| """ |
| 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"] |
|
|
|
|
| @not_implemented_for("directed") |
| @py_random_state(2) |
| @nx._dispatchable |
| 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 |
|
|
