How do you create line segments between two points?

Question

I have this bit of code that plots out the points:

import matplotlib.pyplot as plot
from matplotlib import pyplot

all_data = [[1,10],[2,10],[3,10],[4,10],[5,10],[3,1],[3,2],[3,3],[3,4],[3,5]]
x = []
y = []
for i in xrange(len(all_data)):
    x.append(all_data[i][0])
    y.append(all_data[i][1])
plot.scatter(x,y)

pyplot.show()

but I want all the possible lines that could be made that looks something like this:

I've tried matplotlib path, but it doesn't work well for me.

Answer 1

This can be optimized but it works:

for point in all_data:
    for point2 in all_data:
        pyplot.plot([point[0], point2[0]], [point[1], point2[1]])

Answer 2

import matplotlib.pyplot as plt
import itertools 

fig=plt.figure()
ax=fig.add_subplot(111)
all_data = [[1,10],[2,10],[3,10],[4,10],[5,10],[3,1],[3,2],[3,3],[3,4],[3,5]]
plt.plot(
    *zip(*itertools.chain.from_iterable(itertools.combinations(all_data, 2))),
    color = 'brown', marker = 'o')

plt.show()