How to get the sum of edge weight from a node to a node from a graph-CodePudding

We can sum up the edge weights of the adjacent edges for each vertex using the strength function of the igraph package. Say we have a graph like the below one

Reproducible Data and Code

nodeA <- c("ID_1", "ID_2", "ID_3", "ID_4", "ID_5", "ID_16", "Node_30")
nodeB <- c("ID_11", "ID_3", "ID_4", "ID_5", "ID_3", "ID_11", "Node_3")
edge_weight <- c(0.5, 0.9, 0.8, 0.7, 0.5, 0.09, 0.7)
df_1 <- data.frame(nodeA, nodeB, edge_weight)

graph1 <- graph_from_data_frame(df_1, directed = FALSE)
E(graph2)$weight <- df_1$edge_weight
plot(graph1)

edge_strengts <- strength(graph2)

The output I am getting from strength function is the sum of edge weight from each vertex of the graph.

 ID_1    ID_2    ID_3    ID_4    ID_5   ID_16 Node_30   ID_11  Node_3 
   0.50    0.90    2.20    1.50    1.20    0.09    0.70    0.59    0.70

Now, I have an edge list and I want to get the sum of the edge weight only for those lists (instead of getting the sum of edges for one vertex). For more clarification, say I have the given edge list,

         nodeA      nodeB 
1        ID_2       ID_4  
2        ID_2       ID_5 
3        ID_1       ID_16

I want to get the sum of the edges only for the above-listed edge from the given graph (note that the graph is undirected). The output should something like this

         nodeA      nodeB    some_of_weight
1        ID_2       ID_4     1.70
2        ID_2       ID_5     1.40
3        ID_1       ID_16    0.59

For the first edge (ID_2 to ID_4) the sum is 1.70 (e.g: ID_2 to ID_3 = 0.9, and ID_3 to ID_4 = 0.8, so, 0.9 0.8 = 1.70) and so on for all edge list.

Can you tell me, how can I do this job?

CodePudding user response：

I would use the following approach:

Load packages

library(igraph)
#> 
#> Attaching package: 'igraph'
#> The following objects are masked from 'package:stats':
#> 
#>     decompose, spectrum
#> The following object is masked from 'package:base':
#> 
#>     union

Load data

nodeA <- c("ID_1", "ID_2", "ID_3", "ID_4", "ID_5", "ID_16", "Node_30")
nodeB <- c("ID_11", "ID_3", "ID_4", "ID_5", "ID_3", "ID_11", "Node_3")
df <- data.frame(nodeA, nodeB)
graph <- graph_from_data_frame(df, directed = FALSE)
E(graph)$weight <- c(0.5, 0.9, 0.8, 0.7, 0.5, 0.09, 0.7)

Estimate all pairwise distances between those nodes

all_distances <- distances(
  graph = graph, 
  v = c("ID_2", "ID_2", "ID_1"), 
  to = c("ID_4", "ID_5", "ID_16")
)

Check output

all_distances
#>      ID_4 ID_5 ID_16
#> ID_2  1.7  1.4   Inf
#> ID_2  1.7  1.4   Inf
#> ID_1  Inf  Inf  0.59

Take the diagonal

diag(all_distances)
#> [1] 1.70 1.40 0.59

Please notice that duplicated vertices in the to argument are discarded. For example:

distances(graph, v = c("ID_2", "ID_5", "ID_4"), c("ID_3", "ID_3", "ID_5"))
#> Error in distances(graph, v = c("ID_2", "ID_5", "ID_4"), c("ID_3", "ID_3", : At structural_properties.c:4461 : Duplicate vertices in `to', this is not allowed, Invalid value

In that case, you should compute the “unique” vertices and then take the relevant matches:

idx_from <- c("ID_2", "ID_5", "ID_4")
idx_to <- c("ID_3", "ID_3", "ID_5") # note the duplicated names
idx_to_unique <- unique(idx_to)
all_distances <- distances(graph, idx_from, idx_to_unique)
diag(all_distances[, match(idx_to, idx_to_unique)])
#> [1] 0.9 0.5 0.7

^{Created on 2021-11-06 by the reprex package (v2.0.1)}

CodePudding user response：

Try shortest.paths

transform(
  df_2,
  sum_of_weight = diag(shortest.paths(graph1, v, to))
)

transform(
  df_2,
  sum_of_weight = shortest.paths(graph1)[as.matrix(df_2)]
)

which gives

     v    to sum_of_weight
1 ID_2  ID_4          1.70
2 ID_2  ID_5          1.40
3 ID_1 ID_16          0.59