Computing Assortative Mixing by Degree with the s-Metric in Networks Using Linear Programming
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...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2015-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2015/580361 |
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| Summary: | 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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| ISSN: | 1110-757X 1687-0042 |