Finding interconnected neighbours in a 2d matrix

I have a similar matrix as below

  a| b | c | d | e 
1|1| 0 | 0 | 1 | 0
2|0| 0 | 1 | 0 | 1
3|0| 1 | 0 | 0 | 0
4|0| 1 | 0 | 1 | 0
5|0| 1 | 0 | 0 | 0
6|1| 0 | 0 | 0 | 0

i want to get the neighbors for each alphabets. neighbours are defined as follows for eaxample "a" and "d" are 1 for row 1 hence they are neighbours now "d" is 1 for row 1 and 4 hence any alphabet which is 1 for row 4 will be neighbour for "d" as well as "a". Here "b" is 1 for row 4 and hence will be neigbour to bot "a" and "d". And so on..

the output should be

   a    | b     |  c    |  d    |  e 
   3    | 3     |  2    |  3    |  2
 abd    |abd    |     ce|    abd|     ce
 1,3,4,6|1,3,4,6|    2,5|1,3,4,6|    2,5

where second rows tells the number of neighbours(including the alphabet itself). third row tells the neigbours fourth row tells the rowname connecting these neighbours