computing assortative mixing by degree with the s-metric in networks using linear programming
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2015
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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.
| Reference Key |
waldorp2015journalcomputing
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|---|---|
| Authors | ;Lourens J. Waldorp;Verena D. Schmittmann |
| Journal | Chemico-biological interactions |
| Year | 2015 |
| DOI |
10.1155/2015/580361
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| URL | |
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