Suggestions to plot overlapping lines in matplotlib?

I have the same issue on a plot with a high degree of discretization.

Here the starting situation:

import matplotlib.pyplot as plt
grid=[x for x in range(10)]
graphs=[
        [1,1,1,4,4,4,3,5,6,0],
        [1,1,1,5,5,5,3,5,6,0],
        [1,1,1,0,0,3,3,2,4,0],
        [1,2,4,4,3,2,3,2,4,0],
        [1,2,3,3,4,4,3,2,6,0],
        [1,1,3,3,0,3,3,5,4,3],
        ]

for gg,graph in enumerate(graphs):
    plt.plot(grid,graph,label="g"+str(gg))

plt.legend(loc=3,bbox_to_anchor=(1,0))
plt.show()

No one can say where the green and blue lines run exactly

and my “solution”

import matplotlib.pyplot as plt
grid=[x for x in range(10)]
graphs=[
        [1,1,1,4,4,4,3,5,6,0],
        [1,1,1,5,5,5,3,5,6,0],
        [1,1,1,0,0,3,3,2,4,0],
        [1,2,4,4,3,2,3,2,4,0],
        [1,2,3,3,4,4,3,2,6,0],
        [1,1,3,3,0,3,3,5,4,3],
        ]

for gg,graph in enumerate(graphs):
    lw=10-8*gg/len(graphs)
    ls=['-','--','-.',':'][gg%4]
    plt.plot(grid,graph,label="g"+str(gg), linestyle=ls, linewidth=lw)

plt.legend(loc=3,bbox_to_anchor=(1,0))
plt.show()

I am grateful for suggestions on improvement!