# contracted_edge#

contracted_edge(G, edge, self_loops=True, copy=True)[source]#

Returns the graph that results from contracting the specified edge.

Edge contraction identifies the two endpoints of the edge as a single node incident to any edge that was incident to the original two nodes. A graph that results from edge contraction is called a minor of the original graph.

Parameters:
GNetworkX graph

The graph whose edge will be contracted.

edgetuple

Must be a pair of nodes in `G`.

self_loopsBoolean

If this is True, any edges (including `edge`) joining the endpoints of `edge` in `G` become self-loops on the new node in the returned graph.

copyBoolean (default True)

If this is True, a the contraction will be performed on a copy of `G`, otherwise the contraction will happen in place.

Returns:
Networkx graph

A new graph object of the same type as `G` (leaving `G` unmodified) with endpoints of `edge` identified in a single node. The right node of `edge` will be merged into the left one, so only the left one will appear in the returned graph.

Raises:
ValueError

If `edge` is not an edge in `G`.

Examples

Attempting to contract two nonadjacent nodes yields an error:

```>>> G = nx.cycle_graph(4)
>>> nx.contracted_edge(G, (1, 3))
Traceback (most recent call last):
...
ValueError: Edge (1, 3) does not exist in graph G; cannot contract it
```

Contracting two adjacent nodes in the cycle graph on n nodes yields the cycle graph on n - 1 nodes:

```>>> C5 = nx.cycle_graph(5)
>>> C4 = nx.cycle_graph(4)
>>> M = nx.contracted_edge(C5, (0, 1), self_loops=False)
>>> nx.is_isomorphic(M, C4)
True
```