# contracted_nodes¶

contracted_nodes(G, u, v, self_loops=True, copy=True)[source]

Returns the graph that results from contracting `u` and `v`.

Node contraction identifies the two nodes as a single node incident to any edge that was incident to the original two nodes.

Parameters
GNetworkX graph

The graph whose nodes will be contracted.

u, vnodes

Must be nodes in `G`.

self_loopsBoolean

If this is True, any edges joining `u` and `v` in `G` become self-loops on the new node in the returned graph.

copyBoolean

If this is True (default True), make a copy of `G` and return that instead of directly changing `G`.

Returns
Networkx graph

If Copy is True, A new graph object of the same type as `G` (leaving `G` unmodified) with `u` and `v` identified in a single node. The right node `v` will be merged into the node `u`, so only `u` will appear in the returned graph. If copy is False, Modifies `G` with `u` and `v` identified in a single node. The right node `v` will be merged into the node `u`, so only `u` will appear in the returned graph.

Notes

For multigraphs, the edge keys for the realigned edges may not be the same as the edge keys for the old edges. This is natural because edge keys are unique only within each pair of nodes.

For non-multigraphs where `u` and `v` are adjacent to a third node `w`, the edge (`v`, `w`) will be contracted into the edge (`u`, `w`) with its attributes stored into a “contraction” attribute.

This function is also available as `identified_nodes`.

Examples

Contracting two nonadjacent nodes of the cycle graph on four nodes `C_4` yields the path graph (ignoring parallel edges):

```>>> G = nx.cycle_graph(4)
>>> M = nx.contracted_nodes(G, 1, 3)
>>> P3 = nx.path_graph(3)
>>> nx.is_isomorphic(M, P3)
True
```
```>>> G = nx.MultiGraph(P3)
>>> M = nx.contracted_nodes(G, 0, 2)
>>> M.edges
MultiEdgeView([(0, 1, 0), (0, 1, 1)])
```
```>>> G = nx.Graph([(1, 2), (2, 2)])
>>> H = nx.contracted_nodes(G, 1, 2, self_loops=False)
>>> list(H.nodes())

>>> list(H.edges())
[(1, 1)]
```