vertex.connectivity {igraph} | R Documentation |
The vertex connectivity of a graph or two vertices, this is recently also called group cohesion.
vertex.connectivity(graph, source=NULL, target=NULL, checks=TRUE) vertex.disjoint.paths(graph, source, target) graph.cohesion(graph, checks=TRUE)
graph |
The input graph. |
source |
The id of the source vertex, for
vertex.connectivity it can be NULL , see details
below. |
target |
The id of the target vertex, for
vertex.connectivity it can be NULL , see details
below. |
checks |
Logical constant. Whether to check that the graph is connected and also the degree of the vertices. If the graph is not (strongly) connected then the connectivity is obviously zero. Otherwise if the minimum degree is one then the vertex connectivity is also one. It is a good idea to perform these checks, as they can be done quickly compared to the connectivity calculation itself. They were suggested by Peter McMahan, thanks Peter. |
The vertex connectivity of two vertices (source
and
target
) in a directed graph is the minimum number of vertices
needed to remove from the graph to eliminate all (directed) paths from
source
to target
. vertex.connectivity
calculates this quantity if both the source
and target
arguments are given and they're not NULL
.
The vertex connectivity of a graph is the minimum vertex connectivity
of all (ordered) pairs of vertices in the graph. In other words this
is the minimum number of vertices needed to remove to make the graph
not strongly connected. (If the graph is not strongly connected then
this is zero.) vertex.connectivity
calculates this quantitty if
neither the source
nor target
arguments are
given. (Ie. they are both NULL
.)
A set of vertex disjoint directed paths from source
to vertex
is a set of directed paths between them whose vertices do not contain common
vertices (apart from source
and target
). The maximum number of
vertex disjoint paths between two vertices is the same as their vertex
connectivity.
The cohesion of a graph (as defined by White and Harary, see
references), is the vertex connectivity of the graph. This is
calculated by graph.cohesion
.
These three functions essentially calculate the same measure(s), more
precisely vertex.connectivity
is the most general, the other
two are included only for the ease of using more descriptive function
names.
A scalar real value.
Gabor Csardi csardi@rmki.kfki.hu
Douglas R. White and Frank Harary: The cohesiveness of blocks in social networks: node connectivity and conditional density, TODO: citation
graph.maxflow
, edge.connectivity
,
edge.disjoint.paths
, graph.adhesion
g <- barabasi.game(100, m=1) g <- delete.edges(g, E(g)[ 99 %--% 0 ]) g2 <- barabasi.game(100, m=5) g2 <- delete.edges(g2, E(g2)[ 99 %--% 0]) vertex.connectivity(g, 99, 0) vertex.connectivity(g2, 99, 0) vertex.disjoint.paths(g2, 99, 0) g <- erdos.renyi.game(50, 5/50) g <- as.directed(g) g <- subgraph(g, subcomponent(g, 1)) graph.cohesion(g)