Decide if a graph is subgraph isomorphic to another one

Usage

subgraph_isomorphic(pattern, target, method = c("auto", "lad", "vf2"), ...)

is_subgraph_isomorphic_to(
  pattern,
  target,
  method = c("auto", "lad", "vf2"),
  ...
)

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.

Value

Logical scalar, TRUE if the pattern is isomorphic to a (possibly induced) subgraph of target.

‘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 of target vertex sets, given as numeric vertex ids or symbolic vertex names. The length of the list must be vcount(pattern) and for each vertex in pattern it gives the allowed matching vertices in target. Defaults to NULL.
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.

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 7739136:
#> [1] 2 1 7 6 5
#> 
#> [[2]]
#> + 5/9 vertices, named, from 7739136:
#> [1] 1 2 3 4 5
#> 
#> [[3]]
#> + 5/9 vertices, named, from 7739136:
#> [1] 6 4 3 2 5
#> 
#> [[4]]
#> + 5/9 vertices, named, from 7739136:
#> [1] 8 4 5 6 9
#> 
#> [[5]]
#> + 5/9 vertices, named, from 7739136:
#> [1] 5 4 8 9 6
#> 
#> [[6]]
#> + 5/9 vertices, named, from 7739136:
#> [1] 9 4 5 7 6
#> 
#> [[7]]
#> + 5/9 vertices, named, from 7739136:
#> [1] 1 5 4 6 7
#> 
#> [[8]]
#> + 5/9 vertices, named, from 7739136:
#> [1] 1 5 4 3 2
#> 
#> [[9]]
#> + 5/9 vertices, named, from 7739136:
#> [1] 4 5 1 7 6
#> 
#> [[10]]
#> + 5/9 vertices, named, from 7739136:
#> [1] 7 5 4 9 6
#> 
#> [[11]]
#> + 5/9 vertices, named, from 7739136:
#> [1] 6 5 2 3 4
#> 
#> [[12]]
#> + 5/9 vertices, named, from 7739136:
#> [1] 6 5 2 1 7
#> 
#> [[13]]
#> + 5/9 vertices, named, from 7739136:
#> [1] 2 5 6 7 1
#> 
#> [[14]]
#> + 5/9 vertices, named, from 7739136:
#> [1] 9 6 7 5 4
#> 
#> [[15]]
#> + 5/9 vertices, named, from 7739136:
#> [1] 5 6 9 8 4
#> 
#> [[16]]
#> + 5/9 vertices, named, from 7739136:
#> [1] 4 6 7 1 5
#> 
#> [[17]]
#> + 5/9 vertices, named, from 7739136:
#> [1] 7 6 9 4 5
#> 
#> [[18]]
#> + 5/9 vertices, named, from 7739136:
#> [1] 1 7 6 4 5
#> 
#> [[19]]
#> + 5/9 vertices, named, from 7739136:
#> [1] 6 7 1 2 5
#> 
#> [[20]]
#> + 5/9 vertices, named, from 7739136:
#> [1] 8 9 6 5 4
#> 
subgraph_isomorphisms(pattern, target, induced = TRUE)
#> [[1]]
#> + 5/9 vertices, named, from 7739136:
#> [1] 1 2 3 4 5
#> 
#> [[2]]
#> + 5/9 vertices, named, from 7739136:
#> [1] 6 4 3 2 5
#> 
#> [[3]]
#> + 5/9 vertices, named, from 7739136:
#> [1] 6 5 2 3 4
#> 
#> [[4]]
#> + 5/9 vertices, named, from 7739136:
#> [1] 1 5 4 3 2
#> 
subgraph_isomorphisms(pattern, target, domains = domains)
#> [[1]]
#> + 5/9 vertices, named, from 7739136:
#> [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