GitHub - KwokHing/Network-Analysis-on-MRT-Station: Demo on applying the concept of network analysis on a network of connected railway stations, attempting to identify the important stations (nodes) in this network. Web scraping techniques using rvest package is also briefly discussed upon.

Introduction to basic Network Analysis using railway (Singapore MRT) stations

This demo will provide

a brief introduction to web scraping using Rvest package
a brief introduction to the concept of graph and network analysis using R igraph package
a brief introduction on the metrics used to perform network analysis (such as degree, betweeness, closeness and eigenvector centrality)
investigation into which MRT station is an important node in the Singapore MRT network

Codes Walkthrough

Installing the rvest package to scrape the list of MRT stations from wikipedia

install.packages("rvest")
library(rvest)

Installing package into '/home/nbcommon/R'
(as 'lib' is unspecified)
also installing the dependencies 'xml2', 'selectr'

Loading required package: xml2

Before we can scrape the MRT stations data, we would need to ascertain the correct XPath to use.

navigate to the wikipedia page and fire up the developer tool (F12 for windows or right-click > Inspect)
copy the table XPath

Now we are ready to do some real and dirty work, scraping and cleaning the data!

Data Scraping

url <- "https://en.wikipedia.org/wiki/List_of_Singapore_MRT_stations"

mrt_stn <-  url %>%
  read_html() %>%
  #paste the copied xpath: html_nodes(xpath here)
  html_nodes(xpath='//*[@id="mw-content-text"]/div/table[2]') %>% 
  html_table(fill = TRUE)

mrt <- mrt_stn[[1]]

Data Cleaning

mrt <- mrt[,c(1:2,5,7:8)] 
names(mrt) <- c("Code","Name","Opening","Status","Location")

mrt <- subset(mrt,Code != Name)

mrt <- mrt[2:nrow(mrt),]

mrt$Code <- substr(mrt$Code, 1, 4)
mrt$Code <- iconv(mrt$Code, "ASCII", "UTF-8", sub="")
mrt$Name <- gsub('\\[.\\]',"",mrt$Name)

mrt <- mrt[mrt$Name != 'Reserved Station',]
mrt <- mrt[mrt$Name != 'Punggol Coast',]
mrt <- mrt[mrt$Status != 'TBA',]

Generating the MRT network's edgelist

i. preparing the North-South Line (NSL) edgelist

ns_df <- mrt[substr(mrt$Code,1,2) == 'NS',]

sourceList <- ""
targetList <- ""
for (i in 1:nrow(ns_df)-1) {
  sourceList[i] <- ns_df$Name[i]
  targetList[i] <- ns_df$Name[i+1]
}

ns_edgelist <- data.frame(sourceList, targetList, "NSL")
names(ns_edgelist) <- c("source", "target", "network")

ii. preparing the East-West Line (EWL) edgelist

ew_df <- mrt[substr(mrt$Code,1,2) == 'EW',]

sourceList <- ""
targetList <- ""
for (i in 1:nrow(ew_df)-1) {
  sourceList[i] <- ew_df$Name[i]
  targetList[i] <- ew_df$Name[i+1]
}

ew_edgelist <- data.frame(sourceList, targetList, "EWL")
names(ew_edgelist) <- c("source", "target", "network")

iii. preparing the Changi Airport Branch Line (CAL) edgelist

cg_df <- mrt[substr(mrt$Code,1,2) == 'CG',]

sourceList <- ""
targetList <- ""
for (i in 1:nrow(cg_df)-1) {
  sourceList[i] <- cg_df$Name[i]
  targetList[i] <- cg_df$Name[i+1]
}

cg_edgelist <- data.frame(sourceList, targetList, "CAL")
names(cg_edgelist) <- c("source", "target", "network")

iv. preparing the North-East Line (NEL) edgelist

ne_df <- mrt[substr(mrt$Code,1,2) == 'NE',]

sourceList <- ""
targetList <- ""
for (i in 1:nrow(ne_df)-1) {
  sourceList[i] <- ne_df$Name[i]
  targetList[i] <- ne_df$Name[i+1]
}

ne_edgelist <- data.frame(sourceList, targetList, "NEL")
names(ne_edgelist) <- c("source", "target", "network")

v. preparing the Circle Line (CCL) edgelist

cc_df <- mrt[substr(mrt$Code,1,2) == 'CC',]

sourceList <- ""
targetList <- ""
for (i in 1:nrow(cc_df)-1) {
  sourceList[i] <- cc_df$Name[i]
  targetList[i] <- cc_df$Name[i+1]
}

cc_edgelist <- data.frame(sourceList, targetList, "CCL")
names(cc_edgelist) <- c("source", "target", "network")

vi. preparing the Downtown Line (DTL) edgelist

dt_df <- mrt[substr(mrt$Code,1,2) == 'DT',]

sourceList <- ""
targetList <- ""
for (i in 1:nrow(dt_df)-1) {
  sourceList[i] <- dt_df$Name[i]
  targetList[i] <- dt_df$Name[i+1]
}

dt_edgelist <- data.frame(sourceList, targetList, "DTL")
names(dt_edgelist) <- c("source", "target", "network")

mrt_edgelist <- rbind(ns_edgelist,ew_edgelist,cg_edgelist,ne_edgelist,cc_edgelist,dt_edgelist)

mrt_edgelist

source	target	network
Jurong East	Bukit Batok	NSL
Bukit Batok	Bukit Gombak	NSL
Bukit Gombak	Choa Chu Kang	NSL
Choa Chu Kang	Yew Tee	NSL
Yew Tee	Kranji	NSL
Kranji	Marsiling	NSL
Marsiling	Woodlands	NSL
Woodlands	Admiralty	NSL
Admiralty	Sembawang	NSL
Sembawang	Yishun	NSL
Yishun	Khatib	NSL
Khatib	Yio Chu Kang	NSL
Yio Chu Kang	Ang Mo Kio	NSL
Ang Mo Kio	Bishan	NSL
Bishan	Braddell	NSL
Braddell	Toa Payoh	NSL
Toa Payoh	Novena	NSL
Novena	Newton	NSL
Newton	Orchard	NSL
Orchard	Somerset	NSL
Somerset	Dhoby Ghaut	NSL
Dhoby Ghaut	City Hall	NSL
City Hall	Raffles Place	NSL
Raffles Place	Marina Bay	NSL
Marina Bay	Marina South Pier	NSL
Pasir Ris	Tampines	EWL
Tampines	Simei	EWL
Simei	Tanah Merah	EWL
Tanah Merah	Bedok	EWL
Bedok	Kembangan	EWL
...	...	...
Beauty World	King Albert Park	DTL
King Albert Park	Sixth Avenue	DTL
Sixth Avenue	Tan Kah Kee	DTL
Tan Kah Kee	Botanic Gardens	DTL
Botanic Gardens	Stevens	DTL
Stevens	Newton	DTL
Newton	Little India	DTL
Little India	Rochor	DTL
Rochor	Bugis	DTL
Bugis	Promenade	DTL
Promenade	Bayfront	DTL
Bayfront	Downtown	DTL
Downtown	Telok Ayer	DTL
Telok Ayer	Chinatown	DTL
Chinatown	Fort Canning	DTL
Fort Canning	Bencoolen	DTL
Bencoolen	Jalan Besar	DTL
Jalan Besar	Bendemeer	DTL
Bendemeer	Geylang Bahru	DTL
Geylang Bahru	Mattar	DTL
Mattar	MacPherson	DTL
MacPherson	Ubi	DTL
Ubi	Kaki Bukit	DTL
Kaki Bukit	Bedok North	DTL
Bedok North	Bedok Reservoir	DTL
Bedok Reservoir	Tampines West	DTL
Tampines West	Tampines	DTL
Tampines	Tampines East	DTL
Tampines East	Upper Changi	DTL
Upper Changi	Expo	DTL

mrt_edgelist$target <- as.character(mrt_edgelist$target)
mrt_edgelist$source <- as.character(mrt_edgelist$source)
mrt_edgelist$network <- as.character(mrt_edgelist$network)

Closing the loop for the graph network

mrt_edgelist[nrow(mrt_edgelist)+1,] <- c("Bayfront","Marina Bay","CEL")
mrt_edgelist[nrow(mrt_edgelist)+1,] <- c("Bayfront","Promenade","CCL")
mrt_edgelist[nrow(mrt_edgelist)+1,] <- c("Tanah Merah","Expo","CAL")

Specifying this network to be a undirected graph network

mrt_edgelist$type <- "undirected"

Exporting the mrt edgelist to csv

write.csv(mrt_edgelist, file="mrt_edgelist.csv", row.names=F)

Generating the MRT network's nodelist

mrt_node <- mrt[substr(mrt$Code,1,2) != 'TE',]
names(mrt_node)[2] <- "id"
mrt_node$label <- mrt_node$id

# removing duplicated mrt names/nodes (nodes in a network should be unique)
mrt_nodes <- unique(mrt_node)
mrt_nodes <- mrt_nodes[!duplicated(mrt_nodes$id),]
mrt_nodes$Code <- substr(mrt_nodes$Code, 1, 2)

Exporting the mrt nodes to csv

write.csv(mrt_nodes, file="mrt_nodes.csv", row.names=F)

Visualisation of the MRT network using Gephi

Visualisation of the MRT network using R igraph package

Installing the igraph package to do graph network analysis and plotting

install.packages("igraph")
library(igraph)

Installing package into '/home/nbcommon/R'
(as 'lib' is unspecified)

Attaching package: 'igraph'

The following objects are masked from 'package:stats':

    decompose, spectrum

The following object is masked from 'package:base':

    union

# renaming for igraph edgelist format
names(mrt_edgelist) <- c("from","to","network","type")
# rearranging for igraph nodelist format
mrt_nodes <- mrt_nodes[c(2,6,1,3,4,5)]

Setting up the graph network

g = graph.data.frame(mrt_edgelist, mrt_nodes, directed=F)
# Removing self loops
# g = simplify(g, remove.loops = T)

Checking if multiple edges exists in the graph network

any_multiple(g)
which_multiple(g)
#count_multiple(g)
#which_multiple(simplify(g))
#all(count_multiple(simplify(g)) == 1)
E(g)[38]
E(g)[135]

TRUE

+ 1/136 edge from d7df987 (vertex names):
[1] City Hall--Raffles Place



+ 1/136 edge from d7df987 (vertex names):
[1] Promenade--Bayfront

Removing multiple edges to create a simplified graph

simple_g <- g

simple_g <- delete_edges(simple_g,c(38,135))

any_multiple(simple_g)

FALSE

Displaying descriptive statistics of the graph network

V(simple_g)

+ 119/119 vertices, named, from 24e1b48:
  [1] Jurong East       Bukit Batok       Bukit Gombak      Choa Chu Kang    
  [5] Yew Tee           Kranji            Marsiling         Woodlands        
  [9] Admiralty         Sembawang         Yishun            Khatib           
 [13] Yio Chu Kang      Ang Mo Kio        Bishan            Braddell         
 [17] Toa Payoh         Novena            Newton            Orchard          
 [21] Somerset          Dhoby Ghaut       City Hall         Raffles Place    
 [25] Marina Bay        Marina South Pier Pasir Ris         Tampines         
 [29] Simei             Tanah Merah       Bedok             Kembangan        
 [33] Eunos             Paya Lebar        Aljunied          Kallang          
 [37] Lavender          Bugis             Tanjong Pagar     Outram Park      
+ ... omitted several vertices

E(simple_g)

+ 134/134 edges from 24e1b48 (vertex names):
 [1] Jurong East  --Bukit Batok   Bukit Batok  --Bukit Gombak 
 [3] Bukit Gombak --Choa Chu Kang Choa Chu Kang--Yew Tee      
 [5] Yew Tee      --Kranji        Kranji       --Marsiling    
 [7] Marsiling    --Woodlands     Woodlands    --Admiralty    
 [9] Admiralty    --Sembawang     Sembawang    --Yishun       
[11] Yishun       --Khatib        Khatib       --Yio Chu Kang 
[13] Yio Chu Kang --Ang Mo Kio    Ang Mo Kio   --Bishan       
[15] Bishan       --Braddell      Braddell     --Toa Payoh    
[17] Toa Payoh    --Novena        Novena       --Newton       
[19] Newton       --Orchard       Orchard      --Somerset     
+ ... omitted several edges

# Network Size (num of nodes and edges)
summary(simple_g)
# Network Density
graph.density(simple_g,loop=FALSE)
# greatest distance between any pair of vertices
diameter(simple_g)
# Average Path Length
mean_distance(simple_g, directed=F)

IGRAPH 24e1b48 UN-- 119 134 -- 
+ attr: name (v/c), label (v/c), Code (v/c), Opening (v/c), Status
| (v/c), Location (v/c), network (e/c), type (e/c)

0.0190856003418316

30

10.0371741917106

# Length of all paths in the graph
distances(simple_g)

	Jurong East	Bukit Batok	Bukit Gombak	Choa Chu Kang	Yew Tee	Kranji	Marsiling	Woodlands	Admiralty	Sembawang	...	Bendemeer	Geylang Bahru	Mattar	Ubi	Kaki Bukit	Bedok North	Bedok Reservoir	Tampines West	Tampines East	Upper Changi
Jurong East	0	1	2	3	4	5	6	7	8	9	...	13	14	15	15	16	17	18	19	21	21
Bukit Batok	1	0	1	2	3	4	5	6	7	8	...	14	15	16	16	17	18	19	20	22	22
Bukit Gombak	2	1	0	1	2	3	4	5	6	7	...	15	16	17	17	18	19	20	21	23	23
Choa Chu Kang	3	2	1	0	1	2	3	4	5	6	...	16	17	17	17	18	19	20	21	23	23
Yew Tee	4	3	2	1	0	1	2	3	4	5	...	17	17	16	16	17	18	19	20	22	22
Kranji	5	4	3	2	1	0	1	2	3	4	...	17	16	15	15	16	17	18	19	21	21
Marsiling	6	5	4	3	2	1	0	1	2	3	...	16	15	14	14	15	16	17	18	20	20
Woodlands	7	6	5	4	3	2	1	0	1	2	...	15	14	13	13	14	15	16	17	19	19
Admiralty	8	7	6	5	4	3	2	1	0	1	...	14	13	12	12	13	14	15	16	18	18
Sembawang	9	8	7	6	5	4	3	2	1	0	...	13	12	11	11	12	13	14	15	17	17
Yishun	10	9	8	7	6	5	4	3	2	1	...	12	11	10	10	11	12	13	14	16	16
Khatib	11	10	9	8	7	6	5	4	3	2	...	11	10	9	9	10	11	12	13	15	15
Yio Chu Kang	11	11	10	9	8	7	6	5	4	3	...	10	9	8	8	9	10	11	12	14	14
Ang Mo Kio	10	11	11	10	9	8	7	6	5	4	...	9	8	7	7	8	9	10	11	13	13
Bishan	9	10	11	11	10	9	8	7	6	5	...	8	7	6	6	7	8	9	10	12	12
Braddell	10	11	12	12	11	10	9	8	7	6	...	9	8	7	7	8	9	10	11	13	13
Toa Payoh	10	11	12	13	12	11	10	9	8	7	...	10	9	8	8	9	10	11	12	14	14
Novena	9	10	11	12	13	12	11	10	9	8	...	9	10	9	9	10	11	12	13	15	14
Newton	8	9	10	11	12	13	12	11	10	9	...	8	9	9	9	10	11	12	13	14	13
Orchard	9	10	11	12	13	14	13	12	11	10	...	8	9	10	10	11	12	13	14	15	14
Somerset	10	11	12	13	14	15	14	13	12	11	...	7	8	9	9	10	11	12	13	14	13
Dhoby Ghaut	10	11	12	13	14	15	14	13	12	11	...	6	7	8	8	9	10	11	12	13	12
City Hall	11	12	13	14	15	16	15	14	13	12	...	7	8	7	7	8	9	10	11	12	11
Raffles Place	10	11	12	13	14	15	16	15	14	13	...	7	8	8	8	9	10	11	12	13	12
Marina Bay	11	12	13	14	15	16	17	16	15	14	...	8	9	9	9	10	11	12	13	14	13
Marina South Pier	12	13	14	15	16	17	18	17	16	15	...	9	10	10	10	11	12	13	14	15	14
Pasir Ris	21	22	23	23	22	21	20	19	18	17	...	10	9	8	6	5	4	3	2	2	3
Tampines	20	21	22	22	21	20	19	18	17	16	...	9	8	7	5	4	3	2	1	1	2
Simei	20	21	22	22	21	20	19	18	17	16	...	9	8	7	6	5	4	3	2	2	3
Tanah Merah	19	20	21	21	20	19	18	17	16	15	...	8	7	6	6	6	5	4	3	3	2
...	...	...	...	...	...	...	...	...	...	...		...	...	...	...	...	...	...	...	...	...
Kent Ridge	5	6	7	8	9	10	11	12	13	13	...	11	12	13	14	15	16	17	18	20	20
Haw Par Villa	6	7	8	9	10	11	12	13	14	14	...	10	11	12	14	15	16	17	18	20	19
Pasir Panjang	7	8	9	10	11	12	13	14	15	15	...	9	10	11	13	14	15	16	17	19	18
Labrador Park	8	9	10	11	12	13	14	15	16	16	...	8	9	10	12	13	14	15	16	18	17
Telok Blangah	9	10	11	12	13	14	15	16	17	16	...	7	8	9	11	12	13	14	15	17	16
Bayfront	12	13	14	15	16	17	17	16	15	14	...	7	8	8	8	9	10	11	12	13	12
Bukit Panjang	13	14	15	16	17	18	18	17	16	15	...	17	17	16	16	17	18	19	20	22	22
Cashew	12	13	14	15	16	17	17	16	15	14	...	16	16	15	15	16	17	18	19	21	21
Hillview	11	12	13	14	15	16	16	15	14	13	...	15	15	14	14	15	16	17	18	20	20
Beauty World	10	11	12	13	14	15	15	14	13	12	...	14	14	13	13	14	15	16	17	19	19
King Albert Park	9	10	11	12	13	14	14	13	12	11	...	13	13	12	12	13	14	15	16	18	18
Sixth Avenue	8	9	10	11	12	13	13	12	11	10	...	12	12	11	11	12	13	14	15	17	17
Tan Kah Kee	7	8	9	10	11	12	12	11	10	9	...	11	11	10	10	11	12	13	14	16	16
Stevens	7	8	9	10	11	12	12	11	10	9	...	9	10	10	10	11	12	13	14	15	14
Rochor	10	11	12	13	14	15	14	13	12	11	...	8	8	7	7	8	9	10	11	12	11
Downtown	11	12	13	14	15	16	17	17	16	15	...	6	7	8	9	10	11	12	13	14	13
Telok Ayer	10	11	12	13	14	15	16	16	15	14	...	5	6	7	9	10	11	12	13	15	14
Fort Canning	10	11	12	13	14	15	16	16	15	14	...	3	4	5	7	8	9	10	11	13	13
Bencoolen	11	12	13	14	15	16	17	17	16	15	...	2	3	4	6	7	8	9	10	12	12
Jalan Besar	12	13	14	15	16	17	17	16	15	14	...	1	2	3	5	6	7	8	9	11	11
Bendemeer	13	14	15	16	17	17	16	15	14	13	...	0	1	2	4	5	6	7	8	10	10
Geylang Bahru	14	15	16	17	17	16	15	14	13	12	...	1	0	1	3	4	5	6	7	9	9
Mattar	15	16	17	17	16	15	14	13	12	11	...	2	1	0	2	3	4	5	6	8	8
Ubi	15	16	17	17	16	15	14	13	12	11	...	4	3	2	0	1	2	3	4	6	7
Kaki Bukit	16	17	18	18	17	16	15	14	13	12	...	5	4	3	1	0	1	2	3	5	6
Bedok North	17	18	19	19	18	17	16	15	14	13	...	6	5	4	2	1	0	1	2	4	5
Bedok Reservoir	18	19	20	20	19	18	17	16	15	14	...	7	6	5	3	2	1	0	1	3	4
Tampines West	19	20	21	21	20	19	18	17	16	15	...	8	7	6	4	3	2	1	0	2	3
Tampines East	21	22	23	23	22	21	20	19	18	17	...	10	9	8	6	5	4	3	2	0	1
Upper Changi	21	22	23	23	22	21	20	19	18	17	...	10	9	8	7	6	5	4	3	1	0

In graph theory and network analysis, indicators of centrality identify the most important vertices within a graph. Applications include identifying the most influential person(s) in a social network, key infrastructure nodes in the Internet or urban networks, and super-spreaders of disease. In this scenario, we could identify the important stations in the MRT network using different centrality measures.

Generation of graph attributes: Degree Centrality (in-degree, out-degree and total degree)

Since this is an undirected network, we will use the total degree centrality measure. [in-degree and out-degree will be relevant if it is a directed network graph]

Degree centrality measures how connected an entity is by counting the number of direct links each entity has to others in the network.

V(simple_g)$degree=degree(simple_g, mode="all")

Betweenness centrality measures the number of paths that pass through each entity.

V(simple_g)$betweenness=betweenness(simple_g,normalized=T)

Generation of graph attributes: Closeness Centrality

Closeness centrality (or closeness) of a node is a measure of centrality in a network, calculated as the sum of the length of the shortest paths between the node and all other nodes in the graph. Thus the more central a node is, the closer it is to all other nodes

Closeness centrality measures the proximity of an entity to the other entities in the social network.

V(simple_g)$closeness=closeness(simple_g, normalized=T)

Generation of graph attributes: Eigenvector

Eigenvector measures how connected an entity is and how much direct influence it might have over other connected entities in the network.

V(simple_g)$eigen=evcent(simple_g)$vector

Coreness is a measure that can help identify tightly interlinked groups within a network. A k-core is a maximal group of entities, all of which are connected to at least k other entities in the group.

V(simple_g)$coreness=coreness(simple_g)

Specify graph layout to use

glay = layout_with_lgl(simple_g)

Installing the plyr package for data mapping / transformation

install.packages("plyr")
library(plyr)

Installing package into '/home/nbcommon/R'
(as 'lib' is unspecified)

# Generate node colors based on network:
E(simple_g)$color <- mapvalues(E(simple_g)$network, c("NSL","EWL","CAL","NEL","CCL","DTL","CEL"), c("#D42E12","#009645","#009645","#9900AA","#FA9E0D","#FA9E0D","#005EC4"))

# plot degree graph 
plot(simple_g, layout=glay, edge.color=E(simple_g)$color, edge.width=3, edge.curve=1, 
     vertex.label.cex=.7, vertex.color="white", vertex.frame.color="black", 
     vertex.label.font=1.5, vertex.label=V(simple_g)$label, vertex.label.color="grey40",
     vertex.size=V(simple_g)$degree*3.5)

V(simple_g)$name[degree(simple_g)==max(degree(simple_g))]

'Dhoby Ghaut'

# plot closeness graph
plot(simple_g, layout=glay, edge.color=E(simple_g)$color, edge.width=3, edge.curve=1, 
     vertex.label.cex=.7, vertex.color="white", vertex.frame.color="black", 
     vertex.label.font=.7, vertex.label=V(simple_g)$label, vertex.label.color="grey40",
     vertex.size=V(simple_g)$closeness*90)

V(simple_g)$name[closeness(simple_g)==max(closeness(simple_g))]

'Little India'

# plot betweenness graph
plot(simple_g, layout=glay, edge.color=E(simple_g)$color, edge.width=3, edge.curve=1, 
     vertex.label.cex=.7, vertex.color="white", vertex.frame.color="black", 
     vertex.label.font=1, vertex.label=V(simple_g)$label, vertex.label.color="grey40",
     vertex.size=V(simple_g)$betweenness*60)

V(simple_g)$name[betweenness(simple_g)==max(betweenness(simple_g))]

'Botanic Gardens'

# plot eigenvector graph
plot(simple_g, layout=glay, edge.color=E(simple_g)$color, edge.width=3, edge.curve=1, 
     vertex.label.cex=.7, vertex.color="white", vertex.frame.color="black", 
     vertex.label.font=1, vertex.label=V(simple_g)$label, vertex.label.color="grey40",
     vertex.size=V(simple_g)$eigen*20)

V(simple_g)$name[which.max(V(simple_g)$eigen)]

'Dhoby Ghaut'

attr = data.frame(row.names=V(simple_g)$name,degree=V(simple_g)$degree,
                  coreness=V(simple_g)$coreness,betweenness=V(simple_g)$betweenness,
                  closeness=V(simple_g)$closeness,eigen=V(simple_g)$eigen)

table(attr$degree)
table(attr$coreness)
table(attr$betweenness)
table(attr$closeness)
table(attr$eigen)

 1  2  3  4  5 
 6 92  7 13  1 




 1  2 
24 95 




                  0 0.00195567144719687 0.00402964894490318  0.0047008547008547 
                  6                   1                   1                   1 
0.00582114056690328  0.0068810662031001  0.0123293530073191  0.0127891255009899 
                  1                   1                   1                   1 
 0.0160534067313728  0.0169491525423729  0.0175975938687803  0.0226816498002939 
                  1                   3                   1                   1 
 0.0227057938922346  0.0232110952449936  0.0251684912701862  0.0258203817525851 
                  1                   1                   1                   1 
 0.0267399267399267  0.0270655270655271  0.0278960838282872  0.0288625373371136 
                  1                   1                   1                   1 
 0.0309630733359547  0.0317977690859047   0.033391279153991  0.0336085759814573 
                  1                   1                   1                   3 
 0.0344398225754158  0.0345308802935922  0.0345767540682795  0.0346226278429668 
                  1                   1                   1                   1 
 0.0353928243758752  0.0373026220483848  0.0386443437290895  0.0401395528514173 
                  1                   1                   1                   1 
 0.0412863972186006  0.0418948283355063  0.0421676565744362  0.0422087015307354 
                  1                   1                   1                   1 
 0.0424798051916696  0.0436163020908784  0.0445023902651021  0.0465739533536144 
                  1                   1                   1                   1 
 0.0471775556521319  0.0475807619875416  0.0482295482295482  0.0484378772514366 
                  1                   1                   1                   1 
 0.0486262011685741  0.0490656236418948  0.0493988121106765  0.0499782703172534 
                  1                   1                   1                   3 
 0.0505456564778599   0.052923849534019   0.056188130764402  0.0593220338983051 
                  1                   1                   1                   1 
 0.0604809503114588   0.062344874209281   0.066058235549761   0.066597338631237 
                  1                   1                   3                   1 
 0.0671326476411222  0.0689813952525817  0.0691848954560819  0.0705852527886426 
                  1                   1                   1                   1 
 0.0706214689265537  0.0744724515910957  0.0762518711671254  0.0766843953284631 
                  2                   1                   1                   1 
 0.0799845477811579  0.0818484716789802  0.0819209039548023  0.0904485972282583 
                  1                   2                   1                   1 
 0.0926601960500266  0.0941285017556204  0.0945241199478488   0.096830225643785 
                  1                   1                   1                   1 
 0.0973489787049109  0.0997275166766692   0.105159937363327   0.106567193007871 
                  2                   1                   1                   1 
  0.108431116905693   0.112559756627553   0.120474189965715   0.124850479087767 
                  1                   1                   1                   1 
  0.127480805446907   0.132674199623352   0.137474734932362   0.142346667770397 
                  1                   1                   1                   1 
  0.144993894993895   0.147746321475135    0.15777267302691   0.168727537371605 
                  1                   1                   1                   1 
  0.171709332726282   0.189225871429261   0.190974248601367    0.19911632623497 
                  1                   1                   1                   1 
  0.202158481819499   0.202221601374144   0.205202361982023   0.210415761263219 
                  1                   1                   1                   1 
  0.211503969978546   0.222513330987907   0.226112180349468   0.249501596959224 
                  1                   1                   1                   1 
  0.259219593965357   0.277175900057256   0.314647530749226 
                  1                   1                   1 




 0.053393665158371 0.0563784042044912 0.0596562184024267 0.0632707774798928 
                 1                  1                  1                  1 
0.0672748004561003 0.0708708708708709 0.0711271850512357 0.0717325227963526 
                 1                  1                  1                  1 
0.0718198417528911 0.0721271393643032 0.0727945712523134 0.0762273901808786 
                 1                  1                  1                  1 
0.0767230169050715  0.077124183006536 0.0773263433813893 0.0776826859776168 
                 1                  1                  1                  1 
 0.077990746860542 0.0781456953642384 0.0784053156146179 0.0793544048419637 
                 1                  1                  1                  1 
0.0794078061911171 0.0798376184032476 0.0809327846364883 0.0823447313328681 
                 1                  1                  1                  1 
0.0830401125967628 0.0836286321757619 0.0838068181818182 0.0841654778887304 
                 1                  1                  1                  1 
 0.085383502170767 0.0861313868613139 0.0885221305326332 0.0887218045112782 
                 1                  1                  1                  1 
0.0890566037735849 0.0899390243902439 0.0909090909090909 0.0917573872472784 
                 1                  1                  1                  1 
0.0940239043824701 0.0960130187144019 0.0970394736842105 0.0972794723825227 
                 2                  1                  1                  1 
0.0973597359735974 0.0988274706867672 0.0990764063811923 0.0991596638655462 
                 1                  1                  1                  1 
0.0994102780117944  0.100254885301614  0.101636520241171  0.101811906816221 
                 1                  1                  1                  1 
  0.10251954821894  0.103327495621716  0.105357142857143  0.105545617173524 
                 1                  1                  1                  1 
 0.106594399277326  0.107175295186194    0.1073703366697  0.107468123861566 
                 1                  1                  1                  1 
 0.108058608058608  0.108256880733945   0.10865561694291  0.109158186864015 
                 1                  1                  1                  1 
 0.109461966604824  0.109767441860465  0.109869646182495  0.109972041006524 
                 1                  1                  1                  1 
 0.110383536014967  0.111848341232227  0.112060778727445  0.112595419847328 
                 1                  1                  1                  2 
 0.112702960840497  0.113026819923372  0.113461538461538  0.114451988360815 
                 1                  1                  1                  1 
       0.115234375   0.11545988258317  0.115572967678746  0.116370808678501 
                 1                  2                  1                  1 
 0.117647058823529  0.118592964824121  0.118712273641851  0.119071644803229 
                 1                  1                  2                  1 
 0.119312436804853  0.119433198380567  0.119918699186992  0.121025641025641 
                 1                  2                  1                  1 
 0.121274409044193  0.121524201853759  0.121900826446281  0.122026887280248 
                 1                  2                  1                  1 
 0.122279792746114  0.123044838373306  0.123430962343096  0.124341412012645 
                 1                  1                  1                  1 
 0.124604012671595  0.124867724867725   0.12566560170394  0.125933831376734 
                 1                  1                  1                  1 
 0.126473740621651  0.127292340884574  0.127843986998917  0.127982646420824 
                 1                  1                  1                  2 
 0.128121606948969   0.12910284463895  0.130099228224917  0.131403118040089 
                 1                  1                  1                  2 
 0.131843575418994  0.133182844243792  0.134090909090909  0.135476463834673 
                 1                  1                  1                  1 
 0.136258660508083  0.138173302107728  0.140979689366786 
                 1                  1                  1 




2.51858362053298e-07 7.39028698759823e-07 1.91667562290336e-06 
                   1                    1                    1 
4.88507796089859e-06 1.24176223479958e-05 2.10200818492998e-05 
                   1                    1                    1 
2.67431016136541e-05 3.15519861450127e-05   3.493618354964e-05 
                   1                    1                    1 
5.74522762701692e-05 8.01654591480061e-05 8.14932595885658e-05 
                   1                    1                    1 
0.000141839273885244 0.000167809921265858 0.000177714640335611 
                   1                    1                    1 
0.000185105863472294 0.000203677745616489 0.000204189716771217 
                   1                    1                    1 
0.000223321313009527 0.000287174882385132 0.000321189495444625 
                   1                    1                    1 
0.000358747103161553 0.000417817517967914 0.000492405122926692 
                   1                    1                    1 
0.000517486721433531 0.000517661199389077 0.000521468567890903 
                   1                    1                    1 
0.000543156654683785 0.000647439641568565 0.000655292355512262 
                   1                    1                    1 
0.000704534547681859 0.000910833357740738  0.00127705581286622 
                   1                    1                    1 
 0.00131478499340561  0.00137831538939482  0.00140868023272799 
                   1                    1                    1 
 0.00164950018256149  0.00231391377469838  0.00274166271824377 
                   1                    1                    1 
 0.00282282937525379  0.00325486333280614   0.0035903377056515 
                   1                    1                    1 
 0.00378373757664514  0.00380690651505764  0.00413559846730773 
                   1                    1                    1 
 0.00587889032532363  0.00666655321918628   0.0069682511646331 
                   1                    1                    1 
 0.00729572527509893  0.00738687889451853    0.007573376213864 
                   1                    1                    1 
 0.00827369879931538  0.00912645777319788    0.010485598006559 
                   1                    1                    1 
  0.0105653985966293   0.0116571804822862   0.0124409387540652 
                   1                    1                    1 
   0.012822558121519   0.0133160285498551   0.0149365306059223 
                   1                    1                    1 
   0.016820023102403    0.017624129573429   0.0178684329563004 
                   1                    1                    1 
  0.0200011387088744   0.0208359090163346    0.021022674274045 
                   1                    1                    1 
  0.0231894529515193   0.0234287025398688   0.0246279983079351 
                   1                    1                    1 
  0.0256415713329211   0.0266323211910227   0.0281642727572974 
                   1                    1                    1 
  0.0324649884818062   0.0379494133507986   0.0399540168190206 
                   1                    1                    1 
  0.0426884877753544   0.0431176419956824   0.0450445140766606 
                   1                    1                    1 
  0.0458668393248469   0.0520506817733822    0.053413193322856 
                   1                    1                    1 
  0.0536443324331427   0.0546418749796778   0.0573126934639011 
                   1                    1                    1 
  0.0581815090184332   0.0885708045661908   0.0890729109251433 
                   1                    1                    1 
   0.105253358095607    0.114305811115643    0.114586056646666 
                   1                    1                    1 
   0.114720227435284    0.127090890274223     0.13570780879659 
                   1                    1                    1 
    0.14729346265851    0.188118280674737     0.19157545406345 
                   1                    1                    1 
   0.216775918415613    0.221412875690504    0.232840042447464 
                   1                    1                    1 
   0.249100008151929    0.282979552890921    0.290363348277626 
                   1                    1                    1 
   0.308845224052014    0.320872474237074    0.342513847439296 
                   1                    1                    1 
   0.347566516922269     0.36042054487175    0.374022111837471 
                   1                    1                    1 
   0.440571504738262    0.457523962582117    0.459245894439935 
                   1                    1                    1 
    0.46826186745292     0.52144365496715     0.54751538121932 
                   1                    1                    1 
   0.560619511605635    0.715627468790695    0.734824970607291 
                   1                    1                    1 
   0.814446111403723                    1 
                   1                    1

attr

	degree	coreness	betweenness	closeness	eigen
Jurong East	3	2	0.202158482	0.09601302	1.314785e-03
Bukit Batok	2	2	0.060480950	0.08905660	5.176612e-04
Bukit Gombak	2	2	0.046573953	0.08304011	2.041897e-04
Choa Chu Kang	2	2	0.037302622	0.07940781	8.149326e-05
Yew Tee	2	2	0.033391279	0.07799075	3.493618e-05
Kranji	2	2	0.031797769	0.07712418	2.102008e-05
Marsiling	2	2	0.034622628	0.07840532	2.674310e-05
Woodlands	2	2	0.041286397	0.08093278	5.745228e-05
Admiralty	2	2	0.049398812	0.08416548	1.418393e-04
Sembawang	2	2	0.059322034	0.08852213	3.587471e-04
Yishun	2	2	0.070621469	0.09402390	9.108334e-04
Khatib	2	2	0.081920904	0.10025489	2.313914e-03
Yio Chu Kang	2	2	0.094524120	0.10825688	5.878890e-03
Ang Mo Kio	2	2	0.108431117	0.11871227	1.493653e-02
Bishan	4	2	0.259219594	0.13140312	3.794941e-02
Braddell	2	2	0.048626201	0.12434141	4.311764e-02
Toa Payoh	2	2	0.047177556	0.12304484	8.857080e-02
Novena	2	2	0.052923850	0.12812161	2.167759e-01
Newton	4	2	0.202221601	0.13817330	5.475154e-01
Orchard	2	2	0.006881066	0.12486772	3.425138e-01
Somerset	2	2	0.005821141	0.12566560	4.575240e-01
Dhoby Ghaut	5	2	0.132674200	0.13547646	1.000000e+00
City Hall	3	2	0.076684395	0.13009923	7.348250e-01
Raffles Place	3	2	0.068981395	0.12460401	4.405715e-01
Marina Bay	3	2	0.023211095	0.11302682	3.088452e-01
Marina South Pier	1	1	0.000000000	0.10163652	1.052534e-01
Pasir Ris	1	1	0.000000000	0.07087087	1.777146e-04
Tampines	4	2	0.034576754	0.07622739	5.214686e-04
Simei	2	2	0.016053407	0.07814570	6.474396e-04
Tanah Merah	3	2	0.079984548	0.08380682	1.378315e-03
...	...	...	...	...	...
Kent Ridge	2	2	0.027065527	0.09907641	0.0037837376
Haw Par Villa	2	2	0.022681650	0.09727947	0.0038069065
Pasir Panjang	2	2	0.022705794	0.09735974	0.0073868789
Labrador Park	2	2	0.025168491	0.09882747	0.0178684330
Telok Blangah	2	2	0.030963073	0.10181191	0.0450445141
Bayfront	3	2	0.026739927	0.11346154	0.3604205449
Bukit Panjang	1	1	0.000000000	0.07181984	0.0001678099
Cashew	2	1	0.016949153	0.07732634	0.0004924051
Hillview	2	1	0.033608576	0.08362863	0.0012770558
Beauty World	2	1	0.049978270	0.09090909	0.0032548633
King Albert Park	2	1	0.066058236	0.09941028	0.0082736988
Sixth Avenue	2	1	0.081848472	0.10946197	0.0210226743
Tan Kah Kee	2	1	0.097348979	0.12152420	0.0534131933
Stevens	2	2	0.142346668	0.13409091	0.2328400424
Rochor	2	2	0.094128502	0.13318284	0.5214436550
Downtown	2	2	0.012329353	0.10976744	0.1881182807
Telok Ayer	2	2	0.017597594	0.11545988	0.1915754541
Fort Canning	2	2	0.056188131	0.11764706	0.1472934627
Bencoolen	2	2	0.049065624	0.11206078	0.0581815090
Jalan Besar	2	2	0.044502390	0.10915819	0.0234287025
Bendemeer	2	2	0.041894828	0.10737034	0.0105653986
Geylang Bahru	2	2	0.042208702	0.10746812	0.0075733762
Mattar	2	2	0.047580762	0.11038354	0.0116571805
Ubi	2	2	0.090448597	0.10805861	0.0104855980
Kaki Bukit	2	2	0.076251871	0.09915966	0.0041355985
Bedok North	2	2	0.062344874	0.09175739	0.0016495002
Bedok Reservoir	2	2	0.048437877	0.08538350	0.0007045345
Tampines West	2	2	0.034530880	0.07983762	0.0004178175
Tampines East	2	2	0.001955671	0.07112719	0.0002871749
Upper Changi	2	2	0.004029649	0.07279457	0.0003211895

Summary

From the results obtained from the different centrality measures applied to the MRT network, we could often see that the station 'Dhoby Ghaut' frequently appears as one of the significant nodes suggesting that it could likely be the most important node in the MRT network. The consequences of removing such a node might breaks the network into different smaller networks and reduce connectivity among the network, seriously impairing the connectivity and coverage of the MRT services.

Name		Name	Last commit message	Last commit date
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images		images
LICENSE		LICENSE
MRT_Gephi.gephi		MRT_Gephi.gephi
MRT_Network_Analysis.R		MRT_Network_Analysis.R
README.md		README.md

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Introduction to basic Network Analysis using railway (Singapore MRT) stations

Codes Walkthrough

Data Scraping

Data Cleaning

Generating the MRT network's edgelist

Generating the MRT network's nodelist

Visualisation of the MRT network using Gephi

Visualisation of the MRT network using R igraph package

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Introduction to basic Network Analysis using railway (Singapore MRT) stations

Codes Walkthrough

Data Scraping

Data Cleaning

Generating the MRT network's edgelist

Generating the MRT network's nodelist

Visualisation of the MRT network using Gephi

Visualisation of the MRT network using R igraph package

Summary

About

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