2 - Eigenvalues
Published online by Cambridge University Press: 15 May 2026
Summary
This chapter focuses on the eigenvalues of a prescribed matrix associated with a signed graph. The exposition begins with the concept of main eigenvalues and examines their role in various structural analyses. It then proceeds to specific computations, including determinants, relationships with the spectrum of the underlying graph, and the effects of particular operations on signed graphs and their resulting spectra. Further developments consider signed graphs with specified spectral properties, such as those exhibiting a symmetric spectrum. The chapter also explores eigenvalue bounds, including limit points for the largest eigenvalue, spectral distances between signed graphs, and spectral deviations of a signed graph relative to related signed graphs, providing a detailed and comprehensive analysis of these spectral characteristics.
Keywords
Information
- Type
- Chapter
- Information
- Spectra of Signed Graphs , pp. 22 - 63Publisher: Cambridge University PressPrint publication year: 2026
Accessibility standard: WCAG 2.2 A
Why this information is here
This section outlines the accessibility features of this content - including support for screen readers, full keyboard navigation and high-contrast display options. This may not be relevant for you.Accessibility Information
The PDF of this chapter
complies with version 2.2 of the
Web Content Accessibility Guidelines
(WCAG), offering more comprehensive accessibility measures for a broad range
of users and meets the basic
(A)
level of WCAG compliance, addressing essential accessibility barriers.
Content Navigation
Table of contents navigation
Allows you to navigate directly to chapters, sections, or non‐text items through a linked table of contents, reducing the need for extensive scrolling.
Allows you to navigate directly to chapters, sections, or non‐text items through a linked table of contents, reducing the need for extensive scrolling.
Index navigation
Provides an interactive index, letting you go straight to where a term or subject appears in the text without manual searching.
Provides an interactive index, letting you go straight to where a term or subject appears in the text without manual searching.
Reading Order & Textual Equivalents
Single logical reading order
You will encounter all content (including footnotes, captions, etc.) in a clear, sequential flow, making it easier to follow with assistive tools like screen readers.
You will encounter all content (including footnotes, captions, etc.) in a clear, sequential flow, making it easier to follow with assistive tools like screen readers.
Short alternative textual descriptions
You get concise descriptions (for images, charts, or media clips), ensuring you do not miss crucial information when visual or audio elements are not accessible.
You get concise descriptions (for images, charts, or media clips), ensuring you do not miss crucial information when visual or audio elements are not accessible.