library(tidyverse)
library(igraph)

g <- make_lattice(c(5, 5))

ego(g, order = 1, mindist = 1)

head_of(g, E(g))

he <- ego(g, order = 1, mindist = 1, nodes = head_of(g, E(g)))
te <- ego(g, order = 1, mindist = 1, nodes = tail_of(g, E(g)))


thirdN <- map2(te, he, function(x, y){c(x,y) %>% unique %>% as.numeric()})

elSL <- as_data_frame(g) %>%
  as.tibble() %>%
  mutate(third = thirdN) %>%
  unnest() %>%
  filter(third != from,
         third != to) %>%
  mutate(fourth = ego(g, order = 1, mindist = 1, nodes = third) %>%
           map(as.numeric)) %>%
  unnest() %>%
  filter(fourth != from,
         fourth != to) %>%
  mutate(fifth = ego(g, order = 1, mindist = 1, nodes = fourth) %>%
           map(as.numeric)) %>%
  unnest() %>%
  filter(fifth != from,
         fifth != to,
         fifth != third) %>%
  apply(1, sort) %>%
  t %>%
  as.tibble() %>%
  distinct() %>%
  mutate_all(as.integer)

elY <- as_data_frame(g) %>%
  as.tibble() %>%
  mutate(third = thirdN) %>%
  unnest() %>%
  filter(third != from,
         third != to) %>%
  {
    branch <<- ego(g, order = 1, mindist = 1, nodes = .$third)
    branchData <<- mutate(., fourth = branch %>% map(as.numeric))
    branchData
  } %>%
  unnest() %>%
  filter(fourth != from,
         fourth != to) %>%
  left_join(rename(branchData, fifth = fourth)) %>%
  unnest() %>%
  filter(fifth != from,
         fifth != to,
         fifth != fourth) %>%
  apply(1, sort) %>%
  t %>%
  as.tibble() %>%
  distinct() %>%
  mutate_all(as.integer) %>%
  anti_join(elSL)

elT <- as_data_frame(g) %>%
  as.tibble() %>%
  mutate(third = thirdN) %>%
  unnest %>%
  filter(third != from,
         third != to) %>%
  left_join(rename(., fourth = third)) %>%
  filter(fourth != third) %>%
  left_join(rename(., fifth = third) %>% select(-fourth))  %>%
  filter(fifth != third,
         fifth != fourth) %>%
  apply(1, sort) %>%
  t %>%
  as.tibble() %>%
  distinct() %>%
  anti_join(elSL) %>%
  anti_join(elY) %>%
  mutate_all(as.integer)

set.seed(4)
plot(g)

saveGIF({

  ani.options(interval = 0.2)
  for (i in seq_along(elY$V1)) {
    set.seed(5)
    plot(g,
         vertex.color = ifelse(V(g) %in% unlist(elY[i,]), 'skyblue', 'pink')
    )
    title("All Y length 5")
    ani.pause()
  }}, movie.name = "Ylength5.gif", ani.width = 600, ani.height = 600)

saveGIF({
  ani.options(interval = 0.2)
  for (i in seq_along(elSL$V1)) {
    set.seed(5)
    plot(g,
         vertex.color = ifelse(V(g) %in% unlist(elSL[i,]), 'skyblue', 'pink')
    )
    title("All Straight Line length 5")
    ani.pause()
  }}, movie.name = "SLlength5.gif", ani.width = 600, ani.height = 600)

saveGIF({
  ani.options(interval = 0.2)
  for (i in seq_along(elT$V1)) {
    set.seed(5)
    plot(g,
         vertex.color = ifelse(V(g) %in% unlist(elT[i,]), 'skyblue', 'pink')
    )
    title("All T Line length 5")
    ani.pause()
  }}, movie.name = "Tlength5.gif", ani.width = 600, ani.height = 600)