circulant_graph

circulant_graph(n, offsets, create_using=None)

Returns the circulant graph $C{i}_n(x_1,x_2,...,x_m)$ with $n$ nodes.

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