How to achieve matrix sort in python?

Question

I have a matrix of numbers representing the nodal points as follows:

Element No. Nodes

1 1 2 3 4
2 5 6 7 8
3 2 3 9 10
...........................
...........................
x 9 10 11 12
...........................

so this is a matrix of numbers 4 x n
Elements 1 and 3 are neighbours (as they share nodes 2 3). Similarly elements 3 and x are neighbours (they share nodes 9 and 10). I want to sort the matrix in such a way all the elements are sequentially arranged.

Answer 1

I think you want a topological sort algorithm. See here: http://en.wikipedia.org/wiki/Topological_sorting

Before that though you'll want to preprocess your matrix into a data structure that allows you to easily find the elements adjacent to any given element. A list of lists is one approach:

graph = [
 [3], # nodes adjacent to element 1
 [], # element 2
 [1, x], # element 3
 ...
 [3] # element x
]