Subgraph Isomorphism
Subgraph Isomorphism algorithm receives a target graph 
and a pattern graph 
as input
and searches the target graph for subgraphs that are isomorphic to the pattern graph. The algorithm returns
the mappings of the pattern graph vertices onto the target graph vertices.
and a pattern graph as input
and searches the target graph for subgraphs that are isomorphic to the pattern graph. The algorithm returns
the mappings of the pattern graph vertices onto the target graph vertices.Operation | Computational methods | Programming Interface |
Mathematical formulation
Subgraphs definition
A graph 
is called a subgraph of graph 
if
and 
contains all the endpoints of all the
edges in 
[Gross2014].
is called a subgraph of graph if
and contains all the endpoints of all the
edges in [Gross2014].Further we denote the induced subgraph on the vertex set
as
induced
subgraph, the induced subgraph on the edge set
as non-induced
subgraph.Computing
Given two graphs and , the problem is to determine whether graph 
contains
a subgraph isomorphic to graph and find the exact mapping of subgraph in
graph .
and , the problem is to determine whether graph contains
a subgraph isomorphic to graph and find the exact mapping of subgraph in
graph . is called target
graph, is called pattern
graph.Mapping is a bijection or one-to-one correspondence between vertices of 
and a subgraph of
graph . Two vertices are adjacent if there is an existing edge between them, and non-adjacent otherwise.
Induced subgraph isomorphism preserves both adjacency and non-adjacency relationships between vertices,
while non-induced subgraph isomorphism preserves only adjacency relationship.
and a subgraph of
graph . Two vertices are adjacent if there is an existing edge between them, and non-adjacent otherwise.
Induced subgraph isomorphism preserves both adjacency and non-adjacency relationships between vertices,
while non-induced subgraph isomorphism preserves only adjacency relationship.Example
For the example above, the mappings for subgraph in graph are:
in graph are:- Induced: [3, 0, 1, 4, 2, 5]
- Non-induced: [3, 0, 1, 4, 2, 5], [3, 6, 1, 4, 2, 5], [6, 0, 1, 2, 4, 5], and [4, 0, 1, 5, 6, 2]
The notation [3, 0, 1, 4, 2, 5] means that:
- pattern vertex with id 0 is mapped on vertex in target graph with id 3
- pattern vertex with id 1 is mapped on vertex in target graph with id 0
- pattern vertex with id 2 is mapped on vertex in target graph with id 1
- pattern vertex with id 3 is mapped on vertex in target graph with id 4
- pattern vertex with id 4 is mapped on vertex in target graph with id 2
- pattern vertex with id 5 is mapped on vertex in target graph with id 5
Computation method:
fast
The method defines VF3-light algorithms with Global State Stack parallelization method
and supports induced and non-induced cases.
For more details, see [Carletti2021].
Programming Interface
Refer to API Reference: Subgraph Isomorphism.