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