Degree Distribution Fit Slope

Problem

Fit the slope of the degree distribution on a log-log plot.

Count how many nodes have each positive degree, take logs of degree and count, and compute the least-squares slope of count versus degree. Return 0.0 when fewer than two distinct degrees exist or the fit is degenerate. edges is a list of [u, v] pairs.

Hint

Scale-free networks show an approximately straight line with negative slope on log-log axes.

Test cases

case 1

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

expected: 0.5849625007211563

case 2

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

expected: 0

case 3

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

expected: -1

case 4

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

expected: 0

Starter codePython

import math
def degree_slope(n, edges):
    # Your code here
    pass

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