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The Isomorphic Version of Brualdi’s and Sanderson’s Nestedness

Department of Computer Science, Martin-Luther University, 06120 Halle-Wittenberg, Germany
Author to whom correspondence should be addressed.
Algorithms 2017, 10(3), 74;
Received: 16 January 2017 / Revised: 20 June 2017 / Accepted: 22 June 2017 / Published: 27 June 2017
PDF [297 KB, uploaded 27 June 2017]


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%. View Full-Text
Keywords: discrepancy; nestedness; BR; Ferrers matrix; Brualdi; Sanderson discrepancy; nestedness; BR; Ferrers matrix; Brualdi; Sanderson

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Berger, A.; Schreck, B. The Isomorphic Version of Brualdi’s and Sanderson’s Nestedness. Algorithms 2017, 10, 74.

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