# rustworkx.digraph_is_subgraph_isomorphic#

digraph_is_subgraph_isomorphic(first, second, /, node_matcher=None, edge_matcher=None, id_order=False, induced=True, call_limit=None)#

Determine if 2 directed graphs are subgraph - isomorphic

This checks if 2 graphs are subgraph isomorphic both structurally and also comparing the node data and edge data using the provided matcher functions. The matcher function takes in 2 data objects and will compare them. Since there is an ambiguity in the term ‘subgraph’, do note that we check for an node-induced subgraph if argument induced is set to True. If it is set to False, we check for a non induced subgraph, meaning the second graph can have fewer edges than the subgraph of the first. By default it’s True. A simple example that checks if they’re just equal would be:

```graph_a = rustworkx.PyDiGraph()
graph_b = rustworkx.PyDiGraph()
rustworkx.is_subgraph_isomorphic(graph_a, graph_b,
lambda x, y: x == y)
```

Note

For better performance on large graphs, consider setting id_order=False.

Parameters:
• first (PyDiGraph) – The first graph to compare

• second (PyDiGraph) – The second graph to compare

• node_matcher (callable) – A python callable object that takes 2 positional one for each node data object. If the return of this function evaluates to True then the nodes passed to it are vieded as matching.

• edge_matcher (callable) – A python callable object that takes 2 positional one for each edge data object. If the return of this function evaluates to True then the edges passed to it are vieded as matching.

• id_order (bool) – If set to `True` this function will match the nodes in order specified by their ids. Otherwise it will default to a heuristic matching order based on [VF2] paper.

• induced (bool) – If set to `True` this function will check the existence of a node-induced subgraph of first isomorphic to second graph. Default: `True`.

• call_limit (int) – An optional bound on the number of states that VF2 algorithm visits while searching for a solution. If it exceeds this limit, the algorithm will stop and return `False`.

Returns:

`True` if there is a subgraph of first isomorphic to second, `False` if there is not.

Return type:

bool