Shortest (directed or undirected) paths between vertices
shortest.paths calculates the length of all the
shortest paths from or to the vertices in the
get.shortest.paths calculates one shortest path (the
path itself, and not just its length) from or to the given vertex.
shortest.paths(graph, v=V(graph), mode = c("all", "out", "in"), weights = NULL, algorithm = c("automatic", "unweighted", "dijkstra", "bellman-ford", "johnson")) get.shortest.paths(graph, from, to=V(graph), mode = c("all", "out", "in"), weights = NULL) get.all.shortest.paths(graph, from, to = V(graph), mode = c("all", "out", "in")) average.path.length(graph, directed=TRUE, unconnected=TRUE) path.length.hist (graph, directed = TRUE, verbose = igraph.par("verbose"))
- The graph to work on.
- Numeric vector, the vertices from or to which the shortest paths will be calculated.
- Character constant, gives whether the shortest paths to or
from the given vertices should be calculated for directed graphs. If
outthen the shortest paths from the vertex, if
inthen to it will be c
- Possibly a numeric vector giving edge weights. If this
NULLand the graph has a
weightedge attribute, then the attribute is used. If this is
NAthen no weights are used (even if the graph has a
- Which algorithm to use for the calculation. By default igraph tries to select the fastest suitable algorithm. If there are no weights, then an unweighted breadth-first search is used, otherwise if all weights are positive, then Dijkstra's algo
- Numeric constant, the vertex from or to the shortest paths will be calculated. Note that right now this is not a vector of vertex ids, but only a single vertex.
- Numeric vector, only the shortest paths to these vertices will be calculated. Defaults to all vertices.
- Whether to consider directed paths in directed graphs, this argument is ignored for undirected graphs.
- What to do if the graph is unconnected (not strongly connected if directed paths are considered). If TRUE only the lengths of the existing paths are considered and averaged; if FALSE the length of the missing paths are counted having length
- Logical scalar, whether to draw a progress meter while the calculation is running.
The shortest paths (also called geodesics) are calculated by
using breath-first search in the graph. If no edge weights were
specified, then a breadth-first search is used to calculate the
shortest paths. If edge weigths are given and all of them are
non-zero, then Dijkstra's algorithm is used. Otherwise the
Bellman-Ford algorithm is used for
Please do NOT call
get.all.shortest.paths with negative edge weights, it will not
work, these functions do not use the Belmann-Ford algotithm.
shortest.paths is able to calculate the path length
from or to many vertices at the same time, but
get.shortest.paths works from one source only. This might
change in the future.
Also note that
get.shortest.paths gives only one shortest path,
however, more than one might exist between two vertices.
get.all.shortest.paths calculates all shortest paths from a
vertex to other vertices given in the
path.length.hist calculates a histogram, by calculating the
shortest path length between each pair of vertices. For directed
graphs both directions are considered, so every pair of vertices
appears twice in the histogram.
shortest.pathsa numeric matrix with
length(v)rows. The shortest path length from a vertex to itself is always zero. For unreachable vertices
get.shortest.pathsa list of length
vcount(graph). List element
icontains the vertex ids on the path from vertex
i(or the other way for directed graphs depending on the
modeargument). The vector also contains
ias the first and last elements. If
fromis the same as
ithen it is only included once. If there is no path between two vertices then a numeric vector of length zero is returned as the list element.
get.all.shortest.pathsa list is returned, each list element contains a shortest path from
fromto a vertex in
to. The shortest paths to the same vertex are collected into consecutive elements of the list. For
average.path.lengtha single number is returned.
path.length.histreturns a named list with two entries:
resis a numeric vector, the histogram of distances,
unconnectedis a numeric scalar, the number of pairs for which the first vertex is not reachable from the second. The sum of the two entries is always $n(n-1)$ for directed graphs and $n(n-1)/2$ for undirected graphs.
- Shortest path
West, D.B. (1996). Introduction to Graph Theory. Upper Saddle River, N.J.: Prentice Hall.
g <- graph.ring(10) shortest.paths(g) get.shortest.paths(g, 5) get.all.shortest.paths(g, 0, 5:7) average.path.length(g) ## Weighted shortest paths el <- matrix(nc=3, byrow=TRUE, c(0,1,0, 0,2,2, 0,3,1, 1,2,0, 1,4,5, 1,5,2, 2,1,1, 2,3,1, 2,6,1, 3,2,0, 3,6,2, 4,5,2, 4,7,8, 5,2,2, 5,6,1, 5,8,1, 5,9,3, 7,5,1, 7,8,1, 8,9,4) ) g2 <- add.edges(graph.empty(10), t(el[,1:2]), weight=el[,3]) shortest.paths(g2, mode="out")