# networkx.generators.line.inverse_line_graph¶

inverse_line_graph(G)[source]

Returns the inverse line graph of graph G.

If H is a graph, and G is the line graph of H, such that G = L(H). Then H is the inverse line graph of G.

Not all graphs are line graphs and these do not have an inverse line graph. In these cases this function raises a NetworkXError.

Parameters
Ggraph

A NetworkX Graph

Returns
Hgraph

The inverse line graph of G.

Raises
NetworkXNotImplemented

If G is directed or a multigraph

NetworkXError

If G is not a line graph

Notes

This is an implementation of the Roussopoulos algorithm.

If G consists of multiple components, then the algorithm doesn’t work. You should invert every component seperately:

```>>> K5 = nx.complete_graph(5)
>>> P4 = nx.Graph([("a", "b"), ("b", "c"), ("c", "d")])
>>> G = nx.union(K5, P4)
>>> root_graphs = []
>>> for comp in nx.connected_components(G):
...     root_graphs.append(nx.inverse_line_graph(G.subgraph(comp)))
>>> len(root_graphs)
2
```

References

• Roussopolous, N, “A max {m, n} algorithm for determining the graph H from its line graph G”, Information Processing Letters 2, (1973), 108–112.