Computing Assortative Mixing by Degree with the s -Metric in Networks Using Linear Programming
Joint Authors
Schmittmann, Verena D.
Waldorp, Lourens
Source
Journal of Applied Mathematics
Issue
Vol. 2015, Issue 2015 (31 Dec. 2015), pp.1-9, 9 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2015-02-22
Country of Publication
Egypt
No. of Pages
9
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Waldorp, Lourens& Schmittmann, Verena D.. 2015. Computing Assortative Mixing by Degree with the s -Metric in Networks Using Linear Programming. Journal of Applied Mathematics،Vol. 2015, no. 2015, pp.1-9.
https://search.emarefa.net/detail/BIM-1067104
Modern Language Association (MLA)
Waldorp, Lourens& Schmittmann, Verena D.. Computing Assortative Mixing by Degree with the s -Metric in Networks Using Linear Programming. Journal of Applied Mathematics No. 2015 (2015), pp.1-9.
https://search.emarefa.net/detail/BIM-1067104
American Medical Association (AMA)
Waldorp, Lourens& Schmittmann, Verena D.. Computing Assortative Mixing by Degree with the s -Metric in Networks Using Linear Programming. Journal of Applied Mathematics. 2015. Vol. 2015, no. 2015, pp.1-9.
https://search.emarefa.net/detail/BIM-1067104
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1067104