Laplacian Zero Eigenvalue Count

Problem

Return the multiplicity of the zero eigenvalue of the Laplacian of an undirected graph.

A classical result states that this multiplicity equals the number of connected components, so simply count components, treating isolated nodes as their own component. edges is a list of [u, v] pairs.

Hint

The multiplicity of eigenvalue 0 equals the number of connected components.

Test cases

case 1

in: [4,[[0,1],[1,2]]]

expected: 2

case 2

in: [3,[]]

expected: 3

case 3

in: [5,[[0,1],[1,2],[2,3],[3,4]]]

expected: 1

case 4

in: [4,[[0,1],[2,3]]]

expected: 2

case 5

in: [1,[]]

expected: 1

Starter codePython

def zero_eigenvalue_multiplicity(n, edges):
    # Your code here
    pass

5 test cases · run your code against them in the editor