Random Walk Stationary Uniform Check

Problem

Decide whether the uniform distribution is stationary for the simple random walk on an undirected graph.

This happens exactly when the graph is regular: every node has the same degree, counting isolated nodes as degree 0. edges is a list of [u, v] pairs. Return a boolean.

Hint

Uniform stationarity means the degree sequence is constant.

Test cases

case 1

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

expected: true

case 2

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

expected: false

case 3

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

expected: true

case 4

in: [3,[]]

expected: true

case 5

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

expected: false

Starter codePython

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

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