Create 1D numpy arrays from 2D array of connectivities

Question

I have a list of connectivities for outer/boundary edges of tri mesh shown below:

arranged like this:

edges = \
[[ 1  0]
 [10 11]
 [ 2  1]
 [11 12]
 [ 3  2]
 [12 13]
 [ 4  3]
 [13 14]
 [ 5  4]
 [14 15]
 [ 6  5]
 [15 16]
 [ 7  6]
 [16 17]
 [ 8  7]
 [17 18]
 [ 9  8]
 [18 19]
 [ 0  9]
 [19 10]]

I want to create 2 arrays containing connectivity of loops (inner and outer circles) like this

a = [0 1 2 3 4 5 6 7 8 9]
b = [10 11 12 13 14 15 16 17 18 19]

The loops just happen to have continuous numbering in this case but in general this is not the case and I can have more than 2 loops. In general the 2D edge connectivity can have completely random numbering. My O(n^2) algorithm that picks one point on the loop and finds the next one is too slow. What is an optimal way to extract multiple loop information from 2D connectivity?

Thanks