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12 pages, 297 KiB  
Technical Note
The Isomorphic Version of Brualdi’s and Sanderson’s Nestedness
by Annabell Berger and Berit Schreck
Algorithms 2017, 10(3), 74; https://doi.org/10.3390/a10030074 - 27 Jun 2017
Cited by 4 | Viewed by 3815
Abstract
The discrepancy BR for an m × n 0, 1-matrix from Brualdi and Sanderson in 1998 is defined as the minimum number of 1 s that need to be shifted in each row to the left to achieve its Ferrers matrix, i.e., each [...] Read more.
The discrepancy BR for an m × n 0, 1-matrix from Brualdi and Sanderson in 1998 is defined as the minimum number of 1 s that need to be shifted in each row to the left to achieve its Ferrers matrix, i.e., each row consists of consecutive 1 s followed by consecutive 0 s. For ecological bipartite networks, BR describes a nested set of relationships. Since two different labelled networks can be isomorphic, but possess different discrepancies due to different adjacency matrices, we define a metric determining the minimum discrepancy in an isomorphic class. We give a reduction to k ≤ n minimum weighted perfect matching problems. We show on 289 ecological matrices (given as a benchmark by Atmar and Patterson in 1995) that classical discrepancy can underestimate the nestedness by up to 30%. Full article
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