如何从Python中的邻接列表中选择子矩阵？

Question

I have an adjacency list where each array represents non-zero columns at that row (eg 0th array in the adj. list below means columns 2 and 6 are 1, and everything else is 0).

adj_list = [[2, 6], [1, 3, 24], [2, 4], [3, 5, 21], [4, 6, 10], [1, 5, 7], [6, 8, 9], [7], [7, 10, 14], [5, 9, 11], [10, 12, 18], [11, 13], [12, 14, 15], [9, 13], [13, 16, 17], [15], [15], [11, 19, 20], [18], [18], [4, 22, 23], [21], [21], [2, 25, 26], [24], [24]]

Given this adj. list, I would like to select a submatrix which has identical row and column indices that is given by:

submatrix = (0, 1, 2, 5, 22)

Each element in submatrix indicates a row number.

1) For each row i in submatrix, I need to get ith array from adj_list (which is equivalent to getting ith row from an adjacency matrix)

2) Then from that array, I need to extract the items that match with submatrix

For example, if I am currently looking at 3rd element in submatrix , which is 5, then I need to go to 5th array in adj_list (equivalent of getting 5th row of adj.matrix), which is [1,5,7], and then I need to look which elements in [1,5,7] matches with submatrix (equivalent of getting 1th, 5th and 7th columns of the 5th row). In this case, the result for 5th row should be [0,1,0,1,0] because only 1 and 5 are intersected in two arrays).

How can I efficiently select this submatrix given the adj. list?

Answer 1

adj_list = [[2, 6], [1, 3, 24], [2, 4], [3, 5, 21], [4, 6, 10], [1, 5, 7], [6, 8, 9], [7], [7, 10, 14], [5, 9, 11], [10, 12, 18], [11, 13], [12, 14, 15], [9, 13], [13, 16, 17], [15], [15], [11, 19, 20], [18], [18], [4, 22, 23], [21], [21], [2, 25, 26], [24], [24]]

submatrix = (0, 1, 2, 5, 22)

result = [[i in adj_list[sm] for i in submatrix] for sm in submatrix]

This should do it; though I suspect you might prefer to compute something other than this if you consider your end goal more carefully.