contract_vertices combines a set of vertices into one pseudo-vertex
and returns the reduced network.
contract_vertices(
g,
vertices,
method = c("min", "max", "union", "add"),
attr = NULL,
new_name = "set",
out_as_igraph = TRUE
)network as an igraph object or an adjacency matrix.
Numeric vertor indicating the indeces of the vertices are to be contracted.
Indication of which grouping criterion should be used.method="min" indicates the "minimum" criterion (edge values as distances).method="max" indicates the "maximum" criterion (edge values as non-cumulative strengths).method="add" indicates the "addition" criterion (edge values as cumulative strengths).method="union" indicates the "union" criterion (edge values as probability).
The default is "min". See details for examples.
Either NULL or a character string giving an edge attribute name to
be used as weights.
If NULL, the unweighted network is used to calculate the values of the
resulting contracted network.
If not NULL then the values of the given edge attribute are included
in the adjacency matrix. If the graph has multiple edges, the edge attribute
of an arbitrarily chosen edge (for the multiple edges) is included.
character, name of the new pseudovertex. If not specified, it will be called "set".
logical. If TRUE the resulting network is
returned as an igraph object. If FALSE, the output is
returned as an adjacency matrix.
An igraph object or an adjacency matrix of the contracted network.
This function contracts a set of vertices into a pseudo-vertex and returns the network with that new vertex included (and the contracted vertices excluded).
Weighted ties can be used.
This requires to either provide a weighted adjacency matrix OR
an igraph object with an attribute that is used for weights.
Make sure that this attribute is numeric.
By default, if the igraph object contains an edge attribute called
weight, this attribute will be used as a weight by default, unless
a different edge attribute is explicitly specified as attr.
The method specifies how the (possibly weighted) edges between the
selected vertices and the other vertices are combined into edges between
the new pseudovertex and the other vertices. The default is to use the
min procedure.
NOTE: if g is an igraph object without vertex names, the
names will be added automatically (as integeres, numbered from 1).
This is useful, so it is clear who-is-who after the vertex contraction.
Minimum Criterion: the edge value between a group and an outside vertex
is measured as the minimal value among all the (nonzero) edge values between
any vertex in the group and the outside vertex. Suggested if edge values are
interpreted as distances.
Example: suppose vertex A to C has distance 2 and B to C has distance 1,
then according to the minimum criterion, the distance between C and
the merged set AB is 1. Note that if B and C are not connected,
the algorithm takes the distance between A and C to describe
the distance between AB and C.
Maximum Criterion: the edge value between a group and an outside vertex
is measured as the maximal value among all the (nonzero) edge values between
any vertex in the group and the outside vertex. Suggested if edge values are
interpreted as non-cumulative strengths.
Example: we keep using the above example, but the figure now indicates
the strength of tie. According to the maximum criterion, the strength of tie
between AB and C is 2.
Addition Criterion: the edge value between a group and an outside vertex
is measured as the sum of all the edge values between any vertex in the group
and the outside vertex. Suggested if edge values are as cummulative strengths.
Example: according to the addition criterion, the strength of tie between
AB and C is 3
Union Criterion: the edge value between a group and an outside vertex is measured
as the probability that there is at least one path connecting the group with
the outside vertex. Suggested if edge values are as probability.
Example: suppose A has probability 0.2 to reach C and B has probability
0.5 to reach C, then C can be reached from merged AB with probability
1 - (1 - 0.2) * (1 - 0.5) = 0.6 according to the union criterion.
Based on the contract function from the keyplayer package.
The implementation in our package is more general.
# Create a 5x5 weighted and directed adjacency matrix, where edge values
# represent the strength of tie
W <- matrix(
c(0, 1, 3, 0, 0,
0, 0, 0, 4, 0,
1, 1, 0, 2, 0,
0, 0, 0, 0, 3,
0, 2, 0, 0, 0),
nrow = 5, ncol = 5, byrow = TRUE)
# If the strength is believed to be non-accumulative for a group of vertices,
# it is proper to use the "maximum" criterion to contract vertex 2 and 3
contract_vertices(W, c(2, 3), "max")
#> IGRAPH c5ab2be UN-- 4 12 --
#> + attr: name (v/c)
#> + edges from c5ab2be (vertex names):
#> [1] 1--set 1--set 1--set 4--5 4--5 4--5 4--set 4--set 4--set 4--set
#> [11] 5--set 5--set
# Transform the edge value to probability interpretaion
P <- W * 0.2
# Contract vertex 2 and 3 using the "union" criterion as it is proper for
# probability matrix input
contract_vertices(P, c(2, 3), "union")
#> IGRAPH c5ac902 UN-- 4 0 --
#> + attr: name (v/c)
#> + edges from c5ac902 (vertex names):