summing weights of edges that are k distances from a subset of nodes in igraph

I have a complex, directed graph with 2 way movements between vertices (see below for dummy example). I am trying to generate an output that would give me the sum of edge weights that are directed to a specific set of target vertices (in the example below, vertex = "22", colored purple in the figure) & those target vertices' neighbors. I want to determine this for k1 (colored blue) and k2 (colored green) neighbors of the target vertex.

In other words, I am trying to determine, for each vertex, the sum of all "out" edge values that are directed towards the target vertices & subsequently the sum of all edge values directed towards k1 neighbours of the target vertex.

The network I have is huge (905,352 edges & 141,861 vertices), so I was hoping to solve the problem with igraph functions as I assume that is the fastest approach, but perhaps I am wrong.

library(igraph)

# create sample data for reproducible example
from   <- c(1,2,3,3,4,4,4,4,5,6,6,7,8,8,9,9,10,10,11,11,12,12,13,13,13,13,13,13,13,14,15,15)
to     <- c(13,4,7,11,2,6,11,22,4,4,14,13,13,22,13,22,13,22,3,22,5,22,1,7,8,9,10,22,15,6,13,22)
set.seed(22)
weight <-sample(2:200,length(to))

#create dataframe & convert to igraph
graph_df <- data.frame(from,to,weight)
graph <- graph_from_data_frame(graph_df)

#distance to target vertex "22"
dist <- distances(graph,v="22",mode="in",weights=NA)

ggraph(graph, layout = "graphopt") +              
  geom_edge_link(arrow = arrow(length = unit(3, 'mm')), 
                 end_cap = circle(3, 'mm'),
                 aes(width = weight), alpha = 0.8) + 
  scale_edge_width(range = c(0.1, 2)) +
  geom_node_point(aes(color=factor(-dist),size = factor(-dist))) +
  labs(edge_width = "size movement") +
  theme_graph()

The desired output would be:

vertex  1   2   3    4   5   6   7   8   9  10  11  12  13  14  15 22
k1      0   0   0  129   0   0   0  63  66 115 111 162  86   0  92  0  
k2    138  89  45  102  68 177  17 187  32  94   0   0 482   0 118  0
total 138  89 120  416  68 294  17 250  98 209 161 184 658 152 210  0

where

  k1    = sum of edge weights per  vertex on edges from k1 neighbors to target
  k2    = sum of edge weights per vertex on edges from k1 neighbors to target
  total = sum of all outgoing edge weights per vertex (i.e. the weighted out strength)

I have tried using the distances() function with weights, which gives the correct sum for k1 neighbours, but not for k2 or beyond.

distances(graph,v="22",mode="in")
#result of distances
     1   2   3   4   5   6   7  8  9  10  11  12 13  14 15 22
   224 218 156 129 197 306 103 63 66 115 111 162 86 458 92  0

I have had some luck with dplyr on the edge list dataframe via, but my assumption is there are faster ways to approach this issue:

#dataframe of k1 neighbors  & summed weight
k1<- graph_df %>%
  mutate(k1 = ifelse(to=="22",weight,NA)) %>%
  group_by(from) %>%
  summarise(total=sum(weight,na.rm=TRUE),
            k1=sum(k1,na.rm=TRUE))

#data frame of k2 neighbors & summed weight
k2 <- graph_df %>% 
  mutate(k2=ifelse(to %in% k1$from[k1$k1>0],weight,NA)) %>%
  group_by(from) %>%
  summarise(k2 =sum(k2,na.rm=TRUE)) 

#join
out <- left_join(k1,k2,by="from") %>% rename(vertex=from) 

# A tibble: 15 × 4
   vertex total    k1    k2
    <dbl> <int> <int> <int>
 1      1   138     0   138
 2      2    89     0    89
 3      3   120     0    45
 4      4   416   129   102
 5      5    68     0    68
 6      6   294     0   177
 7      7    17     0    17
 8      8   250    63   187
 9      9    98    66    32
10     10   209   115    94
11     11   161   111     0
12     12   184   162     0
13     13   658    86   482
14     14   152     0     0
15     15   210    92   118

Solution 1:

Perhaps you can try this

graph_df %>%
  group_by(from) %>%
  summarise(total = sum(weight)) %>%
  full_join(
    graph_df %>%
      filter(to %in% 22) %>%
      group_by(from) %>%
      summarise(K1 = sum(weight)) %>%
      full_join(
        graph_df %>%
          filter(to %in% neighbors(graph, "22", mode = "in")) %>%
          group_by(from) %>%
          summarise(K2 = sum(weight))
      )
  ) %>%
  arrange(from) %>%
  replace(is.na(.), 0) %>%
  rename(vertex = from)

which gives

   vertex total    K1    K2
    <dbl> <int> <int> <int>
 1      1   138     0   138
 2      2    89     0    89
 3      3   120     0    45
 4      4   416   129   102
 5      5    68     0    68
 6      6   294     0   177
 7      7    17     0    17
 8      8   250    63   187
 9      9    98    66    32
10     10   209   115    94
11     11   161   111     0
12     12   184   162     0
13     13   658    86   482
14     14   152     0     0
15     15   210    92   118