# dwave.embedding.pegasus.find_clique_embedding¶

find_clique_embedding(k, m=None, target_graph=None)[source]

Find an embedding for a clique in a Pegasus graph.

Given a clique (fully connected graph) and target Pegasus graph, attempts to find an embedding by transforming the Pegasus graph into a $$K_{2,2}$$ Chimera graph and then applying a Chimera clique-finding algorithm. Results are converted back to Pegasus coordinates.

Parameters
• k (int/iterable/networkx.Graph) – A complete graph to embed, formatted as a number of nodes, node labels, or a NetworkX graph.

• m (int) – Number of tiles in a row of a square Pegasus graph. Required to generate an m-by-m Pegasus graph when target_graph is None.

• target_graph (networkx.Graph) – A Pegasus graph. Required when m is None.

Returns

An embedding as a dict, where keys represent the clique’s nodes and values, formatted as lists, represent chains of pegasus coordinates.

Return type

dict

Examples

This example finds an embedding for a $$K_3$$ complete graph in a 2-by-2 Pegaus graph.

>>> from dwave.embedding.pegasus import find_clique_embedding
...
>>> print(find_clique_embedding(3, 2))
{0: [10, 34], 1: [35, 11], 2: [32, 12]}