library(tidyverse)
library(datapasta)

library(igraph)
library(ggplot2)
library(ggraph)

library(cowplot)
library(graphlayouts)

library(visNetwork)
library(gganimate)

0.1 Data

In this tutorial, we will use anonymized results from the student survey, allowing us to analyse the friendship network within the course. To track the dynamics, the survey was conducted in three waves during the year. In one part of the survey, we asked students to identify their colleagues they consider their friends. We will pay special attention to the answers to this question. We will use students GPA as metadata.

source("~/noobsQA/lasi/datapasta_lasi_1.r") #datapasta directory

gpa <- gpa %>% filter(GPA1kurs <= 11) # because some NAs were set as 99

To begin with, let’s build a network based on the first wave of the survey To do this, we convert the existing data frame into a graph using the graph_from_data_frame function from the igraph package.

graph_c1w1 <- graph_from_data_frame(c1w1g[,c(3:4)])

w1 <- c1w1g %>% group_by(source_st) %>% select(source_st, Source_Program) %>% unique() %>%  summarise(program = Source_Program) %>% mutate(num = as.numeric(str_extract(source_st, "(\\d)+"))) %>% arrange(num)

w1r <- c1w1g %>% group_by(target_st) %>% select(target_st, Target_Program) %>% unique() %>%  summarise(program = Target_Program) %>% mutate(num = as.numeric(str_extract(target_st, "(\\d)+"))) %>% arrange(num)

w <- full_join(w1, w1r)

w <- left_join(w, gpa, by = c("source_st" = "un_id"))

V(graph_c1w1)$program = w$program
V(graph_c1w1)$gpa = w$GPA1kurs
ggraph(graph_c1w1) +
  geom_edge_link0(alpha = 0.3, show.legend = FALSE)+
  geom_node_point(aes(color = program ), shape = "circle", show.legend = TRUE)+
  theme_graph()

Good! However, we can make our network more informative by adding such elements as the size of nodes. For example, let’s try to add one of the centrality metrics to the plot – degree.

nodesize <- igraph::degree(graph_c1w1, mode= "in")

ggraph(graph_c1w1, layout = "fr") +
  geom_edge_link0(alpha = 0.3,   show.legend = FALSE)+
  geom_node_point(aes(color = program, size = nodesize), shape = "circle", stroke = 1, show.legend = TRUE)+
  theme_graph()

At this point, we can see that some nodes are significantly bigger than others. Obiously we want to know more information about the, so, we add labels to our nodes.

ggraph(graph_c1w1, layout = "fr") +
  geom_edge_link0(alpha = 0.3,   show.legend = FALSE)+
  geom_node_point(aes(color = program, size = nodesize), shape = "circle", stroke = 1, show.legend = TRUE)+
  geom_node_text(aes(label= name), check_overlap = T, repel = F, size = 5)+
  theme_graph()

Looks really messy, doesnt’t it? Luckily, it is easy to fix. We can labels to only those nodes who have the heighest degree. This allows us to identify the most important people within network.

ggraph(graph_c1w1, layout = "fr") +
  geom_edge_link0(alpha = 0.3,   show.legend = FALSE)+
  geom_node_point(aes(color = program, size = nodesize), shape = "circle", stroke = 1, show.legend = TRUE)+
  geom_node_text(aes(label= name, filter = ( nodesize >= 10) ), repel  = T, size = 5)+
  theme_graph()

As a next stage, we create a fixed layout which will help us to have a more stable representation of a network.

layout <- create_layout(graph = graph_c1w1, layout = 'fr')


ggraph(layout) +
  geom_edge_link0(alpha = 0.3,   show.legend = FALSE)+
  geom_node_point(aes(color = program, size = nodesize), shape = "circle", stroke = 1, show.legend = TRUE)+
  geom_node_text(aes(label= name, filter = ( nodesize >= 10) ), repel  = T, size = 5)+
  theme_graph()

Now, let’s look at different centrality metrics. There are three basic ones: betweenness, degree, and Kleinberg’s authority centrality scores.

ar = arrow(angle = 30, length = unit(2, "mm"), ends = "last", type = "open")


nodesize_btw <- betweenness(graph_c1w1)
btw <-  ggraph(layout) +
  geom_edge_link0(alpha = 0.5,  arrow = ar, show.legend = FALSE, color = "gray66")+
  geom_node_point(aes(color = nodesize_btw ),  shape = "circle", stroke = 1, show.legend = TRUE)+
  scale_colour_gradient(low="blue", high="red") +
  labs(title = "betwennes")+
  theme_graph()

nodesize_dgr <- degree(graph_c1w1, mode = "in")
dgr <-  ggraph(layout) +
  geom_edge_link0(alpha = 0.5,  arrow = ar, show.legend = FALSE, color = "gray66")+
  geom_node_point(aes(color = nodesize_dgr ),   shape = "circle", stroke = 1, show.legend = TRUE)+
  scale_colour_gradient(low="blue", high="red") +
  labs(title = "degree")+
  theme_graph()


nodesize_cnt <- centr_degree(graph_c1w1)
cnt <- ggraph(layout) +
  geom_edge_link0(alpha = 0.5,  arrow = ar, show.legend = FALSE, color = "gray66")+
  geom_node_point(aes(color = nodesize_cnt$res ),   shape = "circle", stroke = 1, show.legend = TRUE)+
  scale_colour_gradient(low="blue", high="red") +
  labs(title = "centrality")+
  theme_graph()

nodesize_aut <- authority_score(graph_c1w1)
nodesize_aut <- as.numeric(nodesize_aut$vector)
egn <- ggraph(layout) +
  geom_edge_link0(alpha = 0.5,  arrow = ar, show.legend = FALSE, color = "gray66")+
  geom_node_point(aes(color = nodesize_aut ),  shape = "circle", stroke = 1, show.legend = TRUE)+
  scale_colour_gradient(low="blue", high="red") +
  labs(title = "authority_score")+
  theme_graph()

plot_grid(btw, dgr, cnt, egn)

Your online position affects academic success, let’s look at the metric authority_score

?authority_score

If very simple, then this is a metric of access to nodes with high centrality

gpa_g <- ggraph(layout) +
  geom_edge_link0(alpha = 0.5,  arrow = ar, show.legend = FALSE, color = "gray66")+
  geom_node_point(aes(color = V(graph_c1w1)$gpa ),   shape = "circle", stroke = 1, show.legend = TRUE)+
  scale_colour_gradient(low="green", high="red") +
  labs(title = "GPA")+
  theme_graph()

authority_score <- authority_score(graph_c1w1)
authority_score <- as.numeric(authority_score$vector)
egn <- ggraph(layout) +
  geom_edge_link0(alpha = 0.5,  arrow = ar, show.legend = FALSE, color = "gray66")+
  geom_node_point(aes(color = authority_score ),  shape = "circle", stroke = 1, show.legend = TRUE)+
  scale_colour_gradient(low="green", high="red") +
  labs(title = "authority_score")+
  theme_graph()

plot_grid(gpa_g, egn)

Sometimes you want to apply custom colors to display a change in the attribute value. some examples colors and palets: + https://www.datanovia.com/en/blog/top-r-color-palettes-to-know-for-great-data-visualization/ + https://www.nceas.ucsb.edu/~frazier/RSpatialGuides/colorPaletteCheatsheet.pdf

gpa_g <- ggraph(layout) +
  geom_edge_link0(alpha = 0.5,  arrow = ar, show.legend = FALSE, color = "gray66")+
  geom_node_point(aes(color = V(graph_c1w1)$gpa ),   shape = "circle", stroke = 1, show.legend = TRUE)+
  scale_colour_gradient(low="#3A1C71", high="#FFAF7B") +
  labs(title = "GPA")+
  theme_graph()


nodesize_aut <- authority_score(graph_c1w1)
nodesize_aut <- as.numeric(nodesize_aut$vector)
egn <- ggraph(layout) +
  geom_edge_link0(alpha = 0.5,  arrow = ar, show.legend = FALSE, color = "gray66")+
  geom_node_point(aes(color = nodesize_aut ),  shape = "circle", stroke = 1, show.legend = TRUE)+
  scale_colour_gradient(low="#3A1C71",  high="#FFAF7B") +
  labs(title = "authority_score")+
  theme_graph()

plot_grid(gpa_g, egn)

It is not always possible to show two metrics on the same chart. Since a person, in principle, does not perceive much information, and unfortunately there are not enough shapes.

ggraph(layout) +
  geom_edge_link0(alpha = 0.5,  arrow = ar, show.legend = FALSE, color = "gray66")+
  geom_node_point(aes(color = V(graph_c1w1)$gpa, shape = program),stroke = 1, show.legend = TRUE)+
  scale_colour_gradient2(low="#009fff", mid = "#d3cce3", high="#ec2f4b", midpoint = 7) +
  labs(title = "GPA")+
  theme_graph()

ggraph(layout) +
  geom_edge_link0(alpha = 0.5,  arrow = ar, show.legend = FALSE, color = "gray66")+
  geom_node_point(aes(size = (gpa-5)*2, color = program), stroke = 1, show.legend = TRUE)+
  labs(title = "GPA")+
  theme_graph()

ggraph(layout) +
  geom_edge_link0(alpha = 0.5,  arrow = ar, show.legend = FALSE, color = "gray66")+
  geom_node_point(aes(size = (gpa-5)*2, shape = as.factor(gpa), color = program), stroke = 1, show.legend = TRUE)+
  labs(title = "GPA")+
  theme_graph()

In most cases, two pictures of the network look more informative. The main thing: do not forget to fix the layout.

g_gpa <-  ggraph(layout) +
  geom_edge_link0(alpha = 0.5,  arrow = ar, show.legend = FALSE, color = "gray66")+
  geom_node_point(aes(color = V(graph_c1w1)$gpa),stroke = 1, show.legend = TRUE)+
  scale_colour_gradient2(low="#009fff", mid = "#d3cce3", high="#ec2f4b", midpoint = 7) +
  labs(title = "GPA")+
  theme_graph()



g_prog <- ggraph(layout) +
  geom_edge_link0(alpha = 0.5,  arrow = ar, show.legend = FALSE, color = "gray66")+
  geom_node_point(aes(color = program ),  shape = "circle", stroke = 1, show.legend = TRUE)+
  scale_fill_brewer(palette = "Set3")+
  labs(title = "program")+
  theme_graph()

plot_grid(g_gpa, g_prog)

It is completely useless to try to display all the names, but sometimes it is important to highlight some nodes on the network. So using the filter, we will leave only students with low grades and high grades in the adjacent charts.

V(graph_c1w1)$gpa_low <- ifelse(V(graph_c1w1)$gpa == 6, 1,0.3) 
V(graph_c1w1)$gpa_high <- ifelse(V(graph_c1w1)$gpa >= 9, 1, 0.3) 
layout <- create_layout(graph = graph_c1w1, layout = 'fr')


ggraph(layout) +
  geom_edge_link0(alpha = 0.5,  arrow = ar, show.legend = FALSE, color = "gray66")+
  geom_node_point(aes(color = program, alpha = gpa_low),  shape = "circle", stroke = 1, show.legend = TRUE)+
  scale_fill_brewer(palette = "Set3")+
  labs(title = "Low gpa students")+
  theme_graph()

ggraph(layout) +
  geom_edge_link0(alpha = 0.5,  arrow = ar, show.legend = FALSE, color = "gray66")+
  geom_node_point(aes(color = program, alpha = gpa_high),  shape = "circle", stroke = 1, show.legend = TRUE)+
  scale_fill_brewer(palette = "Set3")+
  labs(title = "high gpa students")+
  theme_graph()

0.2 interactive creation of graph

There is a package to configure network visualization through a more familiar graphical interface. Install the snahelper package, load it, and then highlight any igraph object (for example graph_c1w1) with the mouse, click on the Addins tab (top panel of rstudio), and select SNAhelper from the list.

# library(snahelper)
# 
# SNAhelperGadget(graph_c1w1)

0.3 centrality, (ego network?)

Usually, most layouts show the entire structure of the network, or try to highlight the community. One example of such a mapping.

ggraph(graph_c1w1, layout = "stress")+
  geom_edge_link0(edge_colour = "grey66", arrow = ar, alpha = 0.5)+
  geom_node_point(aes(color = program, size = nodesize),shape=19)+
  geom_node_text(aes(filter = nodesize >= 10, label = name), family="serif", size = 5)+
  scale_edge_width(range = c(0.2,3))+
  scale_fill_brewer(palette = "Set3")+
  scale_size(range = c(1,6))+
  theme_graph()+
  theme(legend.position = "none")

This layout helps to focus on a specific node, look at its immediate surroundings.

w1_connected <- graph_c1w1 %>% delete.vertices(c("student 15", "student 100", "student 93", "student 143")) #connected graph is a graph without isolated nodes
nodesize_c <- degree(w1_connected, mode = "in")

ggraph(w1_connected, layout = "focus", v = 120)+ #v id of a node, not always same as a name
  geom_edge_link0(edge_colour = "grey66")+
  geom_node_point(aes(fill = program, size=nodesize_c), shape = 21)+
  scale_edge_width_continuous(range = c(0.2,1.2))+
  scale_size_continuous(range = c(1,5))+
  geom_node_text(aes(filter = (nodesize_c >= 10),size = nodesize_c+2, label = name), size = 5,
                 family = "serif")+
  scale_fill_brewer(palette = "Set3")+
  coord_fixed()+
  theme_graph()+
  theme(legend.position = "none")

Add circles to better distinguish the order of the neighborhood.

ggraph(w1_connected, layout = "focus", v = 142)+
  geom_edge_link0(edge_colour = "grey66")+
  draw_circle(col = "#00BFFF", use = "focus", max.circle = 3)+
  geom_node_point(aes(fill = program, size=gpa), shape = 21)+
  scale_edge_width_continuous(range = c(0.2,1.2))+
  scale_size_continuous(range = c(1,5))+
  geom_node_text(aes(filter = (nodesize_c >= 1),size = nodesize_c+2, label = name), size = 5,
                 family = "serif", check_overlap = T)+
  scale_fill_brewer(palette = "Set3")+
  coord_fixed()+
  theme_graph()+
  theme(legend.position = "bottom")

So a student with a low gpa is on the edge of the network, and his neighbors do not have a big degree.

ggraph(w1_connected, layout = "focus", v = 102)+
  geom_edge_link0(edge_colour = "grey66")+
  draw_circle(col = "#00BFFF", use = "focus", max.circle = 3)+
  geom_node_point(aes(fill = program, size=gpa), shape = 21)+
  scale_edge_width_continuous(range = c(0.2,1.2))+
  scale_size_continuous(range = c(1,5))+
  geom_node_text(aes(filter = (nodesize_c >= 1),size = nodesize_c+2, label = name), size = 5,
                 family = "serif", check_overlap = T)+
  scale_fill_brewer(palette = "Set3")+
  coord_fixed()+
  theme_graph()+
  theme(legend.position = "bottom")

In turn, a student with a large GPA is more included in the network, most of his friends are from the same educational program, with the same level of GPA.

0.4 dynamic

Now just run the following chunks. the data for the second and third waves of the same survey are not very well prepared there.

w2 <- graph_from_data_frame(c1w2g[,c(3:4)])
w2 = simplify(w2, remove.multiple = F, remove.loops = T) 
w3 <- graph_from_data_frame(c1w3g[,c(3:4)])
w3 = simplify(w3, remove.multiple = F, remove.loops = T)

w1s <-  degree(graph_c1w1)
w1s <- data.frame(keyName=names(w1s), row.names=NULL)


w3s <-  degree(w3)
w3s <- data.frame(keyName=names(w3s), row.names=NULL)


w2s <-  degree(w2)
w2s <- data.frame(keyName=names(w2s), row.names=NULL)



w2s <- left_join(w2s, w, by = c("keyName"="source_st"))
V(w2)$program <- w2s$program
V(w2)$gpa <- w2s$GPA1kurs
w3s <- left_join(w3s, w, by = c("keyName"="source_st"))
V(w3)$program <- w3s$program
V(w3)$gpa <- w3s$GPA1kurs

One of the solutions to the problem of isolated nodes without information in some waves is to remove them from all waves. However, here we simply add these nodes to the graphs.

comparison1 <-  setdiff(names(V(graph_c1w1)), names(V(w2)) )
comparison2 <-  setdiff(names(V(w2)), names(V(w3)) )
comparison3 <-  setdiff(names(V(w3)), names(V(graph_c1w1)) )
comparison <- c(comparison1,comparison2,comparison3)

comparison <- comparison %>% unique() %>% na.omit()
comparison <- data.frame(source_st = comparison[-22])

comparison <- left_join(comparison, w, by = c("source_st") )
comparison = comparison[,c(-3,-4)]

w1n <- data.frame(source_st = names(V(graph_c1w1)) , present = T)
w2n <- data.frame(source_st = names(V(w2)) , present = T)
w3n <- data.frame(source_st = names(V(w3)) , present = T)

right_join(w1n, comparison, by = "source_st")
w2n <-  right_join(w2n, comparison, by = "source_st")
w3n <-  right_join(w3n, comparison, by = "source_st")

w2n$present[is.na(w2n$present)] <- F
w3n$present[is.na(w3n$present)] <- F

w2n = w2n %>% filter(present == F) %>% select(-present)
w3n = w3n %>% filter(present == F )%>% select(-present)
w1_full <-  graph_c1w1


w2_full <- w2 %>% add.vertices(nrow(w2n), name = w2n$source_st, program = w2n$program, gpa = w2n$GPA1kurs) %>% delete.vertices("NA")

w3_full <- w3 %>% add.vertices(nrow(w3n), name = w3n$source_st, program = w3n$program, gpa = w3n$GPA1kurs) %>% delete.vertices("NA")

write all three networks in one list

tnet <- list(w1_full, w2_full,  w3_full)
xy <- layout_as_dynamic(tnet, alpha = 0.2)

remove the student’s words from the names of the nodes. it will be more beautiful and it takes up less space

V(w1_full)$name <- str_extract(V(w1_full)$name, "(\\d)+")
V(w2_full)$name <- str_extract(V(w2_full)$name, "(\\d)+")
V(w3_full)$name <- str_extract(V(w3_full)$name, "(\\d)+")

Due to the conflict of package versions, the function layout_as_dynamic is not recognized correctly. Therefore, we will substitute the coordinates in layout with a different algorithm in order to correctly display the positions on the charts.

l1 <-  create_layout(tnet[[1]], layout = 'grid')
l1$x <- xy[[1]][,1]
l1$y <- xy[[1]][,2]

l2 <-  create_layout(tnet[[2]], layout = 'grid')
l2$x <- xy[[2]][,1]
l2$y <- xy[[2]][,2]

l3 <-  create_layout(tnet[[3]], layout = 'grid')
l3$x <- xy[[3]][,1]
l3$y <- xy[[3]][,2]


g1degree <- degree(tnet[[1]])
g2degree <- degree(tnet[[2]])
g3degree <- degree(tnet[[3]])

g1 <-  ggraph(l1)+
  geom_edge_link0(edge_width = 0.2,edge_colour = "grey25")+
  geom_node_point(shape=21, aes(size = g1degree, fill = program))+
  theme_graph()+
  theme(legend.position = "none")+
   geom_node_text(aes(label = name, filter = ( g1degree >= 10) ), check_overlap = T, repel  = F, size = 5)+
  labs(title = paste0("Wave ", 1))


g2 <- ggraph(l2)+
  geom_edge_link0(edge_width = 0.2,edge_colour = "grey25")+
  geom_node_point(shape=21,aes(size = g2degree, fill = program))+
  theme_graph()+
  theme(legend.position = "none")+
     geom_node_text(aes(label= name, filter = ( g2degree >= 10) ), check_overlap = T, repel  = F, size = 5)+
  labs(title = paste0("Wave ", 2))



g3 <- ggraph(l3)+
  geom_edge_link0(edge_width = 0.2,edge_colour = "grey25") +
  geom_node_point(shape=21, aes(size = g3degree, fill = program))+
  theme_graph()+
  theme(legend.position = "none")+
       geom_node_text(aes(label= name, filter = ( g3degree >= 10) ), check_overlap = T, repel  = F, size = 5)+
  labs(title = paste0("Wave ", 3))


plot_grid(g1, g2, g3, ncol = 3)

since the second wave practically does not reflect changes, it can be skipped

plot_grid(g1, g3, ncol = 2)

0.5 temporal

We write all three waves in one graph

edges.w1 <- as_tibble(as_edgelist(w1_full, names = TRUE))
edges.w2 <- as_tibble(as_edgelist(w2_full, names = TRUE))
edges.w3 <- as_tibble(as_edgelist(w3_full, names = TRUE))

edges.w1$wave = 1
edges.w2$wave = 2
edges.w3$wave = 3

edges.w123 <- rbind(edges.w1, edges.w2, edges.w3)
w123 <- graph_from_data_frame(edges.w123)

nodesize123 <-  degree(w123)

w123s <- data.frame(keyName=as.numeric(names(nodesize123)))
w123s <- left_join(w123s, w, by = c("keyName"="num"))
V(w123)$program <- w123s$program
V(w123)$gpa <- w123s$GPA1kurs
V(w123)$gpa.omit <- w123s$GPA1kurs
V(w123)$gpa.omit[is.na(V(w123)$gpa.omit)] <- 5

Next, the layout will be calculated for the cumulative graph of all three waves, and the links of each wave will be displayed in their color.

nodesize123 <- degree(w123 ,mode ="in")

ggraph(w123, layout = "fr")+
  geom_edge_link0(edge_width = 0.2, aes(color = as.factor(wave))) +
  geom_node_point(aes(size = nodesize123, color = program), shape = "circle" ) +
  theme_graph()+
  theme(legend.position = "bottom")+
       geom_node_text(aes(label= name, filter =  nodesize123 >= 10 ), check_overlap = T, repel  = F, size = 5)+
  labs(title = paste0("Waves ", ""))

it is also possible to fix the nodes, and display the waves with a regular facet grid (facet_edges)

nodesize123 <- degree(w123 ,mode ="in")
V(w123)$nsize <- nodesize123


ggraph(w123, layout = "fr")+
  geom_edge_link0(edge_width = 0.2) +
  geom_node_point(shape=21, aes(fill = program, size = nsize, alpha = gpa))+
  theme_graph()+
  theme(legend.position = "bottom")+
       geom_node_text(aes(label= name, filter  = gpa.omit == 6), check_overlap = T, repel  = F, size = 5)+
  labs(title = paste0("Waves ", ""))+
  facet_edges(~ wave)

# g.waves <- create_layout(graph = w123, layout = 'fr')
# 
# # remove(gpa)
# # V(w123)$gpa
# 
# firts <- ggraph(g.waves)+
#   geom_edge_link0(edge_width = 0.2, aes( filter = wave == 1 )) +
#   geom_node_point(shape= "circle", aes(size = nodesize123, color = program))+
#   theme_graph()+
#   theme(legend.position = "bottom")+
#        geom_node_text(aes(label= name, alpha = gpa ), check_overlap = T, repel  = F, size = 5)+
#   labs(title = paste0("Wave ", 1))
# 
# second <- ggraph(g.waves)+
#   geom_edge_link0(edge_width = 0.2, aes( filter = wave == 2 )) +
#   geom_node_point(shape= "circle", aes(size = nodesize123, color = program))+
#   theme_graph()+
#   theme(legend.position = "bottom")+
#        geom_node_text(aes(label= name, alpha = gpa ), check_overlap = T, repel  = F, size = 5)+
#   labs(title = paste0("Wave ", 2))
# 
# third <- ggraph(g.waves)+
#   geom_edge_link0(edge_width = 0.2, aes( filter = wave == 3 )) +
#   geom_node_point(shape= "circle", aes(size = nodesize123, color = program))+
#   theme_graph()+
#   theme(legend.position = "bottom")+
#        geom_node_text(aes(label= name), check_overlap = T, repel  = F, size = 5)+
#   labs(title = paste0("Wave ", 3))
# 
# 
# plot_grid(firts, second, third, ncol = 3)

0.6 animation??

Sometimes if something moves, it’s better to show that something is moving.

Animation can hardly be very understandable, but it can be very spectacular.

library(gganimate)
library(gifski)

graph <- ggraph(w123, layout = "fr")+
  geom_edge_link0(edge_width = 0.2, aes(color = as.factor(wave))) +
  scale_fill_brewer(palette = "Set3")+
  geom_node_point(shape=21, aes(size = nodesize123, fill = program))+
  theme_graph()+
  theme(legend.position = "bottom")+
       geom_node_text(aes(label= name, filter =  nodesize123 >= 10 ), check_overlap = T, repel  = F, size = 5)+
  labs(title = paste0("Waves ", ""))

p <- graph +
  labs(subtitle = "Friendship in wave {trunc(frame_time)}") +
  transition_time(wave) +
  ease_aes("exponential-in-out")

# ?transition_time
# ?shadow_wake

#animate(p, fps = 25, duration = 8*3, width = 1000, height = 800)

Add the attenuation and extend the last frame a bit so that everything doesn’t break off very quickly.

p <- graph +
  labs(subtitle = "Friendship in wave {trunc(frame_time)}") +
  transition_time(wave) +
  ease_aes("exponential-in-out")+
  enter_fade() +
  exit_fade()

animate(p,end_pause = 20)

0.7 Interactive plots

visNetwork is a library for R for interactive network visualization however, the syntax is not the easiest, and based on lists. HOWEVER, it could plot igraph objects directly

library(visNetwork)

V(w1_full)$size <- g1degree *2

library(RColorBrewer)
marker = list(color = brewer.pal(nlevels(as.factor(V(w1_full)$program)), "Set3"))

ep <-  data.frame(program = V(w1_full)$program)
ep_c <- data.frame(program = unique(ep), color = marker$color)
ep <- left_join(ep, ep_c)

V(w1_full)$color <- as.character(ep$color)


# get data and plot :
# data <- toVisNetworkData(w1_full)

# visNetwork(nodes = data$nodes, edges = data$edges) %>% 
#   visNodes(size = V(w1_full)$nsize, color = V(w1_full)$program) %>%
#   visOptions(highlightNearest = list(enabled = T, hover = T), 
#              nodesIdSelection = T)

# may take a lot of time, but will allow changing parameter values through package syntax
visIgraph(w1_full)%>% 
  visNodes() %>%
  visOptions(highlightNearest = list(enabled = T, hover = T), 
             nodesIdSelection = T)
# faster, why?
---
title: "Networks <--> Education <--> Vizualization"
author: "Vsevolod Suschevskiy"
date: "`r Sys.Date()`"
linkcolor: violet
output:
  html_document:
    code_download: true
    theme: cosmo
    number_sections: true
    toc: true
    toc_depth: 4
    toc_float: true
    df_print: paged
    fig_caption: true
  pdf_document:
    toc: true
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE, warning = F, message = F)
```

```{r libraries}
library(tidyverse)
library(datapasta)

library(igraph)
library(ggplot2)
library(ggraph)

library(cowplot)
library(graphlayouts)

library(visNetwork)
library(gganimate)
```



## Data

In this tutorial, we will use anonymized results from the student survey, allowing us to analyse the friendship network within the course. To track the dynamics, the survey was conducted in three waves during the year. In one part of the survey, we asked students to identify their colleagues they consider their friends. We will pay special attention to the answers to this question. We will use students GPA as metadata. 

```{r data}
source("~/noobsQA/lasi/datapasta_lasi_1.r") #datapasta directory

gpa <- gpa %>% filter(GPA1kurs <= 11) # because some NAs were set as 99
```


To begin with, let's build a network based on the first wave of the survey To do this, we convert the existing data frame into a graph using the *graph_from_data_frame* function from the *igraph* package. 

```{r create graph}
graph_c1w1 <- graph_from_data_frame(c1w1g[,c(3:4)])

w1 <- c1w1g %>% group_by(source_st) %>% select(source_st, Source_Program) %>% unique() %>%  summarise(program = Source_Program) %>% mutate(num = as.numeric(str_extract(source_st, "(\\d)+"))) %>% arrange(num)

w1r <- c1w1g %>% group_by(target_st) %>% select(target_st, Target_Program) %>% unique() %>%  summarise(program = Target_Program) %>% mutate(num = as.numeric(str_extract(target_st, "(\\d)+"))) %>% arrange(num)

w <- full_join(w1, w1r)

w <- left_join(w, gpa, by = c("source_st" = "un_id"))

V(graph_c1w1)$program = w$program
V(graph_c1w1)$gpa = w$GPA1kurs

```



```{r basic plot}
ggraph(graph_c1w1) +
  geom_edge_link0(alpha = 0.3, show.legend = FALSE)+
  geom_node_point(aes(color = program ), shape = "circle", show.legend = TRUE)+
  theme_graph()
```

Good! However, we can make our network more informative by adding such elements as the size of nodes. For example, let's try to add one of the centrality metrics to the plot -- *degree*. 


```{r degree}
nodesize <- igraph::degree(graph_c1w1, mode= "in")

ggraph(graph_c1w1, layout = "fr") +
  geom_edge_link0(alpha = 0.3,   show.legend = FALSE)+
  geom_node_point(aes(color = program, size = nodesize), shape = "circle", stroke = 1, show.legend = TRUE)+
  theme_graph()
```

At this point, we can see that some nodes are significantly bigger than others. Obiously we want to know more information about the, so, we add labels to our nodes.

```{r names}
ggraph(graph_c1w1, layout = "fr") +
  geom_edge_link0(alpha = 0.3,   show.legend = FALSE)+
  geom_node_point(aes(color = program, size = nodesize), shape = "circle", stroke = 1, show.legend = TRUE)+
  geom_node_text(aes(label= name), check_overlap = T, repel = F, size = 5)+
  theme_graph()
```

Looks really messy, doesnt't it? Luckily, it is easy to fix. We can labels to only those nodes who have the heighest degree. This allows us to identify the most important people within network.

```{r names and filter}
ggraph(graph_c1w1, layout = "fr") +
  geom_edge_link0(alpha = 0.3,   show.legend = FALSE)+
  geom_node_point(aes(color = program, size = nodesize), shape = "circle", stroke = 1, show.legend = TRUE)+
  geom_node_text(aes(label= name, filter = ( nodesize >= 10) ), repel  = T, size = 5)+
  theme_graph()
```

As a next stage, we create a fixed layout which will help us to have a more stable representation of a network.

```{r layout}
layout <- create_layout(graph = graph_c1w1, layout = 'fr')


ggraph(layout) +
  geom_edge_link0(alpha = 0.3,   show.legend = FALSE)+
  geom_node_point(aes(color = program, size = nodesize), shape = "circle", stroke = 1, show.legend = TRUE)+
  geom_node_text(aes(label= name, filter = ( nodesize >= 10) ), repel  = T, size = 5)+
  theme_graph()
```

Now, let's look at different centrality metrics. There are three basic ones: *betweenness*, *degree*, and *Kleinberg's authority centrality scores*.

```{r different metrics}
ar = arrow(angle = 30, length = unit(2, "mm"), ends = "last", type = "open")


nodesize_btw <- betweenness(graph_c1w1)
btw <-  ggraph(layout) +
  geom_edge_link0(alpha = 0.5,  arrow = ar, show.legend = FALSE, color = "gray66")+
  geom_node_point(aes(color = nodesize_btw ),  shape = "circle", stroke = 1, show.legend = TRUE)+
  scale_colour_gradient(low="blue", high="red") +
  labs(title = "betwennes")+
  theme_graph()

nodesize_dgr <- degree(graph_c1w1, mode = "in")
dgr <-  ggraph(layout) +
  geom_edge_link0(alpha = 0.5,  arrow = ar, show.legend = FALSE, color = "gray66")+
  geom_node_point(aes(color = nodesize_dgr ),   shape = "circle", stroke = 1, show.legend = TRUE)+
  scale_colour_gradient(low="blue", high="red") +
  labs(title = "degree")+
  theme_graph()


nodesize_cnt <- centr_degree(graph_c1w1)
cnt <- ggraph(layout) +
  geom_edge_link0(alpha = 0.5,  arrow = ar, show.legend = FALSE, color = "gray66")+
  geom_node_point(aes(color = nodesize_cnt$res ),   shape = "circle", stroke = 1, show.legend = TRUE)+
  scale_colour_gradient(low="blue", high="red") +
  labs(title = "centrality")+
  theme_graph()

nodesize_aut <- authority_score(graph_c1w1)
nodesize_aut <- as.numeric(nodesize_aut$vector)
egn <- ggraph(layout) +
  geom_edge_link0(alpha = 0.5,  arrow = ar, show.legend = FALSE, color = "gray66")+
  geom_node_point(aes(color = nodesize_aut ),  shape = "circle", stroke = 1, show.legend = TRUE)+
  scale_colour_gradient(low="blue", high="red") +
  labs(title = "authority_score")+
  theme_graph()

plot_grid(btw, dgr, cnt, egn)

```

Your online position affects academic success, let's look at the metric authority_score

```{r authority_score}
?authority_score
```

If very simple, then this is a metric of access to nodes with high centrality

```{r gpa and hub}

gpa_g <- ggraph(layout) +
  geom_edge_link0(alpha = 0.5,  arrow = ar, show.legend = FALSE, color = "gray66")+
  geom_node_point(aes(color = V(graph_c1w1)$gpa ),   shape = "circle", stroke = 1, show.legend = TRUE)+
  scale_colour_gradient(low="green", high="red") +
  labs(title = "GPA")+
  theme_graph()

authority_score <- authority_score(graph_c1w1)
authority_score <- as.numeric(authority_score$vector)
egn <- ggraph(layout) +
  geom_edge_link0(alpha = 0.5,  arrow = ar, show.legend = FALSE, color = "gray66")+
  geom_node_point(aes(color = authority_score ),  shape = "circle", stroke = 1, show.legend = TRUE)+
  scale_colour_gradient(low="green", high="red") +
  labs(title = "authority_score")+
  theme_graph()

plot_grid(gpa_g, egn)
```

Sometimes you want to apply custom colors to display a change in the attribute value.
some examples colors and palets:
+ https://www.datanovia.com/en/blog/top-r-color-palettes-to-know-for-great-data-visualization/
+ https://www.nceas.ucsb.edu/~frazier/RSpatialGuides/colorPaletteCheatsheet.pdf

```{r nice colour}
gpa_g <- ggraph(layout) +
  geom_edge_link0(alpha = 0.5,  arrow = ar, show.legend = FALSE, color = "gray66")+
  geom_node_point(aes(color = V(graph_c1w1)$gpa ),   shape = "circle", stroke = 1, show.legend = TRUE)+
  scale_colour_gradient(low="#3A1C71", high="#FFAF7B") +
  labs(title = "GPA")+
  theme_graph()


nodesize_aut <- authority_score(graph_c1w1)
nodesize_aut <- as.numeric(nodesize_aut$vector)
egn <- ggraph(layout) +
  geom_edge_link0(alpha = 0.5,  arrow = ar, show.legend = FALSE, color = "gray66")+
  geom_node_point(aes(color = nodesize_aut ),  shape = "circle", stroke = 1, show.legend = TRUE)+
  scale_colour_gradient(low="#3A1C71",  high="#FFAF7B") +
  labs(title = "authority_score")+
  theme_graph()

plot_grid(gpa_g, egn)
```
It is not always possible to show two metrics on the same chart. Since a person, in principle, does not perceive much information, and unfortunately there are not enough shapes.

```{r gpa and program (BAD)}

ggraph(layout) +
  geom_edge_link0(alpha = 0.5,  arrow = ar, show.legend = FALSE, color = "gray66")+
  geom_node_point(aes(color = V(graph_c1w1)$gpa, shape = program),stroke = 1, show.legend = TRUE)+
  scale_colour_gradient2(low="#009fff", mid = "#d3cce3", high="#ec2f4b", midpoint = 7) +
  labs(title = "GPA")+
  theme_graph()

ggraph(layout) +
  geom_edge_link0(alpha = 0.5,  arrow = ar, show.legend = FALSE, color = "gray66")+
  geom_node_point(aes(size = (gpa-5)*2, color = program), stroke = 1, show.legend = TRUE)+
  labs(title = "GPA")+
  theme_graph()

ggraph(layout) +
  geom_edge_link0(alpha = 0.5,  arrow = ar, show.legend = FALSE, color = "gray66")+
  geom_node_point(aes(size = (gpa-5)*2, shape = as.factor(gpa), color = program), stroke = 1, show.legend = TRUE)+
  labs(title = "GPA")+
  theme_graph()
```

In most cases, two pictures of the network look more informative. The main thing: do not forget to fix the layout.

```{r 2 plots for gpa and }

g_gpa <-  ggraph(layout) +
  geom_edge_link0(alpha = 0.5,  arrow = ar, show.legend = FALSE, color = "gray66")+
  geom_node_point(aes(color = V(graph_c1w1)$gpa),stroke = 1, show.legend = TRUE)+
  scale_colour_gradient2(low="#009fff", mid = "#d3cce3", high="#ec2f4b", midpoint = 7) +
  labs(title = "GPA")+
  theme_graph()



g_prog <- ggraph(layout) +
  geom_edge_link0(alpha = 0.5,  arrow = ar, show.legend = FALSE, color = "gray66")+
  geom_node_point(aes(color = program ),  shape = "circle", stroke = 1, show.legend = TRUE)+
  scale_fill_brewer(palette = "Set3")+
  labs(title = "program")+
  theme_graph()

plot_grid(g_gpa, g_prog)

```

It is completely useless to try to display all the names, but sometimes it is important to highlight some nodes on the network. So using the filter, we will leave only students with low grades and high grades in the adjacent charts.

```{r filter and alpha}

V(graph_c1w1)$gpa_low <- ifelse(V(graph_c1w1)$gpa == 6, 1,0.3) 
V(graph_c1w1)$gpa_high <- ifelse(V(graph_c1w1)$gpa >= 9, 1, 0.3) 
layout <- create_layout(graph = graph_c1w1, layout = 'fr')


ggraph(layout) +
  geom_edge_link0(alpha = 0.5,  arrow = ar, show.legend = FALSE, color = "gray66")+
  geom_node_point(aes(color = program, alpha = gpa_low),  shape = "circle", stroke = 1, show.legend = TRUE)+
  scale_fill_brewer(palette = "Set3")+
  labs(title = "Low gpa students")+
  theme_graph()

ggraph(layout) +
  geom_edge_link0(alpha = 0.5,  arrow = ar, show.legend = FALSE, color = "gray66")+
  geom_node_point(aes(color = program, alpha = gpa_high),  shape = "circle", stroke = 1, show.legend = TRUE)+
  scale_fill_brewer(palette = "Set3")+
  labs(title = "high gpa students")+
  theme_graph()
```

## interactive creation of graph

There is a package to configure network visualization through a more familiar graphical interface. Install the snahelper package, load it, and then highlight any igraph object (for example graph_c1w1) with the mouse, click on the Addins tab (top panel of rstudio), and select __SNAhelper__ from the list.

```{r snahelper plot ui}
# library(snahelper)
# 
# SNAhelperGadget(graph_c1w1)
```

## centrality, (ego network?)

Usually, most layouts show the entire structure of the network, or try to highlight the community. One example of such a mapping.

```{r stress}
ggraph(graph_c1w1, layout = "stress")+
  geom_edge_link0(edge_colour = "grey66", arrow = ar, alpha = 0.5)+
  geom_node_point(aes(color = program, size = nodesize),shape=19)+
  geom_node_text(aes(filter = nodesize >= 10, label = name), family="serif", size = 5)+
  scale_edge_width(range = c(0.2,3))+
  scale_fill_brewer(palette = "Set3")+
  scale_size(range = c(1,6))+
  theme_graph()+
  theme(legend.position = "none")
```

This layout helps to __focus__ on a specific node, look at its immediate surroundings.

```{r}
w1_connected <- graph_c1w1 %>% delete.vertices(c("student 15", "student 100", "student 93", "student 143")) #connected graph is a graph without isolated nodes
nodesize_c <- degree(w1_connected, mode = "in")

ggraph(w1_connected, layout = "focus", v = 120)+ #v id of a node, not always same as a name
  geom_edge_link0(edge_colour = "grey66")+
  geom_node_point(aes(fill = program, size=nodesize_c), shape = 21)+
  scale_edge_width_continuous(range = c(0.2,1.2))+
  scale_size_continuous(range = c(1,5))+
  geom_node_text(aes(filter = (nodesize_c >= 10),size = nodesize_c+2, label = name), size = 5,
                 family = "serif")+
  scale_fill_brewer(palette = "Set3")+
  coord_fixed()+
  theme_graph()+
  theme(legend.position = "none")
```

Add circles to better distinguish the order of the neighborhood.

```{r low gpa centered}
ggraph(w1_connected, layout = "focus", v = 142)+
  geom_edge_link0(edge_colour = "grey66")+
  draw_circle(col = "#00BFFF", use = "focus", max.circle = 3)+
  geom_node_point(aes(fill = program, size=gpa), shape = 21)+
  scale_edge_width_continuous(range = c(0.2,1.2))+
  scale_size_continuous(range = c(1,5))+
  geom_node_text(aes(filter = (nodesize_c >= 1),size = nodesize_c+2, label = name), size = 5,
                 family = "serif", check_overlap = T)+
  scale_fill_brewer(palette = "Set3")+
  coord_fixed()+
  theme_graph()+
  theme(legend.position = "bottom")
```

So a student with a low gpa is on the edge of the network, and his neighbors do not have a big degree.

```{r high centered}
ggraph(w1_connected, layout = "focus", v = 102)+
  geom_edge_link0(edge_colour = "grey66")+
  draw_circle(col = "#00BFFF", use = "focus", max.circle = 3)+
  geom_node_point(aes(fill = program, size=gpa), shape = 21)+
  scale_edge_width_continuous(range = c(0.2,1.2))+
  scale_size_continuous(range = c(1,5))+
  geom_node_text(aes(filter = (nodesize_c >= 1),size = nodesize_c+2, label = name), size = 5,
                 family = "serif", check_overlap = T)+
  scale_fill_brewer(palette = "Set3")+
  coord_fixed()+
  theme_graph()+
  theme(legend.position = "bottom")
```

In turn, a student with a large GPA is more included in the network, most of his friends are from the same educational program, with the same level of GPA.


## dynamic 

Now just run the following chunks. the data for the second and third waves of the same survey are not very well prepared there.

```{r two last waves ignore plz}


w2 <- graph_from_data_frame(c1w2g[,c(3:4)])
w2 = simplify(w2, remove.multiple = F, remove.loops = T) 
w3 <- graph_from_data_frame(c1w3g[,c(3:4)])
w3 = simplify(w3, remove.multiple = F, remove.loops = T)

w1s <-  degree(graph_c1w1)
w1s <- data.frame(keyName=names(w1s), row.names=NULL)


w3s <-  degree(w3)
w3s <- data.frame(keyName=names(w3s), row.names=NULL)


w2s <-  degree(w2)
w2s <- data.frame(keyName=names(w2s), row.names=NULL)



w2s <- left_join(w2s, w, by = c("keyName"="source_st"))
V(w2)$program <- w2s$program
V(w2)$gpa <- w2s$GPA1kurs
w3s <- left_join(w3s, w, by = c("keyName"="source_st"))
V(w3)$program <- w3s$program
V(w3)$gpa <- w3s$GPA1kurs
```

One of the solutions to the problem of isolated nodes without information in some waves is to remove them from all waves. However, here we simply add these nodes to the graphs.

```{r missings ignore x2}
comparison1 <-  setdiff(names(V(graph_c1w1)), names(V(w2)) )
comparison2 <-  setdiff(names(V(w2)), names(V(w3)) )
comparison3 <-  setdiff(names(V(w3)), names(V(graph_c1w1)) )
comparison <- c(comparison1,comparison2,comparison3)

comparison <- comparison %>% unique() %>% na.omit()
comparison <- data.frame(source_st = comparison[-22])

comparison <- left_join(comparison, w, by = c("source_st") )
comparison = comparison[,c(-3,-4)]

w1n <- data.frame(source_st = names(V(graph_c1w1)) , present = T)
w2n <- data.frame(source_st = names(V(w2)) , present = T)
w3n <- data.frame(source_st = names(V(w3)) , present = T)

right_join(w1n, comparison, by = "source_st")
w2n <-  right_join(w2n, comparison, by = "source_st")
w3n <-  right_join(w3n, comparison, by = "source_st")

w2n$present[is.na(w2n$present)] <- F
w3n$present[is.na(w3n$present)] <- F

w2n = w2n %>% filter(present == F) %>% select(-present)
w3n = w3n %>% filter(present == F )%>% select(-present)
```

```{r add missings to nets}
w1_full <-  graph_c1w1


w2_full <- w2 %>% add.vertices(nrow(w2n), name = w2n$source_st, program = w2n$program, gpa = w2n$GPA1kurs) %>% delete.vertices("NA")

w3_full <- w3 %>% add.vertices(nrow(w3n), name = w3n$source_st, program = w3n$program, gpa = w3n$GPA1kurs) %>% delete.vertices("NA")
```

write all three networks in one list

```{r networks to list}
tnet <- list(w1_full, w2_full,  w3_full)
xy <- layout_as_dynamic(tnet, alpha = 0.2)
```

remove the student’s words from the names of the nodes. it will be more beautiful and it takes up less space

```{r remove word student}
V(w1_full)$name <- str_extract(V(w1_full)$name, "(\\d)+")
V(w2_full)$name <- str_extract(V(w2_full)$name, "(\\d)+")
V(w3_full)$name <- str_extract(V(w3_full)$name, "(\\d)+")
```

Due to the conflict of package versions, the function layout_as_dynamic is not recognized correctly. Therefore, we will substitute the coordinates in layout with a different algorithm in order to correctly display the positions on the charts.

```{r masking layout with new coordinates}
l1 <-  create_layout(tnet[[1]], layout = 'grid')
l1$x <- xy[[1]][,1]
l1$y <- xy[[1]][,2]

l2 <-  create_layout(tnet[[2]], layout = 'grid')
l2$x <- xy[[2]][,1]
l2$y <- xy[[2]][,2]

l3 <-  create_layout(tnet[[3]], layout = 'grid')
l3$x <- xy[[3]][,1]
l3$y <- xy[[3]][,2]


g1degree <- degree(tnet[[1]])
g2degree <- degree(tnet[[2]])
g3degree <- degree(tnet[[3]])

g1 <-  ggraph(l1)+
  geom_edge_link0(edge_width = 0.2,edge_colour = "grey25")+
  geom_node_point(shape=21, aes(size = g1degree, fill = program))+
  theme_graph()+
  theme(legend.position = "none")+
   geom_node_text(aes(label = name, filter = ( g1degree >= 10) ), check_overlap = T, repel  = F, size = 5)+
  labs(title = paste0("Wave ", 1))


g2 <- ggraph(l2)+
  geom_edge_link0(edge_width = 0.2,edge_colour = "grey25")+
  geom_node_point(shape=21,aes(size = g2degree, fill = program))+
  theme_graph()+
  theme(legend.position = "none")+
     geom_node_text(aes(label= name, filter = ( g2degree >= 10) ), check_overlap = T, repel  = F, size = 5)+
  labs(title = paste0("Wave ", 2))



g3 <- ggraph(l3)+
  geom_edge_link0(edge_width = 0.2,edge_colour = "grey25") +
  geom_node_point(shape=21, aes(size = g3degree, fill = program))+
  theme_graph()+
  theme(legend.position = "none")+
       geom_node_text(aes(label= name, filter = ( g3degree >= 10) ), check_overlap = T, repel  = F, size = 5)+
  labs(title = paste0("Wave ", 3))


plot_grid(g1, g2, g3, ncol = 3)
```

since the second wave practically does not reflect changes, it can be skipped

```{r scince second is not really different}
plot_grid(g1, g3, ncol = 2)
```

## temporal

We write all three waves in one graph

```{r merge waves}
edges.w1 <- as_tibble(as_edgelist(w1_full, names = TRUE))
edges.w2 <- as_tibble(as_edgelist(w2_full, names = TRUE))
edges.w3 <- as_tibble(as_edgelist(w3_full, names = TRUE))

edges.w1$wave = 1
edges.w2$wave = 2
edges.w3$wave = 3

edges.w123 <- rbind(edges.w1, edges.w2, edges.w3)
w123 <- graph_from_data_frame(edges.w123)

nodesize123 <-  degree(w123)

w123s <- data.frame(keyName=as.numeric(names(nodesize123)))
w123s <- left_join(w123s, w, by = c("keyName"="num"))
V(w123)$program <- w123s$program
V(w123)$gpa <- w123s$GPA1kurs
V(w123)$gpa.omit <- w123s$GPA1kurs
V(w123)$gpa.omit[is.na(V(w123)$gpa.omit)] <- 5
```

Next, the layout will be calculated for the cumulative graph of all three waves, and the links of each wave will be displayed in their color.

```{r plot 123}
nodesize123 <- degree(w123 ,mode ="in")

ggraph(w123, layout = "fr")+
  geom_edge_link0(edge_width = 0.2, aes(color = as.factor(wave))) +
  geom_node_point(aes(size = nodesize123, color = program), shape = "circle" ) +
  theme_graph()+
  theme(legend.position = "bottom")+
       geom_node_text(aes(label= name, filter =  nodesize123 >= 10 ), check_overlap = T, repel  = F, size = 5)+
  labs(title = paste0("Waves ", ""))

```

it is also possible to fix the nodes, and display the waves with a regular facet grid (_facet_edges_)

```{r facet grid}

nodesize123 <- degree(w123 ,mode ="in")
V(w123)$nsize <- nodesize123


ggraph(w123, layout = "fr")+
  geom_edge_link0(edge_width = 0.2) +
  geom_node_point(shape=21, aes(fill = program, size = nsize, alpha = gpa))+
  theme_graph()+
  theme(legend.position = "bottom")+
       geom_node_text(aes(label= name, filter  = gpa.omit == 6), check_overlap = T, repel  = F, size = 5)+
  labs(title = paste0("Waves ", ""))+
  facet_edges(~ wave)

```



```{r waves}
# g.waves <- create_layout(graph = w123, layout = 'fr')
# 
# # remove(gpa)
# # V(w123)$gpa
# 
# firts <- ggraph(g.waves)+
#   geom_edge_link0(edge_width = 0.2, aes( filter = wave == 1 )) +
#   geom_node_point(shape= "circle", aes(size = nodesize123, color = program))+
#   theme_graph()+
#   theme(legend.position = "bottom")+
#        geom_node_text(aes(label= name, alpha = gpa ), check_overlap = T, repel  = F, size = 5)+
#   labs(title = paste0("Wave ", 1))
# 
# second <- ggraph(g.waves)+
#   geom_edge_link0(edge_width = 0.2, aes( filter = wave == 2 )) +
#   geom_node_point(shape= "circle", aes(size = nodesize123, color = program))+
#   theme_graph()+
#   theme(legend.position = "bottom")+
#        geom_node_text(aes(label= name, alpha = gpa ), check_overlap = T, repel  = F, size = 5)+
#   labs(title = paste0("Wave ", 2))
# 
# third <- ggraph(g.waves)+
#   geom_edge_link0(edge_width = 0.2, aes( filter = wave == 3 )) +
#   geom_node_point(shape= "circle", aes(size = nodesize123, color = program))+
#   theme_graph()+
#   theme(legend.position = "bottom")+
#        geom_node_text(aes(label= name), check_overlap = T, repel  = F, size = 5)+
#   labs(title = paste0("Wave ", 3))
# 
# 
# plot_grid(firts, second, third, ncol = 3)
```

## animation??

Sometimes if something moves, it’s better to show that something is moving.

Animation can hardly be very understandable, but it can be very spectacular.

```{r animation}
library(gganimate)
library(gifski)

graph <- ggraph(w123, layout = "fr")+
  geom_edge_link0(edge_width = 0.2, aes(color = as.factor(wave))) +
  scale_fill_brewer(palette = "Set3")+
  geom_node_point(shape=21, aes(size = nodesize123, fill = program))+
  theme_graph()+
  theme(legend.position = "bottom")+
       geom_node_text(aes(label= name, filter =  nodesize123 >= 10 ), check_overlap = T, repel  = F, size = 5)+
  labs(title = paste0("Waves ", ""))

p <- graph +
  labs(subtitle = "Friendship in wave {trunc(frame_time)}") +
  transition_time(wave) +
  ease_aes("exponential-in-out")

# ?transition_time
# ?shadow_wake

#animate(p, fps = 25, duration = 8*3, width = 1000, height = 800) 
```

Add the attenuation and extend the last frame a bit so that everything doesn't break off very quickly.

```{r animation wit a fade}
p <- graph +
  labs(subtitle = "Friendship in wave {trunc(frame_time)}") +
  transition_time(wave) +
  ease_aes("exponential-in-out")+
  enter_fade() +
  exit_fade()

animate(p,end_pause = 20)
```

## Interactive plots

visNetwork is a library for R for interactive network visualization
however, the syntax is not the easiest, and based on lists. 
HOWEVER, it could plot igraph objects directly

```{r interactive}
library(visNetwork)

V(w1_full)$size <- g1degree *2

library(RColorBrewer)
marker = list(color = brewer.pal(nlevels(as.factor(V(w1_full)$program)), "Set3"))

ep <-  data.frame(program = V(w1_full)$program)
ep_c <- data.frame(program = unique(ep), color = marker$color)
ep <- left_join(ep, ep_c)

V(w1_full)$color <- as.character(ep$color)


# get data and plot :
# data <- toVisNetworkData(w1_full)

# visNetwork(nodes = data$nodes, edges = data$edges) %>% 
#   visNodes(size = V(w1_full)$nsize, color = V(w1_full)$program) %>%
#   visOptions(highlightNearest = list(enabled = T, hover = T), 
#              nodesIdSelection = T)

# may take a lot of time, but will allow changing parameter values through package syntax
```

```{r directly}

visIgraph(w1_full)%>% 
  visNodes() %>%
  visOptions(highlightNearest = list(enabled = T, hover = T), 
             nodesIdSelection = T)

# faster, why?
```

