Packages

Here are the pacakges needed to run the codes:

library(RCurl)
library(knitr)
library(igraph)
library(dplyr)
library(ndtv)
library(networkDynamic)
library(animation)
library(network)
library(tsna)

Data

Data used in this project was acquired from UB Sponsored Projects Services (SPS) with the help of my advisor, Dr. Ling Bian. A total of 7,714 proposals submitted from UB between the fiscal year 2011 and 2015 involving 1,446 investigators are included in a series of spreadsheets.

These spreadsheets are preprocessed and organized into a relational database. The database is made up of three parts:

1. Collborated Investigators: These investigators collborated on proposals. Each record includes the identifier of PI/co-PI (ID1) and one co-PI (ID2), the ID of proposal they submitted together (PID), the year they submitted the proposal (Year), and the status of the proposal(Awarded).

corp <- getURL("https://raw.githubusercontent.com/LittlePennyPaw/Data/master/Data_Corp.csv", 
    ssl.verifyhost = FALSE, ssl.verifypeer = FALSE)
corp_frame <- read.csv(textConnection(corp), header = T)
knitr::kable(head(corp_frame), caption = "Example of Collborated Investigators Table")

2. Single Investigators: These investigators worked on their own. Each record includes the identifier of PI (ID), the ID of the proposal (PID), the year the proposal was submitted (Year), and the status of the proposal (Awarded).

single <- getURL("https://raw.githubusercontent.com/LittlePennyPaw/Data/master/Data_SIngle.csv", 
    ssl.verifyhost = FALSE, ssl.verifypeer = FALSE)
single_frame <- read.csv(textConnection(single), header = T)
knitr::kable(head(single_frame), caption = "Example of Single Investigators Table")

3. Investigator Information: Each record includes the identifier of investigator (ID), his/her department and school affiliation (Department/School).

dept_2011 <- getURL("https://raw.githubusercontent.com/LittlePennyPaw/Data/master/Dept_2011.csv", 
    ssl.verifyhost = FALSE, ssl.verifypeer = FALSE)
dept2011_frame <- read.csv(textConnection(dept_2011), header = T)
dept_2012 <- getURL("https://raw.githubusercontent.com/LittlePennyPaw/Data/master/Dept_2012.csv", 
    ssl.verifyhost = FALSE, ssl.verifypeer = FALSE)
dept2012_frame <- read.csv(textConnection(dept_2012), header = T)
dept_2013 <- getURL("https://raw.githubusercontent.com/LittlePennyPaw/Data/master/Dept_2013.csv", 
    ssl.verifyhost = FALSE, ssl.verifypeer = FALSE)
dept2013_frame <- read.csv(textConnection(dept_2013), header = T)
dept_2014 <- getURL("https://raw.githubusercontent.com/LittlePennyPaw/Data/master/Dept_2014.csv", 
    ssl.verifyhost = FALSE, ssl.verifypeer = FALSE)
dept2014_frame <- read.csv(textConnection(dept_2014), header = T)
dept_2015 <- getURL("https://raw.githubusercontent.com/LittlePennyPaw/Data/master/Dept_2015.csv", 
    ssl.verifyhost = FALSE, ssl.verifypeer = FALSE)
dept2015_frame <- read.csv(textConnection(dept_2015), header = T)
knitr::kable(head(dept2011_frame), caption = "Example of Investigator Information Table")

Methodology

Corresponding to the three research objectives, three sets of methods will be applied in the study.

Before diving into analyses, a university-wide investigator network is built for each fiscal year. In these networks, nodes represent investigators and edges are established if two investigators collaborated on a proposal. Single investigators will be represented as isolated nodes. Each node is assigned properties, including investigator ID, and his/her department and school affiliation. Each edge is also assigned properties, including proposal ID and whether it was awarded.

# constructing five university-wide investigator networks assign colors to
# nodes based on school affiliation
color_matrix <- matrix(c("deeppink1", "dodgerblue2", "cadetblue1", "brown2", 
    "darkorchid2", "darkseagreen3", "green2", "gray0", "darkorange1", "firebrick1", 
    "darkgreen", "darkgoldenrod3", "coral1", "antiquewhite3"))
school_matrix <- matrix(nrow = 14)

mats <- list(dept2011_frame, dept2012_frame, dept2013_frame, dept2014_frame, 
    dept2015_frame)
corps <- list()
singles <- list()
networks <- list()
for (j in 1:5) {
    year <- 2010 + j
    corps[[j]] <- filter(corp_frame, Year == toString(year))
    singles[[j]] <- filter(single_frame, Year == toString(year))
    networks[[j]] <- graph.data.frame(corps[[j]], vertice = mats[[j]], directed = F)
    V(networks[[j]])$color <- V(networks[[j]])$School
    
    for (i in 1:14) {
        V(networks[[j]])$color <- gsub(unique(mats[[j]]$School)[i], color_matrix[i], 
            V(networks[[j]])$color)
    }
}

for (i in 1:14) {
    school_matrix[i] <- toString(unique(dept2011_frame$School)[i])
}

1. Identifying Topological Characteristics at University Level:
Given the five investigator networks at the university level, three sets of metrics, i.e., density, average path length, and centrality are used to analyze their topological characteristics.

The density is used to explore whether the investigators often work with many other investigators.

The average path length over the network is utilized to identify the number of ‘investigator steps’ between two investigators.

The centrality metrics are introduced to identify the ‘star’ investigators who are central and critical in the network. The top five investigators with the highest values of degree centrality, betweenness centrality, and closeness centrality are identified. one of the top ‘star’ investigator will be featured in the individual level ego network.

# Density and average pathlength
tyTable <- matrix(nrow = 2, ncol = 5)
for (i in 1:5) {
    tyTable[1, i] <- round(edge_density(networks[[i]], loops = F), 4)
    tyTable[2, i] <- round(mean_distance(networks[[i]], directed = F), 4)
}
rownames(tyTable) <- c("Density", "Average Pathlength")
colnames(tyTable) <- c("2011", "2012", "2013", "2014", "2015")

# Degree Centrality - Top 5
dcTable <- matrix(nrow = 5, ncol = 5)
for (i in 1:5) {
    D <- igraph::degree(networks[[i]])
    DD <- as.matrix(head(sort(D, decreasing = T), n = 5))
    dcTable[, i] <- rownames(DD)
}
rownames(dcTable) <- c("Top1", "Top2", "Top3", "Top4", "Top5")
colnames(dcTable) <- c("2011", "2012", "2013", "2014", "2015")

# Betweeness Centrality - Top5
bcTable <- matrix(nrow = 5, ncol = 5)
for (i in 1:5) {
    B <- igraph::betweenness(networks[[1]], directed = F, weights = NA)
    BB <- as.matrix(head(sort(B, decreasing = T), n = 5))
    bcTable[, i] <- rownames(BB)
}
rownames(bcTable) <- c("Top1", "Top2", "Top3", "Top4", "Top5")
colnames(bcTable) <- c("2011", "2012", "2013", "2014", "2015")

# Closeness Centrality - Top 5
ccTable <- matrix(nrow = 5, ncol = 5)
for (i in 1:5) {
    C <- igraph::closeness(networks[[1]], mode = "all", weights = NA)
    CC <- as.matrix(head(sort(C, decreasing = T), n = 5))
    ccTable[, i] <- rownames(CC)
}
rownames(ccTable) <- c("Top1", "Top2", "Top3", "Top4", "Top5")
colnames(ccTable) <- c("2011", "2012", "2013", "2014", "2015")

2. Testing the Community Structure at Local Level:
A local network at Geography Department is constructed out of my own curiosity and whether it has community structure is tested using Newman-Girvan algorithm. This algorithm of community detection is based on edge betweenness. Groups that consist of densely connected nodes and between which there are only looser connections will be identified as communities(Girvan & Newman, 2012). Edges with high betweenness values are removed sequentially in the algorithm and the community boundaries are determined.

The modularity of the local network will be analyzed. A high modularity value will reflect the existence of the community structure in the local network, suggesting the occurrence of established investigator groups. In this case, the number of communities will be calculated.

corp_geo <- filter(corp_frame, grepl("GEO", ID1) | grepl("GEO", ID2))
networks_geo <- graph.data.frame(corp_geo, directed = F)
V(networks_geo)$color <- ifelse(grepl("GEO", V(networks_geo)$name), "gold", 
    "gray")
ceb <- cluster_edge_betweenness(networks_geo)

3. Visualizing the Evolvement at Individual Level:
Ego networks are widely used to discuss social relationships (Leskovec & Mcauley, 2012; Arnaboldi et al., 2012). The nodes in Ego networks consist of a focal node (‘ego’) and the nodes to whom ego is directly connected to (‘alters’). Based on the above analysis of topological characteristics, a ‘star’ investigator with high centrality values across the five fiscal years will be chosen as an ego. An ego network will be built around him/her and the evolvement of this ego network will be visualized in animation.

egonode <- getURL("https://raw.githubusercontent.com/LittlePennyPaw/Data/master/egonode.csv", 
    ssl.verifyhost = FALSE, ssl.verifypeer = FALSE)
node_frame <- read.csv(textConnection(egonode), header = T)
egoedge <- getURL("https://raw.githubusercontent.com/LittlePennyPaw/Data/master/egoedge.csv", 
    ssl.verifyhost = FALSE, ssl.verifypeer = FALSE)
edge_frame <- read.csv(textConnection(egoedge), header = T)

# build the networkDynamic object specifying nodes and edges
egonet <- networkDynamic(vertex.spells = node_frame[, c(3, 4, 1)], edge.spells = edge_frame[, 
    c(5, 6, 1, 3)])

## Initializing base.net of size 36 imputed from maximum vertex id in edge records
## Created net.obs.period to describe network
##  Network observation period info:
##   Number of observation spells: 1 
##   Maximal time range observed: 0 until 3.5 
##   Temporal mode: continuous 
##   Time unit: unknown 
##   Suggested time increment: NA

# assign static attributes in the network
network::set.edge.attribute(egonet, "award", as.vector(edge_frame$Award))
network::set.edge.attribute(egonet, "proposal", as.vector(edge_frame$Proposal))
network::set.vertex.attribute(egonet, "year", as.vector(node_frame$Year))
network.vertex.names(egonet) <- as.character(node_frame$vertex_name)

# configure the network
slice.par <- list(start = 0, end = 3.25, interval = 0.25, aggregate.dur = 0, 
    rule = "latest")
compute.animation(egonet, slice.par = slice.par, animation.mode = "kamadakawai")

Topological Characteristics at University Level

The table below shows that density is very low for all fiscal networks compared to previous studies on scientific collaboration networks (Newman, 2001a, 2001b, 2001c). This observation implies that the network is sparse. Investigators in these networks do not collaborate very often with many others across the campus, although they may have their own dedicated collaborators. One reason behind this situation may be the requirement of certain types of proposals. For example, the Career Award of the National Science Foundation (NSF) requires only one investigator. The average path length ranges from 4.6 to 6.2 during the five fiscal years, meaning that it takes about 4 to 6 ‘investigator steps’ for two investigators to work together. These values are similar to previous studies on scientific collaboration networks (Newman, 2000; Barabási et al., 2002) and can be all seen as small. These low values indicate a strong interconnection between investigators in the already established groups.

knitr::kable(tyTable, caption = "Topological Characteristics of the investigator networks")

Results of the third set of topological characteristics include degree, betweenness, and closeness centralities. The top five investigators with the highest values of degree centralities have more collaborators than any others and are heavily involved in the scientific collaboration. These investigators are mainly from the School of Engineering and Applied Sciences, the School of Public Health and Health Professions, and the School of Medicine and Biomedical Sciences.

knitr::kable(dcTable, caption = "Top 5 Degree Centrality")

Similar to the results of degree centrality, the top five investigators with the highest values of betweenness centrality are mainly from the School of Engineering and Applied Sciences, the School of Public Health and Health Professions, and the School of Medicine and Biomedical Sciences. They are considered to be the hub in the networks and play an important role in facilitating the collaborations between investigators.

knitr::kable(bcTable, caption = "Top 5 Betweeness Centrality")

The table below shows the information of the top five investigators with the highest values of closeness centrality during the five-year period. These investigators are mainly from the School of Engineering and Applied Sciences and the School of Medicine and Biomedical Sciences. They are considered to have high interconnections with other investigators in the networks.

knitr::kable(ccTable, caption = "Top 5 Closeness Centrality")

Community Structure at Local Level

The local network at Geography Department is displayed as below. Orange nodes represent investigators from Geography Department and grey nodes are their direct collaborators from other departments. All five fiscal years are taken into account.

# plot the local network
plot(networks_geo, vertex.size = 8, vertex.frame.color = "Gray", edge.width = 1, 
    layout = layout_nicely(networks_geo), main = "Local Investigator Network at Geography Department", 
    vertex.label = networks_geo$name, vertex.label.cex = 0.6, vertex.label.dist = 1, 
    vertex.label.color = "black")

Test if community structure exists using ‘modularity’ function: 0.725161, The modularity of the local network turns out to be high, showing the existence of the community structure. This result iterates the above finding that investigators have strong interconnections in their established groups.

modularity(ceb)

## [1] 0.725161

Get the number of communities in the local network using ‘length’ function: 10. This calculation suggested that there are in total 10 communities in this local network.

length(ceb)

## [1] 10

The community graph follows to show the division of communities around investigators from Geography Department. The nodes that belong to a community are assigned the same color.

# plot the community gragh
plot(ceb, networks_geo, vertex.label.cex = 0.6, vertex.size = 8, vertex.label.dist = 1, 
    vertex.label.color = "black", vertex.label.degree = -pi/2, vertex.label.font = 3, 
    main = "Community Graph of the Local Network")

The dendrogram below offers a closer view of the community structure. Those investigators who belong to the same community (10 in total) are assigned the same color. Investigators who are connected more closely will form even smaller communities as shown in the dendrogram.

# plot the dendPlot of the structure
dendPlot(ceb, mode = "phylo", type = "fan", label.offset = 0.2, cex = 0.7, main = "Dendrogram showing Detailed Community Structure")

Ego Network Evolvement at Individual Level

According to the findings in centralities, a professor from the Chemistry Department (whose ID is CHE18) is at the top of the lists many times and on average have collaborated with more than 40 faculties in a year. He is highly capable of scientific collaborations and thus is chosen as the ‘ego’ in the ego network visualization.

The animated network below shows the temporal change of this ego network between the fiscal year 2011 and 2013. Dark red nodes include ego himself (CHE18) and other investigators who collaborated with him in 2011. As time went by, more investigators joined collaborated proposal writing with this professor and new alters are included in the ego network. Red nodes are those investigators joined in 2012 and pink are joined in 2013. Like the previous networks, edges show the collaboration on proposal writing. Orange edges denote awarded proposals while grey edges denote unawarded proposals.

# render the animation
render.d3movie(egonet, output.mode = "htmlWidget", displaylabels = T, label.cex = 0.6, 
    label.color = "darkgrey", vertex.col = ifelse(egonet %v% "year" == "1", 
        "darkred", (ifelse(egonet %v% "year" == "2", "red", "pink"))), edge.col = ifelse(egonet %e% 
        "award" == "YES", "orange", "darkgrey"), vertex.border = "lightgrey", 
    vertex.cex = 1, usearrows = F, nodeSizeFactor = 0.05)

# timeline plot for the egonet
timeline(egonet, slice.par = slice.par, displaylabels = F, main = "Timeline Plot showing Evolvement of Ego Network", 
    edge.col = ifelse(egonet %e% "award" == "YES", "orange", "darkgrey"), vertex.col = ifelse(egonet %v% 
        "year" == "1", "darkred", (ifelse(egonet %v% "year" == "2", "red", "pink"))))

The above timeline plot further illustrated the evolvement of the ego network, showing the addition of alters and the increase of edges. The colors assigned correspond to those in the animated ego network. We can clearly see that only a few new alters are included in 2013. It could suggest that the collaboration group around this investigator is nearly fully formed by that time.