You can just pass a list of the two points you want to connect to plt.plot. To make this easily expandable to as many points as you want, you could define a function like so.
import matplotlib.pyplot as plt
x=[-1 ,0.5 ,1,-0.5]
y=[ 0.5, 1, -0.5, -1]
plt.plot(x,y, 'ro')
def connectpoints(x,y,p1,p2):
x1, x2 = x[p1], x[p2]
y1, y2 = y[p1], y[p2]
plt.plot([x1,x2],[y1,y2],'k-')
connectpoints(x,y,0,1)
connectpoints(x,y,2,3)
plt.axis('equal')
plt.show()
Note, that function is a general function that can connect any two points in your list together.
To expand this to 2N points, assuming you always connect point i to point i+1, we can just put it in a for loop:
import numpy as np
for i in np.arange(0,len(x),2):
connectpoints(x,y,i,i+1)
In that case of always connecting point i to point i+1, you could simply do:
for i in np.arange(0,len(x),2):
plt.plot(x[i:i+2],y[i:i+2],'k-')