How do you create line segments between two points?

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.