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| """ | |
| Algorithm to find a maximal (not maximum) independent set. | |
| """ | |
| import networkx as nx | |
| from networkx.utils import not_implemented_for, py_random_state | |
| __all__ = ["maximal_independent_set"] | |
| def maximal_independent_set(G, nodes=None, seed=None): | |
| """Returns a random maximal independent set guaranteed to contain | |
| a given set of nodes. | |
| An independent set is a set of nodes such that the subgraph | |
| of G induced by these nodes contains no edges. A maximal | |
| independent set is an independent set such that it is not possible | |
| to add a new node and still get an independent set. | |
| Parameters | |
| ---------- | |
| G : NetworkX graph | |
| nodes : list or iterable | |
| Nodes that must be part of the independent set. This set of nodes | |
| must be independent. | |
| seed : integer, random_state, or None (default) | |
| Indicator of random number generation state. | |
| See :ref:`Randomness<randomness>`. | |
| Returns | |
| ------- | |
| indep_nodes : list | |
| List of nodes that are part of a maximal independent set. | |
| Raises | |
| ------ | |
| NetworkXUnfeasible | |
| If the nodes in the provided list are not part of the graph or | |
| do not form an independent set, an exception is raised. | |
| NetworkXNotImplemented | |
| If `G` is directed. | |
| Examples | |
| -------- | |
| >>> G = nx.path_graph(5) | |
| >>> nx.maximal_independent_set(G) # doctest: +SKIP | |
| [4, 0, 2] | |
| >>> nx.maximal_independent_set(G, [1]) # doctest: +SKIP | |
| [1, 3] | |
| Notes | |
| ----- | |
| This algorithm does not solve the maximum independent set problem. | |
| """ | |
| if not nodes: | |
| nodes = {seed.choice(list(G))} | |
| else: | |
| nodes = set(nodes) | |
| if not nodes.issubset(G): | |
| raise nx.NetworkXUnfeasible(f"{nodes} is not a subset of the nodes of G") | |
| neighbors = set.union(*[set(G.adj[v]) for v in nodes]) | |
| if set.intersection(neighbors, nodes): | |
| raise nx.NetworkXUnfeasible(f"{nodes} is not an independent set of G") | |
| indep_nodes = list(nodes) | |
| available_nodes = set(G.nodes()).difference(neighbors.union(nodes)) | |
| while available_nodes: | |
| node = seed.choice(list(available_nodes)) | |
| indep_nodes.append(node) | |
| available_nodes.difference_update(list(G.adj[node]) + [node]) | |
| return indep_nodes | |