For your setup:
Unless you are authoring in C there is no need to pass parameters M and N since they are implicitly given as the lenghts of the vectors/edges lists.
Instead of S and T you could name these parameters start_index and target_index.

what kind of book should I read to think of good solution by myself?

"1770277824944 should equal 0"
Expected and actual values are reversed.

This kata has performance requirements but the input range is not mentioned.

Tests are broken:

Traceback (most recent call last):
  File "/workspace/default/tests.py", line 34, in <module>
    random_tests()
TypeError: 'NoneType' object is not callable

Please fix your description markup and formatting. This is unreadable.
Maybe get help on Discord for some Math MarkDown too.

Welp, this shouldn't pass.