distances calculates the length of all the shortest paths from
or to the vertices in the network. shortest_paths calculates one
shortest path (the path itself, and not just its length) from or to the
given vertex.
distance_table(graph, directed = TRUE)mean_distance(
graph,
weights = NULL,
directed = TRUE,
unconnected = TRUE,
details = FALSE
)
distances(
graph,
v = V(graph),
to = V(graph),
mode = c("all", "out", "in"),
weights = NULL,
algorithm = c("automatic", "unweighted", "dijkstra", "bellman-ford", "johnson")
)
shortest_paths(
graph,
from,
to = V(graph),
mode = c("out", "all", "in"),
weights = NULL,
output = c("vpath", "epath", "both"),
predecessors = FALSE,
inbound.edges = FALSE,
algorithm = c("automatic", "unweighted", "dijkstra", "bellman-ford")
)
all_shortest_paths(
graph,
from,
to = V(graph),
mode = c("out", "all", "in"),
weights = NULL
)
For distances a numeric matrix with length(to)
columns and length(v) rows. The shortest path length from a vertex to
itself is always zero. For unreachable vertices Inf is included.
For shortest_paths a named list with four entries is returned:
This itself is a list, of length length(to); list
element i contains the vertex ids on the path from vertex from
to vertex to[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. If this
output is not requested in the output argument, then it will be
NULL.
This is a list similar to vpath, but the
vectors of the list contain the edge ids along the shortest paths, instead
of the vertex ids. This entry is set to NULL if it is not requested
in the output argument.
Numeric vector, the
predecessor of each vertex in the to argument, or NULL if it
was not requested.
Numeric vector, the inbound edge
for each vertex, or NULL, if it was not requested.
For 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 mean_distance a single number is returned if details=FALSE,
or a named list with two entries: res is the mean distance as a numeric
scalar and unconnected is the number of unconnected vertex pairs,
also as a numeric scalar.
distance_table 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.
The graph to work on.
Whether to consider directed paths in directed graphs, this argument is ignored for undirected graphs.
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).
What to do if the graph is unconnected (not trongly 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 considered as having infinite length, making the mean distance infinite as well.
Whether to provide additional details in the result.
Functions accepting this argument (like mean_distance) return
additional information like the number of disconnected vertex pairs in
the result when this parameter is set to TRUE.
Numeric vector, the vertices from which the shortest paths will be calculated.
Numeric vector, the vertices to which the shortest paths will be
calculated. By default it includes all vertices. Note that for
distances every vertex must be included here at most once. (This
is not required for shortest_paths.
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.
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 algorithm is used. If there are negative weights and we do the calculation for more than 100 sources, then Johnson's algorithm is used. Otherwise the Bellman-Ford algorithm is used. You can override igraph's choice by explicitly giving this parameter. Note that the igraph C core might still override your choice in obvious cases, i.e. if there are no edge weights, then the unweighted algorithm will be used, regardless of this argument.
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.
Character scalar, defines how to report the shortest paths. “vpath” means that the vertices along the paths are reported, this form was used prior to igraph version 0.6. “epath” means that the edges along the paths are reported. “both” means that both forms are returned, in a named list with components “vpath” and “epath”.
Logical scalar, whether to return the predecessor vertex
for each vertex. The predecessor of vertex i in the tree is the
vertex from which vertex i was reached. The predecessor of the start
vertex (in the from argument) is itself by definition. If the
predecessor is zero, it means that the given vertex was not reached from the
source during the search. Note that the search terminates if all the
vertices in to are reached.
Logical scalar, whether to return the inbound edge for
each vertex. The inbound edge of vertex i in the tree is the edge via
which vertex i was reached. The start vertex and vertices that were
not reached during the search will have zero in the corresponding entry of
the vector. Note that the search terminates if all the vertices in to
are reached.
Gabor Csardi csardi.gabor@gmail.com
The shortest path, or geodesic between two pair of vertices is a path with the minimal number of vertices. The functions documented in this manual page all calculate shortest paths between vertex pairs.
distances calculates the lengths of pairwise shortest paths from
a set of vertices (from) to another set of vertices (to). It
uses different algorithms, depending on the algorithm argument and
the weight edge attribute of the graph. The implemented algorithms
are breadth-first search (‘unweighted’), this only works for
unweighted graphs; the Dijkstra algorithm (‘dijkstra’), this
works for graphs with non-negative edge weights; the Bellman-Ford algorithm
(‘bellman-ford’), and Johnson's algorithm
(‘"johnson"’). The latter two algorithms work with arbitrary
edge weights, but (naturally) only for graphs that don't have a negative
cycle.
igraph can choose automatically between algorithms, and chooses the most
efficient one that is appropriate for the supplied weights (if any). For
automatic algorithm selection, supply ‘automatic’ as the
algorithm argument. (This is also the default.)
shortest_paths calculates a single shortest path (i.e. the path
itself, not just its length) between the source vertex given in from,
to the target vertices given in to. shortest_paths uses
breadth-first search for unweighted graphs and Dijkstra's algorithm for
weighted graphs. The latter only works if the edge weights are non-negative.
all_shortest_paths calculates all shortest paths between
pairs of vertices. More precisely, between the from vertex to the
vertices given in to. It uses a breadth-first search for unweighted
graphs and Dijkstra's algorithm for weighted ones. The latter only supports
non-negative edge weights.
mean_distance calculates the average path length in a graph, by
calculating the shortest paths between all pairs of vertices (both ways for
directed graphs). It uses a breadth-=first search for unweighted graphs and
Dijkstra's algorithm for weighted ones. The latter only supports non-negative
edge weights.
distance_table 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.
West, D.B. (1996). Introduction to Graph Theory. Upper Saddle River, N.J.: Prentice Hall.
g <- make_ring(10)
distances(g)
shortest_paths(g, 5)
all_shortest_paths(g, 1, 6:8)
mean_distance(g)
## Weighted shortest paths
el <- matrix(ncol=3, byrow=TRUE,
c(1,2,0, 1,3,2, 1,4,1, 2,3,0, 2,5,5, 2,6,2, 3,2,1, 3,4,1,
3,7,1, 4,3,0, 4,7,2, 5,6,2, 5,8,8, 6,3,2, 6,7,1, 6,9,1,
6,10,3, 8,6,1, 8,9,1, 9,10,4) )
g2 <- add_edges(make_empty_graph(10), t(el[,1:2]), weight=el[,3])
distances(g2, mode="out")
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