Cosine Neighbor Similarity

Problem

Compute the cosine similarity between the adjacency rows of nodes u and v in an undirected graph.

For unweighted graphs the dot product is the number of common neighbors and each norm is the square root of the degree, so the score is common / sqrt(deg(u) * deg(v)). Return 0.0 when either node is isolated. edges is a list of [u, v] pairs.

Hint

Cosine similarity normalizes the shared-neighbor count by both degrees.

Test cases

case 1

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

expected: 0.5

case 2

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

expected: 0

case 3

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

expected: 1

case 4

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

expected: 0

Starter codePython

import math
def cosine_similarity(n, edges, u, v):
    # Your code here
    pass

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