Decide if a graph is subgraph isomorphic to another one
Arguments
- pattern
The smaller graph, it might be directed or undirected. Undirected graphs are treated as directed graphs with mutual edges.
- target
The bigger graph, it might be directed or undirected. Undirected graphs are treated as directed graphs with mutual edges.
- method
The method to use. Possible values: ‘auto’, ‘lad’, ‘vf2’. See their details below.
- ...
Additional arguments, passed to the various methods.
‘auto’ method
This method currently selects ‘lad’, always, as it seems to be superior on most graphs.
‘lad’ method
This is the LAD algorithm by Solnon, see the reference below. It has the following extra arguments:
- domains
If not
NULL
, then it specifies matching restrictions. It must be a list oftarget
vertex sets, given as numeric vertex ids or symbolic vertex names. The length of the list must bevcount(pattern)
and for each vertex inpattern
it gives the allowed matching vertices intarget
. Defaults toNULL
.- induced
Logical scalar, whether to search for an induced subgraph. It is
FALSE
by default.- time.limit
The processor time limit for the computation, in seconds. It defaults to
Inf
, which means no limit.
‘vf2’ method
This method uses the VF2 algorithm by Cordella, Foggia et al., see references below. It supports vertex and edge colors and have the following extra arguments:
- vertex.color1, vertex.color2
Optional integer vectors giving the colors of the vertices for colored graph isomorphism. If they are not given, but the graph has a “color” vertex attribute, then it will be used. If you want to ignore these attributes, then supply
NULL
for both of these arguments. See also examples below.- edge.color1, edge.color2
Optional integer vectors giving the colors of the edges for edge-colored (sub)graph isomorphism. If they are not given, but the graph has a “color” edge attribute, then it will be used. If you want to ignore these attributes, then supply
NULL
for both of these arguments.
References
LP Cordella, P Foggia, C Sansone, and M Vento: An improved algorithm for matching large graphs, Proc. of the 3rd IAPR TC-15 Workshop on Graphbased Representations in Pattern Recognition, 149–159, 2001.
C. Solnon: AllDifferent-based Filtering for Subgraph Isomorphism, Artificial Intelligence 174(12-13):850–864, 2010.
See also
Other graph isomorphism:
canonical_permutation()
,
count_isomorphisms()
,
count_subgraph_isomorphisms()
,
graph_from_isomorphism_class()
,
isomorphic()
,
isomorphism_class()
,
isomorphisms()
,
subgraph_isomorphisms()
Examples
# A LAD example
pattern <- make_graph(
~ 1:2:3:4:5,
1 - 2:5, 2 - 1:5:3, 3 - 2:4, 4 - 3:5, 5 - 4:2:1
)
target <- make_graph(
~ 1:2:3:4:5:6:7:8:9,
1 - 2:5:7, 2 - 1:5:3, 3 - 2:4, 4 - 3:5:6:8:9,
5 - 1:2:4:6:7, 6 - 7:5:4:9, 7 - 1:5:6,
8 - 4:9, 9 - 6:4:8
)
domains <- list(
`1` = c(1, 3, 9), `2` = c(5, 6, 7, 8), `3` = c(2, 4, 6, 7, 8, 9),
`4` = c(1, 3, 9), `5` = c(2, 4, 8, 9)
)
subgraph_isomorphisms(pattern, target)
#> [[1]]
#> + 5/9 vertices, named, from 097130e:
#> [1] 2 1 7 6 5
#>
#> [[2]]
#> + 5/9 vertices, named, from 097130e:
#> [1] 1 2 3 4 5
#>
#> [[3]]
#> + 5/9 vertices, named, from 097130e:
#> [1] 6 4 3 2 5
#>
#> [[4]]
#> + 5/9 vertices, named, from 097130e:
#> [1] 8 4 5 6 9
#>
#> [[5]]
#> + 5/9 vertices, named, from 097130e:
#> [1] 5 4 8 9 6
#>
#> [[6]]
#> + 5/9 vertices, named, from 097130e:
#> [1] 9 4 5 7 6
#>
#> [[7]]
#> + 5/9 vertices, named, from 097130e:
#> [1] 1 5 4 6 7
#>
#> [[8]]
#> + 5/9 vertices, named, from 097130e:
#> [1] 1 5 4 3 2
#>
#> [[9]]
#> + 5/9 vertices, named, from 097130e:
#> [1] 4 5 1 7 6
#>
#> [[10]]
#> + 5/9 vertices, named, from 097130e:
#> [1] 7 5 4 9 6
#>
#> [[11]]
#> + 5/9 vertices, named, from 097130e:
#> [1] 6 5 2 3 4
#>
#> [[12]]
#> + 5/9 vertices, named, from 097130e:
#> [1] 6 5 2 1 7
#>
#> [[13]]
#> + 5/9 vertices, named, from 097130e:
#> [1] 2 5 6 7 1
#>
#> [[14]]
#> + 5/9 vertices, named, from 097130e:
#> [1] 9 6 7 5 4
#>
#> [[15]]
#> + 5/9 vertices, named, from 097130e:
#> [1] 5 6 9 8 4
#>
#> [[16]]
#> + 5/9 vertices, named, from 097130e:
#> [1] 4 6 7 1 5
#>
#> [[17]]
#> + 5/9 vertices, named, from 097130e:
#> [1] 7 6 9 4 5
#>
#> [[18]]
#> + 5/9 vertices, named, from 097130e:
#> [1] 1 7 6 4 5
#>
#> [[19]]
#> + 5/9 vertices, named, from 097130e:
#> [1] 6 7 1 2 5
#>
#> [[20]]
#> + 5/9 vertices, named, from 097130e:
#> [1] 8 9 6 5 4
#>
subgraph_isomorphisms(pattern, target, induced = TRUE)
#> [[1]]
#> + 5/9 vertices, named, from 097130e:
#> [1] 1 2 3 4 5
#>
#> [[2]]
#> + 5/9 vertices, named, from 097130e:
#> [1] 6 4 3 2 5
#>
#> [[3]]
#> + 5/9 vertices, named, from 097130e:
#> [1] 6 5 2 3 4
#>
#> [[4]]
#> + 5/9 vertices, named, from 097130e:
#> [1] 1 5 4 3 2
#>
subgraph_isomorphisms(pattern, target, domains = domains)
#> [[1]]
#> + 5/9 vertices, named, from 097130e:
#> [1] 1 5 4 3 2
#>
# Directed LAD example
pattern <- make_graph(~ 1:2:3, 1 -+ 2:3)
dring <- make_ring(10, directed = TRUE)
subgraph_isomorphic(pattern, dring)
#> [1] FALSE