| shortest.paths {igraph} | R Documentation |
shortest.paths calculates the length of all the
shortest paths from or to the vertices in the
network. 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)
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"))
graph |
The graph to work on. |
v |
Numeric vector, the vertices from or to which the shortest paths will be calculated. |
mode |
Character constant, gives whether the shortest paths to or
from the given vertices should be calculated for directed graphs. If
out then the shortest paths from the vertex, if
in then to it will be considered. If all, the
default, then the corresponding undirected graph will be used,
ie. not directed paths are searched. This argument is ignored for
undirected graphs. |
weights |
Possibly a numeric vector giving edge weights. If this
is NULL and the graph has a weight edge attribute,
then the attribute is used. If this is NA then no weights are
used (even if the graph has a weight attribute). |
from |
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. |
to |
Numeric vector, only the shortest paths to these vertices will be calculated. Defaults to all vertices. |
directed |
Whether to consider directed paths in directed graphs, this argument is ignored for undirected graphs. |
unconnected |
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
vcount(graph), one longer than the longest possible geodesic
in the network. |
verbose |
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 shortest.paths.
Please do NOT call get.shortest.paths and
get.all.shortest.paths with negative edge weights, it will not
work, these functions do not use the Belmann-Ford algotithm.
Note that 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 to argument.
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.
For shortest.paths a numeric matrix with vcount(graph)
columns and length(v) rows. The shortest path length from a vertex to
itself is always zero. For unreachable vertices Inf is included.
For get.shortest.paths a list of length
vcount(graph). List element i contains the vertex ids on
the path from vertex from to vertex i (or the other way
for directed graphs depending on the mode argument). The vector
also contains from and i as the first and last
elements. If from is the same as i then 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.
For get.all.shortest.paths a list is returned, each list
element contains a shortest path from from to a vertex in
to. The shortest paths to the same vertex are collected into
consecutive elements of the list.
For average.path.length a single number is returned.
path.length.hist returns a named list with two entries:
res is a numeric vector, the histogram of distances,
unconnected is 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.
Gabor Csardi csardi@rmki.kfki.hu
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")