Core-Periphery Check

Problem

Check whether a labeled partition matches the idealized core-periphery model.

The core nodes must form a clique, the periphery nodes must be independent (no edges among them), and every periphery node must have at least one core neighbor. Return a boolean. edges is a list of [u, v] pairs and core is a 0/1 list marking core nodes.

Hint

The idealized model has a dense core and a star-like periphery.

Test cases

case 1

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

expected: true

case 2

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

expected: true

case 3

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

expected: false

case 4

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

expected: false

case 5

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

expected: false

Starter codePython

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

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