# circulant_graph#

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

Returns the circulant graph $$Ci_n(x_1, x_2, ..., x_m)$$ with $$n$$ nodes.

The circulant graph $$Ci_n(x_1, ..., x_m)$$ consists of $$n$$ nodes $$0, ..., n-1$$ such that node $$i$$ is connected to nodes $$(i + x) \mod n$$ and $$(i - x) \mod n$$ for all $$x$$ in $$x_1, ..., x_m$$. Thus $$Ci_n(1)$$ is a cycle graph.

Parameters:
ninteger

The number of nodes in the graph.

offsetslist of integers

A list of node offsets, $$x_1$$ up to $$x_m$$, as described above.

create_usingNetworkX graph constructor, optional (default=nx.Graph)

Graph type to create. If graph instance, then cleared before populated.

Returns:
NetworkX Graph of type create_using

Examples

Many well-known graph families are subfamilies of the circulant graphs; for example, to create the cycle graph on n points, we connect every node to nodes on either side (with offset plus or minus one). For n = 10,

>>> G = nx.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 create the complete graph on 5 points with the set of offsets [1, 2]:

>>> G = nx.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