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, …, n1` 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 wellknown 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