Cycle products and efficient vectors in reciprocal matrices

2023/12/16 by Susana Furtado, Furtado, Susana, Charles R. Johnson +1 · 2 citations
Computer Science · Engineering · Mathematics · #05C20 #15B48 #90B50 #91B06 #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Matrix Theory and Algorithms #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2312.10481

openalex publication_date 2023/12/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We focus upon the relationship between Hamiltonian cycle products and efficient vectors for a reciprocal matrix A, to more deeply understand the latter. This facilitates a new description of the set of efficient vectors (as a union of convex subsets), greater understanding of convexity within this set and of order reversals in efficient vectors. A straightforward description of all efficient vectors for an n-by-n, column perturbed consistent matrix is given; it is the union of at most (n-1) choose 2 convex sets.

Cited by

• Exact bounds for efficient consistent matrices obtained from a reciprocal matrix
• Completions of pairwise comparison data that minimize the triad measure of inconsistency

Related

• Exact bounds for efficient consistent matrices obtained from a reciprocal matrix
• Efficiency of the convex hull of the columns of certain triple perturbed consistent matrices
• Efficient vectors for block perturbed consistent matrices
• Efficiency analysis for the Perron vector of a reciprocal matrix
• The complete set of efficient vectors for a reciprocal matrix