Using R in Teaching from Network Science
Amir Barghi, Department of Mathematics and Statistics, Saint Michael’s College
Yeast Protein Interaction Network
Loading Packages
library(tidyverse)
library(igraph)
library(igraphdata)
library(ggraph)
library(latex2exp)Loading the Data Set
Data from igraphdata::yeast
Data Source: von Mering, C., Krause, R., Snel, B. et al. Comparative assessment of large-scale data sets of protein–protein interactions. Nature 417, 399–403 (2002). https://doi.org/10.1038/nature750
data(yeast)
g <- yeastV(g)## + 2617/2617 vertices, named, from 65c41bb:
## [1] YLR197W YOR039W YDR473C YOR332W YER090W YDR394W YER021W
## [8] YPR029C YIL106W YKL166C YGL026C YOR061W YGL115W YGL049C
## [15] YDL140C YLR291C YGR158C YDR328C YOL094C YDR460W YBR154C
## [22] YOR116C YIL062C YPR010C YER027C YPL093W YER006W YFR052W
## [29] YOR261C YHR052W YDR280W YOR260W YMR193W YGR162W YPR187W
## [36] YDR101C YOL041C YHR197W YBL045C YOR207C YPL259C YLL008W
## [43] YPL043W YGL220W YOR117W YOR310C YBL046W YNL002C YBR126C
## [50] YKL014C YCR077C YLR208W YHR107C YPL012W YGL237C YOR341W
## [57] YPL203W YMR049C YLR409C YMR146C YMR061W YIL112W YJL203W
## [64] YLR222C YBR251W YDL160C YLR370C YLL036C YBR135W YIL021W
## + ... omitted several verticesE(g)## + 11855/11855 edges from 65c41bb (vertex names):
## [1] YLR197W--YDL014W YOR039W--YOR061W YDR473C--YPR178W YOR332W--YLR447C
## [5] YER090W--YKL211C YDR394W--YGR232W YER021W--YPR108W YPR029C--YKL135C
## [9] YIL106W--YGR092W YKL166C--YIL033C YGL026C--YKL211C YOR061W--YGL019W
## [13] YGL115W--YER027C YGL049C--YGR162W YDR394W--YOR117W YDL140C--YML010W
## [17] YLR291C--YKR026C YGR158C--YDL111C YDR328C--YDL132W YOL094C--YNL290W
## [21] YDR460W--YPR025C YBR154C--YOR341W YBR154C--YOR116C YIL062C--YKL013C
## [25] YBR154C--YOR207C YBR154C--YPR010C YER027C--YDR477W YLR291C--YGR083C
## [29] YPL093W--YDR496C YER006W--YMR049C YER006W--YMR290C YFR052W--YHR200W
## [33] YOR261C--YFR004W YHR052W--YDR496C YDL140C--YBR154C YDR394W--YOR259C
## [37] YDR280W--YGR195W YOR260W--YDR211W YMR193W--YML009C YGR162W--YOL139C
## + ... omitted several edgescomponents(g)$no## [1] 92components(g)$csize## [1] 2375 3 5 5 7 6 4 3 5 2 7 2 2 7 3
## [16] 2 2 4 2 2 2 2 2 2 2 2 2 2 2 2
## [31] 2 4 2 2 2 2 2 5 2 2 3 2 2 3 2
## [46] 2 5 3 3 2 2 2 2 3 3 2 2 2 2 2
## [61] 2 2 2 2 2 2 2 2 2 2 2 3 5 3 3
## [76] 4 2 2 2 2 2 3 2 2 4 2 2 2 2 2
## [91] 2 2glimpse(vertex_attr(g))## List of 3
## $ name : chr [1:2617] "YLR197W" "YOR039W" "YDR473C" "YOR332W" ...
## $ Class : chr [1:2617] "T" "T" "T" "O" ...
## $ Description: chr [1:2617] "SIK1 involved in pre-rRNA processing" "CKB2 casein kinase II beta' chain" "PRP3 essential splicing factor" "VMA4 H+-ATPase V1 domain 27 KD subunit, vacuolar" ...glimpse(edge_attr(g))## List of 1
## $ Confidence: chr [1:11855] "high" "high" "high" "high" ...vertex_attr(g, name = 'Class')[1:10]## [1] "T" "T" "T" "O" "G" "F" "F" "O" "D" "C"edge_attr(g, name = 'Confidence')[1:10]## [1] "high" "high" "high" "high" "high" "high" "high" "high" "high" "high"Visualizing the Yeast Network
set.seed(42)
ggraph(g, layout = 'lgl') +
geom_edge_fan(edge_linetype = 3, color = 'dark blue', alpha = 0.25) +
geom_node_point(color = 'dark red', size = 1, alpha = 0.75) +
theme_graph(base_family = 'Helvetica') +
labs(title = 'Yeast Interaction Network',
subtitle = 'Displayed Using Layout Generator for Larger Graphs')
set.seed(42)
ggraph(g, layout = 'drl') +
geom_edge_fan(edge_linetype = 3, color = 'dark blue', alpha = 0.25) +
geom_node_point(color = 'dark red', size = 1, alpha = 0.75) +
theme_graph(base_family = 'Helvetica') +
labs(title = 'Yeast Interaction Network',
subtitle = 'Displayed Using Distributed Recursive Layout')
set.seed(42)
ggraph(g, layout = 'mds') +
geom_edge_fan(edge_linetype = 3, color = 'dark blue', alpha = 0.25) +
geom_node_point(color = 'dark red', size = 1, alpha = 0.75) +
theme_graph(base_family = 'Helvetica') +
labs(title = 'Yeast Interaction Network',
subtitle = 'Displayed Using Multidimensional Scaling Layout')
Summary Statistics of the Yeast Network
suppressMessages(df <- bind_cols(enframe(eccentricity(g)),
enframe(betweenness(g)),
enframe(degree(g)),
enframe(transitivity(g, type = c('local')))))
df <- df %>% select(name...1, value...2, value...4, value...6, value...8)
names(df) <- c('name', 'eccentricity', 'betweenness', 'degree', 'clustering')
head(df)tail(df)glimpse(df)## Rows: 2,617
## Columns: 5
## $ name <chr> "YLR197W", "YOR039W", "YDR473C", "YOR332W", "YER090W", "Y…
## $ eccentricity <dbl> 9, 9, 11, 10, 9, 8, 9, 14, 13, 9, 10, 9, 11, 9, 10, 10, 9…
## $ betweenness <dbl> 4522.729086, 1274.738111, 12293.315437, 2009.662274, 9015…
## $ degree <dbl> 40, 19, 9, 13, 21, 37, 21, 5, 6, 2, 15, 23, 5, 24, 43, 13…
## $ clustering <dbl> 0.48333333, 0.69005848, 0.77777778, 0.57692308, 0.1952381…df %>%
summarize(avg_deg = mean(degree),
delta = max(degree),
prop = sum(degree <= avg_deg) / n(),
diam = max(eccentricity),
radius = min(eccentricity),
avg_cc = mean(clustering, na.rm = TRUE),
avg_distance = mean_distance(g, directed = FALSE, unconnected = TRUE))(d <- mean_distance(g, directed = FALSE, unconnected = TRUE))## [1] 5.095629mean(distances(g))## [1] InfFig. 2.18(a) on p. 66
distance_table(g)## $res
## [1] 11855 67910 276506 670068 786151 550965 274661 114390 43508 16152
## [11] 5473 1378 306 56 16
##
## $unconnected
## [1] 603641D <- data.frame(1:length(distance_table(g)$res),
distance_table(g)$res / sum(distance_table(g)$res))
names(D) <- c('x', 'y')
D %>%
ggplot(aes(x = x, y = y)) +
geom_point() +
geom_line(aes(x = d), color = 'blue') +
labs(title = 'Distribution of Distance (Proportions) in the Yeast Network') +
labs(x = 'distance', y = 'density')
The Degree Distribution
df %>%
ggplot(aes(x = degree, y = ..density..)) +
geom_density(fill = 'red') +
labs(title = 'KDE of Degrees in the Yeast Network')
df %>%
ggplot(aes(x = degree, y = ..density..)) +
geom_histogram(binwidth = 1, fill = 'blue') +
labs(title = 'Histogram of Degrees in the Yeast Network')
df %>%
filter(degree <= 20) %>%
ggplot(aes(x = degree, y = ..density..)) +
geom_density(fill = 'red') +
labs(title = 'KDE of Degrees in the Yeast Network',
subtitle = TeX('for Nodes with Degree $\\leq 20$'))
df %>%
filter(degree <= 20) %>%
ggplot(aes(x = degree, y = ..density..)) +
geom_histogram(binwidth = 1, fill = 'blue') +
labs(title = 'Histogram of Degrees in the Yeast Network',
subtitle = TeX('for Nodes with Degree $\\leq 20$'))
Fig. 2.18(b) on p. 66
df %>%
group_by(degree) %>%
summarise(cc_deg = mean(clustering, na.rm = TRUE)) %>%
ungroup() %>%
ggplot(aes(x = degree, y = cc_deg)) +
geom_point(na.rm = TRUE, color = 'blue') +
scale_x_log10() +
scale_y_log10() +
labs(title = 'Relation Between Local Clustering Coefficient and Degree',
subtitle = 'in the Yeast Network') +
labs(x = TeX('$p_k$'), y = TeX('$C_k$'))
Local Clustering Coefficient Distribution
df %>%
ggplot(aes(x = clustering, y = ..density..)) +
geom_density(fill = 'red', na.rm = TRUE) +
labs(title = 'KDE of Local Clustering Coefficients in the Yeast Network')
df %>%
ggplot(aes(x = clustering, y = ..density..)) +
geom_histogram(binwidth = .1, fill = 'blue', na.rm = TRUE) +
labs(title = 'Histogram of Local Clustering Coefficients in the Yeast Network')
log(gorder(g)) / log(mean(df$degree))## [1] 3.570896mean_distance(g, directed = FALSE, unconnected = TRUE)## [1] 5.095629diameter(g)## [1] 15C <- mean(df$clustering, na.rm = TRUE)
M <- mean(df$degree)
df %>%
group_by(degree) %>%
summarise(cc_deg = mean(clustering)) %>%
ungroup()Fig. 3.13(d) on p. 96
df %>%
group_by(degree) %>%
summarise(cc_deg = mean(clustering)) %>%
ggplot(aes(x = degree, y = cc_deg)) +
geom_point(na.rm = TRUE, color = 'blue') +
geom_line(aes(y = C), color = 'blue') +
geom_line(aes(y = M / gorder(g)), color = 'red') +
scale_x_log10() +
scale_y_log10() +
labs(title = 'Relation Between Local Clustering Coefficient and Degree',
subtitle = 'The blue line is the average local clustering coefficient; \nthe red one is the one predicted by the random model.') +
labs(x = 'k', y = TeX('$C(k)$'))
Visualizing Other Relations with Degree
df %>%
ggplot(aes(x = degree, y = betweenness)) +
geom_point(na.rm = TRUE, size = 0.5, color = 'red') +
labs(title = 'Relationship Between Betweenness Centrality and Degree')
df %>%
ggplot(aes(x = degree, y = betweenness + 0.00000001)) +
geom_point(na.rm = TRUE, size = 0.5, color = 'red') +
scale_y_log10() +
labs(title = TeX('Relationship Between $\\log_{10}$ of Betweenness Centrality and Degree')) +
labs(y = '$\\log_{10}$(betweenness)')
df %>%
filter(betweenness > 0) %>%
ggplot(aes(x = degree, y = betweenness)) +
geom_point(na.rm = TRUE, size = 0.5, color = 'red') +
scale_y_log10() +
labs(title = TeX('Relationship Between $\\log_{10}$ of Betweenness Centrality and Degree')) +
labs(y = TeX('$\\log_{10}$(betweenness)'))
df %>%
ggplot(aes(x = degree, y = eccentricity)) +
geom_point(na.rm = TRUE, size = 0.5, color = 'orange') +
labs(title = 'Relationship Between Eccentricity and Degree')
df %>%
ggplot(aes(x = degree, y = clustering)) +
geom_point(na.rm = TRUE, size = 0.5, color = 'blue') +
labs(title = 'Relationship Between Local Clustering Coefficient and Degree')
References
- Albert-Laszlo Barabasi, Network Science, Cambridge University Press, 2016. Network Science is available online at http://networksciencebook.com/ under the following license: “This book’s text and illustrations are licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported License.”
- von Mering, C., Krause, R., Snel, B. et al. Comparative assessment of large-scale data sets of protein–protein interactions. Nature 417, 399–403 (2002). https://doi.org/10.1038/nature750