1 - Introduction
Published online by Cambridge University Press: 15 May 2026
Summary
This chapter establishes the terminology and notation necessary for the study of signed graphs and introduces their two fundamental concepts, balance and switching equivalence. It provides formal definitions of the key matrices associated with signed graphs, including the adjacency matrix, Laplacian matrix, and net Laplacian matrix, and discusses their basic properties in detail. The chapter also examines foundational results concerning the characteristic polynomials and eigenvalues of these matrices, highlighting their role in analysing the structural and spectral properties of signed graphs. In addition, the standard structural balance criteria are extended and generalized through spectral criteria, which can be computed efficiently in polynomial time, providing a practical framework for assessing balance in larger and more complex networks.
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- Spectra of Signed Graphs , pp. 1 - 21Publisher: Cambridge University PressPrint publication year: 2026
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