networkx.circulant_graph¶

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

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

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 : Graph, optional (default None) If provided this graph is cleared of nodes and edges and filled with the new graph. Usually used to set the type of the graph.
Returns:	The graph Ci_n(x_1, ..., x_m) consisting of n vertices 0, ..., n-1 such that the vertex with label i is connected to the vertices labelled (i + x) and (i - x), for all x in x_1 up to x_m, with the indices taken modulo n.

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