One could use the `is_subgraph`

method of `H`

, with `induced=True`

.

Or if the question is up to isomorphism, use the `search_subgraph`

method of `G`

.

Define the two graphs:

```
sage: G = graphs.PetersenGraph()
sage: H = Graph({1: [2, 3, 4]})
```

Is the small one a subgraph:

```
sage: H.is_subgraph(G)
False
sage: H.is_subgraph(G, induced=True)
False
```

Up to isomorphism:

```
sage: G.subgraph_search(H)
Subgraph of (Petersen graph): Graph on 4 vertices
sage: G.subgraph_search(H, induced=True)
Subgraph of (Petersen graph): Graph on 4 vertices
```

See the documentation of these methods and related methods:

```
sage: H.is_subgraph?
sage: G.subgraph_search?
```

Related methods exist to

count the number of (induced or not) subgraphs of `G`

isomorphic to `H`

:

```
sage: G.subgraph_search_count?
```

generate all (induced or not) subgraphs of `G`

isomorphic to `H`

:

```
sage: G.subgraph_search_iterator?
```

See an example of usage in @David Coudert's comment.