# shortest.paths

0th

Percentile

##### Shortest (directed or undirected) paths between vertices

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.

Keywords
graphs
##### Usage
shortest.paths(graph, v=V(graph), mode = "all")
get.shortest.paths(graph, from, to=V(graph), mode = "all")
get.all.shortest.paths(graph, from, to = V(graph), mode = "all")
average.path.length(graph, directed=TRUE, unconnected=TRUE)
##### Arguments
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 c
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
##### Details

The shortest paths (also called geodesics) are calculated by using breath-first search in the graph. Right now edge weights are not used, ie. every edge weight is one.

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 exists between two vertices.

get.all.shortest.paths calculates all shortest paths from a vertex to other vertices given in the to argument.

##### Value

• 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 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.

##### References

West, D.B. (1996). Introduction to Graph Theory. Upper Saddle River, N.J.: Prentice Hall.

##### Aliases
• shortest.paths
• get.shortest.paths
• get.all.shortest.paths
• average.path.length
##### Examples
g <- graph.ring(10)
shortest.paths(g)
get.shortest.paths(g, 5)
get.all.shortest.paths(g, 0, 5:7)
average.path.length(g)
Documentation reproduced from package igraph, version 0.4.4, License: GPL version 2 or later (June, 1991)

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