# subgraph_isomorphic

##### Decide if a graph is subgraph isomorphic to another one

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.

##### See Also

Other graph isomorphism: `count_isomorphisms`

,
`graph.count.isomorphisms.vf2`

;
`count_subgraph_isomorphisms`

,
`graph.count.subisomorphisms.vf2`

;
`graph.get.isomorphisms.vf2`

,
`isomorphisms`

;
`graph.get.subisomorphisms.vf2`

,
`subgraph_isomorphisms`

;
`graph.isoclass`

,
`graph.isoclass.subgraph`

,
`isomorphism_class`

;
`graph.isocreate`

,
`graph_from_isomorphism_class`

;
`graph.isomorphic`

,
`graph.isomorphic.34`

,
`graph.isomorphic.bliss`

,
`graph.isomorphic.vf2`

,
`is_isomorphic_to`

, `isomorphic`

##### Examples

```
# NOT RUN {
# 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)
subgraph_isomorphisms(pattern, target, induced = TRUE)
subgraph_isomorphisms(pattern, target, domains = domains)
# Directed LAD example
pattern <- make_graph(~ 1:2:3, 1 -+ 2:3)
uring <- make_ring(10)
dring <- make_ring(10, directed = TRUE)
subgraph_isomorphic(pattern, uring)
subgraph_isomorphic(pattern, dring)
# }
```

*Documentation reproduced from package igraph, version 1.0.1, License: GPL (>= 2)*