Reorder Sets of Coordinates into Continuous Path

Say I have a series of coordinates represented by matrices:

%[x1 y1; x2 y2;...]
a = [0 0; 2 3; 4 5; 5 4];
b = [0 0; 4 2; 5 5; 1 1];
c = [2 2; 6 7; 3 3; 1 1];

I would like to reorder them to form a continous path in the correct order without repeats, i.e.

aNew = [5 4; 4 5; 2 3; 0 0];
bNew = b; %remains the same since the end of "aNew" is the start of "b"
cNew = [1 1; 3 3; 6 7; 2 2];
compiled = [5 4; 4 5; 2 3; 0 0; 4 2; 5 5; 1 1; 3 3; 6 7; 2 2];

The "start" and "end" coordinates aren't a concern; "a" and "c" in the example above could stay the same while only "b" is rearranged. Is there an efficient MATLAB indexing method to reorder and compile the coordinates?