Matplotlib plotting additional lines

I have data like this:

X = array([ 24.41,  54.98,  89.57, 114.26, 133.61, 202.14, 250.99, 321.31,
       333.47, 373.79, 422.02, 447.41, 522.47, 549.53,  20.15,  39.12,
        73.42, 134.03, 179.86, 262.52, 337.23, 432.68, 253.24, 346.62,
       450.1 , 552.22, 656.2 ,  33.84,  60.41,  94.88, 147.73, 206.76,
       237.12, 372.72, 495.47, 544.47,  28.93,  49.87,  85.15, 143.84,
       226.86, 339.15, 393.32, 524.7 , 623.86,  39.22,  96.44, 156.92,
       223.88, 271.78, 349.52, 429.66, 523.03, 622.05, 748.29, 646.89,
       749.27, 851.37, 851.61])
y = array([ 0.70168044,  4.93931985,  8.71831269, 10.84590729, 12.22458808,
       15.46380214, 16.61898425, 17.29600649, 17.34369784, 17.43434118,
       17.50907445, 17.57419685, 18.00322011, 18.26260499,  0.03686716,
        2.85433237,  7.0779359 , 12.25192523, 14.65463193, 16.79352551,
       17.35594282, 17.53284075, 16.65553712, 17.38224061, 17.58297862,
       18.29143563, 19.71214346,  2.10666383,  5.59990814,  9.21325511,
       13.08716841, 15.60686344, 16.36464679, 17.43271999, 17.80134835,
       18.20983513,  1.38643181,  4.29326544,  8.28990266, 12.86092195,
       16.1416266 , 17.36179504, 17.46194981, 18.02244612, 19.22640164,
        2.86822848,  9.35464796, 13.58885705, 16.07082828, 16.91213557,
       17.38928103, 17.52563605, 18.00801144, 19.19976288, 20.8797045 ,
       19.5713721 , 20.88735117, 20.40458438, 20.39937509])

When I plot them using:

import matplotlib.pyplot as plt
plt.plot(X, y, "ro", markersize=6)
plt.plot(X, y)

I get:

My expectation would be one line that connects from red point to red point, but no matter how I tweak the parameters a subset of points get connected by straight lines. I am reading through the documentation and can't figure out what parameters to tweak to stop these lines from appearing.