How would I identify a gap in a set of curve data, and get its value?

Question

I have a set of 2-D data (x,y) and it produces a set of curves, and sometimes the set of curves do not overlap, and there is a distinct separation between the groups of curves, how would I identify and get this separation?

Here is some sample data and its plot

enter image description here

0.0000 -0.4270
0.1000 -0.4239
0.2000 -0.4141
0.3000 -0.3979
0.4000 -0.3753
0.5000 -0.3464
0.6000 -0.3113
0.7000 -0.2705
0.8000 -0.2244
0.9000 -0.1732
1.0000 -0.1174
1.0000 -0.4270
0.9000 -0.0578
0.8000 0.0050
0.7000 0.0698
0.6000 0.1361
0.5000 0.2026
0.4000 0.2685
0.3000 0.3327
0.2000 0.3920
0.1000 0.4396
0.0000 0.4597
0.0000 0.4597
0.1000 0.4463
0.2000 0.4160
0.3000 0.3812
0.4000 0.3474
0.5000 0.3172
0.6000 0.2917
0.7000 0.2715
0.8000 0.2569
0.9000 0.2480
1.0000 0.2450
1.0000 0.4597
1.0000 0.4597
1.0000 0.2450
0.9000 0.2480
0.8000 0.2569
0.7000 0.2715
0.6000 0.2917
0.5000 0.3172
0.4000 0.3474
0.3000 0.3812
0.2000 0.4160
0.1000 0.4463
0.0000 0.4597
0.0000 0.6484
0.1000 0.6402
0.2000 0.6191
0.3000 0.5918
0.4000 0.5639
0.5000 0.5389
0.6000 0.5186
0.7000 0.5046
0.8000 0.4973
0.9000 0.4975
1.0000 0.5063
1.0000 0.6484
1.0000 0.6484
1.0000 0.5063
0.9000 0.5239
0.8000 0.5508
0.7000 0.5874
0.6000 0.6333
0.5000 0.6876
0.4000 0.7450
0.3000 0.7622
0.2000 0.7078
0.1000 0.6657
0.0000 0.6484
0.0000 0.6484
0.1000 0.6657
0.2000 0.7078
0.3000 0.7622
0.4000 0.8222
0.5000 0.8864
0.6000 0.9527
0.7000 1.0206
0.8000 1.0899
0.9000 1.1586
1.0000 1.2059
1.0000 0.6484
1.0000 0.7146
1.0000 1.2059
0.9000 1.1586
0.8000 1.0899
0.7000 1.0206
0.6000 0.9527
0.5000 0.8864
0.4000 0.8222
0.3000 0.7869
0.2000 0.7731
0.1000 0.7338
0.0000 0.7146

This for the curious, is a band dispersions diagram, from solid state physics.

• Becuzz: What part of this are you struggling with?
• CodesInChaos: You can take the minimum and maximum of each curve to obtain the interval it covers. Then union all the intervals and what remains are the gaps.
• user22866: @CodesInChaos thats a very good way to do it, why dont you add that as an answer? i think it will solve my problem.
• user22866: @Becuzz two issues: 1. How to identify a line/curve's start/ending , 2. how to "look" for the curve as answered by CodesInChaos comment.
• Jim G.: I'm voting to close this question as off-topic because it's a better fit for math.stackexchange.com.