# dimod.generators.independent_set¶

independent_set(edges: , nodes: = None) [source]

Generate a binary quadratic model encoding an independent set problem.

Given a graph G, an independent set is a set of nodes such that the subgraph of G induced by these nodes contains no edges.

Parameters
• edges – Edges of the graph.

• nodes – Nodes of the graph.

Returns

A binary quadratic model (BQM) with variables and interactions corresponding to `nodes` and `edges`. Each interaction has a quadratic bias of 1 and each node has a linear bias of 0.

Examples

Generate an independent set BQM from a list of edges.

```>>> dimod.generators.independent_set([(0, 1), (1, 2)])
BinaryQuadraticModel({0: 0.0, 1: 0.0, 2: 0.0}, {(1, 0): 1.0, (2, 1): 1.0}, 0.0, 'BINARY')
```

Generate an independent set BQM from a list of edges and nodes.

```>>> dimod.generators.independent_set([(0, 1)], [0, 1, 2])
BinaryQuadraticModel({0: 0.0, 1: 0.0, 2: 0.0}, {(1, 0): 1.0}, 0.0, 'BINARY')
```

Generate an independent set BQM from a `networkx.Graph`.

```>>> import networkx as nx
>>> G = nx.complete_graph(2)
>>> dimod.generators.independent_set(G.edges, G.nodes)
BinaryQuadraticModel({0: 0.0, 1: 0.0}, {(1, 0): 1.0}, 0.0, 'BINARY')
```