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2015 Computing Assortative Mixing by Degree with the s -Metric in Networks Using Linear Programming
Lourens J. Waldorp, Verena D. Schmittmann
J. Appl. Math. 2015: 1-9 (2015). DOI: 10.1155/2015/580361

Abstract

Calculation of assortative mixing by degree in networks indicates whether nodes with similar degree are connected to each other. In networks with scale-free distribution high values of assortative mixing by degree can be an indication of a hub-like core in networks. Degree correlation has generally been used to measure assortative mixing of a network. But it has been shown that degree correlation cannot always distinguish properly between different networks with nodes that have the same degrees. The so-called s -metric has been shown to be a better choice to calculate assortative mixing. The s -metric is normalized with respect to the class of networks without self-loops, multiple edges, and multiple components, while degree correlation is always normalized with respect to unrestricted networks, where self-loops, multiple edges, and multiple components are allowed. The challenge in computing the normalized s -metric is in obtaining the minimum and maximum value within a specific class of networks. We show that this can be solved by using linear programming. We use Lagrangian relaxation and the subgradient algorithm to obtain a solution to the s -metric problem. Several examples are given to illustrate the principles and some simulations indicate that the solutions are generally accurate.

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Lourens J. Waldorp. Verena D. Schmittmann. "Computing Assortative Mixing by Degree with the s -Metric in Networks Using Linear Programming." J. Appl. Math. 2015 1 - 9, 2015. https://doi.org/10.1155/2015/580361

Information

Published: 2015
First available in Project Euclid: 15 April 2015

zbMATH: 1343.05143
MathSciNet: MR3319189
Digital Object Identifier: 10.1155/2015/580361

Rights: Copyright © 2015 Hindawi

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