## New network is more split apart
[1] 7

Adding Attributes

We can also add an attribute to the network. Here we add vertex attribute that indicates what component everyone is in:

comps <- components(trimmed_net)
V(trimmed_net)$Comp <- LETTERS[comps$membership]
V(trimmed_net)$Comp[1:10]
 [1] "A" "A" "A" "A" "A" "A" "A" "A" "A" "A"

comps$membership returns a numeric indicator of membership in a component. I use LETTERS[] to convert that into a letter instead of a number.

Other Formats

Loading Network Formatted Data

The read_graph() function can load in a variety of native network formats. You should set format= when you call it:

For example using this ground squirrel data

net <- read_graph("data/ground_squirrel_smith_2016a.graphml", 
    format="graphml")
net
IGRAPH 3cc471b U-W- 60 340 -- 
+ attr: btw_soc (v/n), btw_spat (v/n), Node_All days_detected (v/n),
| stage_current_year (v/c), sex (v/c), fur_mark (v/c), id (v/c), weight
| (e/n)
+ edges from 3cc471b:
 [1] 1-- 2 1-- 4 1-- 5 1--13 1-- 6 1-- 7 1--14 1--15 1-- 9 1--16 1--10 1--17
[13] 1--11 1--12 2-- 3 2-- 4 2-- 5 2-- 6 2-- 7 2-- 8 2-- 9 2--10 2--11 2--12
[25] 3--20 3--48 3-- 8 4--19 4--23 4-- 5 4-- 6 4-- 7 4--14 4--26 4--15 4-- 8
[37] 4-- 9 4--11 4--12 5--19 5--20 5--13 5-- 6 5-- 7 5--54 5--30 5--15 5-- 9
[49] 5--10 5--12 6--19 6-- 7 6--28 6--15 6-- 8 6-- 9 6--11 6--12 7--19 7--18
[61] 7--38 7--14 7--15 7-- 8 7-- 9 7--10 7--11 7--12 8--48 8-- 9 8--47 8--11
+ ... omitted several edges

Putting it Together

Test your Knowledge

The next slide has a bunch of datasets for networks. I want you to do the following:

  • Find a network you think is interesting, download it.
  • Open the network in R
  • Calculate the number of vertices, edges, and the number of components.
  • Create a vertex attribute for component membership.

Databases of Data