condensation

condensation(G, scc=None)

Returns the condensation of G.

The condensation of G is the graph with each of the strongly connected components contracted into a single node.

Parameters:

GNetworkX DiGraph

A directed graph.

scc: list or generator (optional, default=None)

Strongly connected components. If provided, the elements in scc must partition the nodes in G. If not provided, it will be calculated as scc=nx.strongly_connected_components(G).

Returns:

CNetworkX DiGraph

The condensation graph C of G. The node labels are integers corresponding to the index of the component in the list of strongly connected components of G. C has a graph attribute named ‘mapping’ with a dictionary mapping the original nodes to the nodes in C to which they belong. Each node in C also has a node attribute ‘members’ with the set of original nodes in G that form the SCC that the node in C represents.

Raises:

NetworkXNotImplemented

If G is undirected.

Notes

After contracting all strongly connected components to a single node, the resulting graph is a directed acyclic graph.

Examples

Contracting two sets of strongly connected nodes into two distinct SCC using the barbell graph.

>>> G = nx.barbell_graph(4, 0)
>>> G.remove_edge(3, 4)
>>> G = nx.DiGraph(G)
>>> H = nx.condensation(G)
>>> H.nodes.data()
NodeDataView({0: {'members': {0, 1, 2, 3}}, 1: {'members': {4, 5, 6, 7}}})
>>> H.graph["mapping"]
{0: 0, 1: 0, 2: 0, 3: 0, 4: 1, 5: 1, 6: 1, 7: 1}

Contracting a complete graph into one single SCC.

>>> G = nx.complete_graph(7, create_using=nx.DiGraph)
>>> H = nx.condensation(G)
>>> H.nodes
NodeView((0,))
>>> H.nodes.data()
NodeDataView({0: {'members': {0, 1, 2, 3, 4, 5, 6}}})