how to check if there exists a unique shortest path between two vertices in igraph

问题

I'd like to identify if there exist a unique shortest path or multiple shortest paths between two vertices with igraph. If I use length(all_shortest_paths(g, i,j), that actually helps me, but I feel like there are so many redundant operations. I rather prefer first to get one shortest path with get.shortest.paths(g, i,j), and then see if there is another. However, I could not figure out how to do this.

Can someone help me how to identify whether there is another shortest path different than the first one obtained by get.shortest.paths(g, i,j)?

Here is an example graph

library(igraph)
data <- read.table(text="
1 2
1 4
1 5
2 3
2 4
3 4
5 7
5 8
3 6", header=FALSE)
gmatrix <- data.matrix(data, rownames.force = NA) #convert into a matrix to use in igraph
g <- graph_from_edgelist(gmatrix, directed = FALSE)

For instance, if I'd like to find the shortest path from 1 to 3, I use all_shortest_paths(g, 1,3), and it gives me the following result.

$res
$res[[1]]
+ 3/9 vertices, from 634c426:
[1] 1 4 3

$res[[2]]
+ 3/9 vertices, from 634c426:
[1] 1 2 3

What I want is to get the first shortest path. For instance

get.shortest.paths(g, 1,3)
$vpath
$vpath[[1]]
+ 3/9 vertices, from 634c426:
[1] 1 2 3

Now, I want to see if there is any other path different than [1] 1 2 3. In a larger graph, since there are tens of possible shortest paths, I don't want to use all_shortest_paths(g, i,j) to make that query.

Overall, my question is: how can I check whether there exists a unique shortest path between two vertices or not? I will give two vertices as my input, in return I should get TRUE or FALSE indicating if there is a unique shortest path.

回答1:

After getting responded for How to assign edge weights to certain edges in R igraph, here is one solution. Please note that the initial network is an undirected graph with no edge weights.

p <- get.shortest.paths(g, i, j)$vpath[[1]] #shortest path between node i and node j
g <- set_edge_attr(g, "weight", value = ifelse(E(g) %in% E(g, path = p), 1.50, 1)) #Assign slightly larger edge weights to the edges existing in path p
q <- get.shortest.paths(g, i,j , weights = E(g)$weight)$vpath[[1]] #recalculate the shortest path with edge weights
g <- delete_edge_attr(g, "weight")
if(all(p %in% q))
#If paths p and q are the same, then the shortest path is unique

However, this is definitely not a good solution due to the high running time. When I try this method for 400 nodes, it takes several minutes to stop.

来源：https://stackoverflow.com/questions/57529808/how-to-check-if-there-exists-a-unique-shortest-path-between-two-vertices-in-igra

标签

igraph

graph-theory

shortest-path