How to create a graph of 2n nodes on a circle w/ each node is connected to all others except the opposite node + f(n) on either side of the opposite - numpy

Question

I would like to create a graph that puts 2n points spaced uniformly on a unit circle, and connects each node to all other nodes except the opposite node, as well as k nodes on either side of the opposite node, where k is a function of n.
I am using the NetworkX package to create the graph.
I know how to manually specify the number of nodes to exclude on either side of the opposite node, but I don't know how to use a function of n instead of doing it manually. I'm sure it is quite simple, but how can this be done?
For example, the code below will exclude the opposite node as well as 5 nodes on either side of the opposite node.
import networkx as nx
import numpy as np
import matplotlib.pyplot as plt
def create_circle_graph(n):
G = nx.Graph()
theta = np.linspace(0, 2*np.pi, 2*n, endpoint=False)
for i in range(2*n):
G.add_node(i, pos=np.array([np.cos(theta[i]), np.sin(theta[i])]))
for j in range(i+1, 2*n):
if (i + n) % (2 * n) != j and (i + n + 1) % (2 * n) != j and (i + n - 1) % (2 * n) != j and (i + n + 2) % (2 * n) != j and (i + n - 2) % (2 * n) != j and (i + n + 3) % (2 * n) != j and (i + n - 3) % (2 * n) != j and (i + n + 4) % (2 * n) != j and (i + n - 4) % (2 * n) != j and (i + n + 5) % (2 * n) != j and (i + n - 5) % (2 * n) != j:
G.add_edge(i, j)
return G
n = 10
G = create_circle_graph(n)
pos = nx.get_node_attributes(G, 'pos')
nx.draw(G, pos, with_labels=True)
plt.show()

Answer 1

The main difficulty is to find the appropriate if statement while creating the edges. Once you figure that part out the rest is pretty straightforward since you can use nx.circular_layout(G) to automatically position your nodes.
Below is a possible approach for this task:
import networkx as nx
import numpy as np
import matplotlib.pyplot as plt
def create_circle_graph(n,k): #2*n the number and k the radius of the neighborhood
G = nx.Graph()
[G.add_node(i) for i in range(2*n)] # create nodes
for i in range(2*n):
for j in range(2*n):
if i<j and (j-i<n-k or j-i>n+k): #appropriate if statement for this task
G.add_edge(i,j)
return G
And here is an example of the code with n=5 and varying values for k:
n=5
fig,axs=plt.subplots(1,5,figsize=(15,10))
for k,ax in enumerate(fig.axes): #loop through k and subplots
G=create_circle_graph(n,k)
posG=nx.circular_layout(G) #set up positions for the nodes
ax.set_title('k='+str(k))
nx.draw(G,pos=posG,with_labels=True,ax=ax)
ax.set_aspect('equal')
plt.tight_layout()
plt.show()