networkx.generators.classic.circulant_graph¶

circulant_graph(n, offsets, create_using=None)[source]¶

Generates the circulant graph \(Ci_n(x_1, x_2, ..., x_m)\) with \(n\) vertices.

Returns

The graph :math:`Ci_n(x_1, …, x_m)` consisting of :math:`n` vertices :math:`0, …, n-1` such
that the vertex with label :math:`i` is connected to the vertices labelled :math:`(i + x)`
and :math:`(i - x)`, for all :math:`x` in :math:`x_1` up to :math:`x_m`, with the indices taken modulo :math:`n`.

Parameters

n (integer) – The number of vertices the generated graph is to contain.
offsets (list of integers) – A list of vertex offsets, \(x_1\) up to \(x_m\), as described above.
create_using (NetworkX graph constructor, optional (default=nx.Graph)) – Graph type to create. If graph instance, then cleared before populated.

Examples

Many well-known graph families are subfamilies of the circulant graphs; for example, to generate the cycle graph on n points, we connect every vertex to every other at offset plus or minus one. For n = 10,

>>> import networkx
>>> G = networkx.generators.classic.circulant_graph(10, [1])
>>> edges = [
...     (0, 9),
...     (0, 1),
...     (1, 2),
...     (2, 3),
...     (3, 4),
...     (4, 5),
...     (5, 6),
...     (6, 7),
...     (7, 8),
...     (8, 9),
... ]
...
>>> sorted(edges) == sorted(G.edges())
True

Similarly, we can generate the complete graph on 5 points with the set of offsets [1, 2]:

>>> G = networkx.generators.classic.circulant_graph(5, [1, 2])
>>> edges = [
...     (0, 1),
...     (0, 2),
...     (0, 3),
...     (0, 4),
...     (1, 2),
...     (1, 3),
...     (1, 4),
...     (2, 3),
...     (2, 4),
...     (3, 4),
... ]
...
>>> sorted(edges) == sorted(G.edges())
True