Pareto singular values of Boolean matrices and analysis of bipartite graphs

IF 1 3区数学 Q1 MATHEMATICS

Linear Algebra and its Applications Pub Date : 2025-01-16 DOI:10.1016/j.laa.2025.01.015

Alberto Seeger , David Sossa

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引用次数: 0

Abstract

The complementarity eigenvalues of a graph

G = (V, E)

, which are defined as the Pareto eigenvalues of the adjacency matrix

A_{G}

, provide a rich information on structural properties of the graph. Complementarity eigenvalues are of special relevance for connected graphs. For instance, it has been conjectured that the complementarity eigenvalues of a connected graph determine the graph up to isomorphism. Analogously, the Pareto singular values of the biadjacency matrix

B_{G}

of a connected bipartite graph

G = (U, W, E)

reflect various structural properties of the bipartite graph under consideration. The theory of Pareto singular values of general matrices was initiated in our paper entitled Cone-constrained singular value problems published in the Journal of Convex Analysis (30, 2023, pp. 1285-1306). In this work we explore various aspects of such a theory, paying special attention to Pareto singular values of Boolean matrices and their role in the analysis of bipartite graphs.

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来源期刊

Linear Algebra and its Applications 数学-应用数学

CiteScore

2.20

自引率

9.10%

发文量

333

审稿时长

13.8 months

期刊介绍： Linear Algebra and its Applications publishes articles that contribute new information or new insights to matrix theory and finite dimensional linear algebra in their algebraic, arithmetic, combinatorial, geometric, or numerical aspects. It also publishes articles that give significant applications of matrix theory or linear algebra to other branches of mathematics and to other sciences. Articles that provide new information or perspectives on the historical development of matrix theory and linear algebra are also welcome. Expository articles which can serve as an introduction to a subject for workers in related areas and which bring one to the frontiers of research are encouraged. Reviews of books are published occasionally as are conference reports that provide an historical record of major meetings on matrix theory and linear algebra.