# Social Network Analysis

## Definition

Social networks are simply networks of social interactions and personal

relationships. Think about our group of friends and how we got to know

them. Maybe we met them while ago from our schooling, or maybe we met

them through a hobby or through our community. In fact, 72% of all

Internet users are active on social media today, including in social

interactions and developing personal relationships. However, to

understand about social networks, we only don’t need to go through

internet or social media, they may come in variety of form in our daily

life.

## Social Network Analysis

Social network analysis (SNA), also known as network science, is a field

of data analytics that uses networks and graph theory to understand

social structures. We can see network around us such as road network,

online network, network of social media such as facebook, twitter etc.

Learning SNA allow us to explore insight of various data sources.

## SNA Graph

We all are familier about the graph which simply the collection of non

zero vertex and edge. In order to build SNA graphs, two key components

are required actors and relationships. Here, actors represents the vertex

and relationship means the edge between two actors. Let us write SNA

graph in R code. To do this, we should have `igraph`

package

already install in our R or R studio.

`library(igraph)`

```
##
## Attaching package: 'igraph'
## The following objects are masked from 'package:stats':
##
## decompose, spectrum
## The following object is masked from 'package:base':
##
## union
```

```
g <- graph(c(1,2))
plot(g)
```

In figure, we can see the directed graph from node 1 to node 2. From above

graph, it is also clear that by default it gives directed graph. In

above figure we can not clearly see node and edge so let’s increase its

size and give different color to the node.

```
plot(g,
vertex.color = 'green',
vertex.size = 40,
edge.color ='red',
edge.size = 20)
```

Now we change the node color and node font size. Add more node on graph for

this we follow the following code.

```
g <- graph(c(1,2,2,3,3,4,4,1))
plot(g,
vertex.color = 'green',
vertex.size =40,
edge.color = 'red',
edge.size = 20)
```

We got the graph with four vertex 1,2,3,4. Here, we also got directed graph.

Let’s make it for this we need to write directed is false.

```
g <- graph(c(1,2,2,3,3,4,4,1),directed = FALSE)
plot(g,
vertex.color = 'green',
vertex.size =40,
edge.color = 'red',
edge.size = 20)
```

We got our desirable type of graph. Now let’s move forward. We can give the

number of vertex with out writing them for this look following code.

```
g <- graph(c(1,2,2,3,3,4,4,1),
directed = F, n=7)
plot(g,
vertex.color = 'green',
vertex.size =40,
edge.color = 'red',
edge.size = 20)
```

In above graph we have given seven vertex numbers. Among them we can see three isolated

nodes. The reason to come isolated node is that we did not specify the

edge or relationship between them. Also from graph we can make sense

that this is not directed graph.

## Adjacency Matrix

Let's see what will happen if we type only `g[]`

.

`g[]`

```
## 7 x 7 sparse Matrix of class "dgCMatrix"
##
## [1,] . 1 . 1 . . .
## [2,] 1 . 1 . . . .
## [3,] . 1 . 1 . . .
## [4,] 1 . 1 . . . .
## [5,] . . . . . . .
## [6,] . . . . . . .
## [7,] . . . . . . .
```

This gives us the 7 by 7 adjacency matrix. Adjacency matrix is matrix

where we give 1 if there is edge between two vertex if not then we

give 0. But in above matrix it gave simply `.`

instead of zero.

Let us try to build our graph by keeping text data in place of number.

```
g1 <-
graph(c("Binu","Binita","Binita","Rita"
,"Rita","Binu","Binu","Rita", "Anju",
"Binita"))
plot(g1,
vertex.color = "green",
vertex.size = 40,
edge.color = "red",
edge.size = 5)
```

If we want to check the features of `g1`

we simply type `g1`

and press control and

enter key. We got following output.

`g1`

```
## IGRAPH d030509 DN-- 4 5 --
## + attr: name (v/c)
## + edges from d030509 (vertex names):
## [1] Binu ->Binita Binita->Rita Rita ->Binu Binu ->Rita Anju ->Binita
```

It showed that in graph there are 4 nodes 5 edges. And edges are directed

from

`Binu ->Binita, Binita->Rita, Rita ->Binu, Binu ->Rita, Anju ->Binita`

.

## Degree

Degree means numbers of connection to each node.

Let’s check the degree of graph `g1`

. To check degree we can do

`degree(g1)`

or `degree(g1, mode='all')`

.

`degree(g1) `

```
## Binu Binita Rita Anju
## 3 3 3 1
```

Degree of Binu is 3 similarly Anju has degree 1.

`degree(g1, mode='all')`

```
## Binu Binita Rita Anju
## 3 3 3 1
```

## Diameter

Diameter means number of edged inside and outside

of SND. Now, let’s check the diameter of graph.

```
diameter(g1, directed = F, weights =
NA)
```

`## [1] 2`

We got two diameter. i.e `Anju <- Binita <- Rita`

, `Anju <- Binita <- Binu`

.

## Edge density

Edge density means `ecount(g1)/(vcount(g1)*(vcount(g1) -1))`

. We can

calculate it from following code.

`edge_density(g1, loops = F)`

`## [1] 0.4166667`

We got the value of edge density 0.4166667.

## Reciprocity

Total edges = 5

Tied edges = 2

Reciprocity = 2/5 = 0.4

`reciprocity(g1)`

`## [1] 0.4`

## Closeness

Now getting closeness of graph.

`closeness(g1, mode = "all", weights = NA)`

```
## Binu Binita Rita Anju
## 0.2500000 0.3333333 0.2500000 0.2000000
```

From above result we can see that Binita is closest to the others three

persons and Anju is farthest from other three persons.

## Betweenness

Let’s calculate between of g1

`betweenness(g1, directed = T, weights = NA)`

```
## Binu Binita Rita Anju
## 1 2 2 0
```

Binita and Rita has 2 inner edge similarly Binu has one inner edge and

Anju has no inner edge.

## Edge Betweenness

For every pair of vertices in a connected graph, there exists at least

one shortest path between the vertices.

`edge_betweenness(g1, directed = T, weights = NA)`

`## [1] 2 4 4 1 3`

## SNA in TwitterData

Here I have loaded`Twitterdata`

from my local machine.

`load("F:/MDS R/termDocMatrix.rdata")`

```
m<- as.matrix(termDocMatrix)
termM <- m %*% t(m)
termM[1:10,1:10]
```

```
## Terms
## Terms analysis applications code computing data examples introduction
## analysis 23 0 1 0 4 4 2
## applications 0 9 0 0 8 0 0
## code 1 0 9 0 1 6 0
## computing 0 0 0 10 2 0 0
## data 4 8 1 2 85 5 3
## examples 4 0 6 0 5 17 2
## introduction 2 0 0 0 3 2 10
## mining 4 7 3 1 50 5 3
## network 12 0 1 0 0 2 2
## package 2 1 0 2 12 2 0
## Terms
## Terms mining network package
## analysis 4 12 2
## applications 7 0 1
## code 3 1 0
## computing 1 0 2
## data 50 0 12
## examples 5 2 2
## introduction 3 2 0
## mining 64 1 6
## network 1 17 1
## package 6 1 27
```

Now we have built a term-term adjacency matrix, where the rows and

columns represents terms, and every entry is the number of

co-occurrences of two terms. Next we can build a graph with

`graph.adjacency()`

from package igraph.

```
g <- graph.adjacency(termM,weighted = T,mode = 'undirected')
g
```

```
## IGRAPH d066e18 UNW- 21 151 --
## + attr: name (v/c), weight (e/n)
## + edges from d066e18 (vertex names):
## [1] analysis --analysis analysis --code
## [3] analysis --data analysis --examples
## [5] analysis --introduction analysis --mining
## [7] analysis --network analysis --package
## [9] analysis --positions analysis --postdoctoral
## [11] analysis --r analysis --research
## [13] analysis --series analysis --slides
## [15] analysis --social analysis --time
## + ... omitted several edges
```

Here we have built graph on `termDocMatrix`

. In result we can see the edges

between different dodes.

```
g <- simplify(g)
g
```

```
## IGRAPH d06a87e UNW- 21 130 --
## + attr: name (v/c), weight (e/n)
## + edges from d06a87e (vertex names):
## [1] analysis --code analysis --data
## [3] analysis --examples analysis --introduction
## [5] analysis --mining analysis --network
## [7] analysis --package analysis --positions
## [9] analysis --postdoctoral analysis --r
## [11] analysis --research analysis --series
## [13] analysis --slides analysis --social
## [15] analysis --time analysis --tutorial
## + ... omitted several edges
```

Function `simplify()`

in igraph handly removes self-loops from a network.

We can see in previous graph there are 151 edges in second graph there

are only 130 edges. Hence there are 21 self loops they are omitted from

the graph.

## Check Degree of graph and nodes of the graph.

```
V(g)$label <- V(g)$name
V(g)$label
```

```
## [1] "analysis" "applications" "code" "computing" "data"
## [6] "examples" "introduction" "mining" "network" "package"
## [11] "parallel" "positions" "postdoctoral" "r" "research"
## [16] "series" "slides" "social" "time" "tutorial"
## [21] "users"
```

```
V(g)$degree <- degree(g)
V(g)$degree
```

`## [1] 17 6 9 9 18 14 12 20 14 13 8 7 8 17 9 11 15 11 11 16 15`

We found degree of graph is 20.

## Histogram on the basis of degree

```
hist(V(g)$degree, breaks = 100,col = 'green', main = "Frequency Of Degree",
xlab = " Degree of vertices", ylab = " Frequency")
```

We can see most of nodes have degree 9 and 11. We all khow what is degree of

graph, number of edges that are incident to the node is called degree of

graph.

## Let’s Plot Graph on the Data.

Let's set `set.seed(3952)`

. Where set.seed gives same sample with the same seed value.

```
set.seed(3952)
layout1 <- layout.fruchterman.reingold(g)
plot(g, layout=layout1)
```

A different layout can be generated with the first line of code below. The

second line produces an interactive plot, which allows us to manually

rearrange the layout

`plot(g, layout=layout.kamada.kawai)`

## Make it better.

```
V(g)$label.cex <- 2.2 * V(g)$degree / max(V(g)$degree)+ .2
V(g)$label.color <- rgb(0, 0, .2, .8)
V(g)$frame.color <- NA
egam <- (log(E(g)$weight)+.4) / max(log(E(g)$weight)+.4)
E(g)$color <- rgb(.5, .5, 0, egam)
E(g)$width <- egam
# plot the graph in layout1
plot(g, layout=layout1)
```

Here size of words appear according to their degree. From graph we can

clearly see that node mining has maximum degree.

## Community detection

Communities are seen as groups, clusters, coherent subgroups, or modules

in different fields; community detection in a social network is

identifying sets of nodes in such a way that the connections of nodes

within a set are more than their connection to other network nodes.

`comm <- cluster_edge_betweenness(g)`

```
## Warning in cluster_edge_betweenness(g): At community.c:461 :Membership vector
## will be selected based on the lowest modularity score.
## Warning in cluster_edge_betweenness(g): At community.c:468 :Modularity
## calculation with weighted edge betweenness community detection might not make
## sense -- modularity treats edge weights as similarities while edge betwenness
## treats them as distances
```

`plot(comm,g)`

There are dense connection within the group within the community the

connection is sparse.

```
prop <- cluster_label_prop(g)
plot(prop, g)
```

This is different type of algorithms to detect community which is different

from previous one.

## Hubs

Nodes with most outer edges. We need to find hub score.

```
hs <- hub_score(g,weights = NA)$vector
hs
```

```
## analysis applications code computing data examples
## 0.9047777 0.3589289 0.5606314 0.5223206 0.9065063 0.8195307
## introduction mining network package parallel positions
## 0.7307838 1.0000000 0.7483791 0.7210610 0.4939614 0.3733995
## postdoctoral r research series slides social
## 0.4095660 0.9147530 0.4481802 0.6761093 0.8510808 0.6018664
## time tutorial users
## 0.6761093 0.8899001 0.8342594
```

## Authority

Nodes with most inner edges. We need to find authority score

```
as <- authority_score(g, weights = NA)$vector
as
```

```
## analysis applications code computing data examples
## 0.9047777 0.3589289 0.5606314 0.5223206 0.9065063 0.8195307
## introduction mining network package parallel positions
## 0.7307838 1.0000000 0.7483791 0.7210610 0.4939614 0.3733995
## postdoctoral r research series slides social
## 0.4095660 0.9147530 0.4481802 0.6761093 0.8510808 0.6018664
## time tutorial users
## 0.6761093 0.8899001 0.8342594
```

## Hub in Plot

```
par(mfrow = c(1,2))
plot(g,vertex.size= hs*50, main = "Hubs",
vertex.label = NA,
vertex.colour = rainbow(50))
```

## Authority in Plot

```
plot(g,vertex.size= as*30, main = "Authorities",
vertex.label = NA,
vertex.colour = rainbow(50))
```

Hub are expected to contain large number of outgoing link. And authority are

expected to contain large number of incoming link from hubs.

## Application of SNA in Real World

Social network analysis can provide information about the reach of

gangs, the impact of gangs, and gang activity. The approach may also

allow we to identify those who may be at risk of gang-association and/or

being exploited by gangs.

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