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cycle_basis(G, root=None)

A basis for cycles of a network is a minimal collection of cycles such that any cycle in the network can be written as a sum of cycles in the basis. Here summation of cycles is defined as "exclusive or" of the edges. Cycle bases are useful, e.g. when deriving equations for electric circuits using Kirchhoff's Laws.

Notes

This is adapted from algorithm CACM 491 .

Parameters

G : NetworkX Graph
root : node, optional: Specify starting node for basis.

Returns

A list of cycle lists. Each cycle list is a list of nodes
which forms a cycle (loop) in G.

Returns a list of cycles which form a basis for cycles of G.

Examples

>>> G = nx.Graph()
... nx.add_cycle(G, [0, 1, 2, 3])
... nx.add_cycle(G, [0, 3, 4, 5])
... print(nx.cycle_basis(G, 0))
[[3, 4, 5, 0], [1, 2, 3, 0]]

See :

Back References

The following pages refer to to this document either explicitly or contain code examples using this.

networkx.algorithms.cycles.minimum_cycle_basis networkx.algorithms.cycles.recursive_simple_cycles networkx.algorithms.cycles.cycle_basis networkx.algorithms.cycles.simple_cycles

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