The question is related to spectral graph theory. Wrt Fiedler number and algebraic connectivity of graphs, sometimes academic literature uses second largest eigenvalue, sometimes second smallest. For example, I’m looking at

Nikiforov, V. (2013). The influence of Miroslav Fiedler on spectral graph theory

Fiedler number is defined as 2nd smallest eigenvalue of normalized Laplacian, while as later on the paper, the algebraic connectivity is described utilizing 2nd largest eigenvalue of adjacency matrix.

Are these two terms (2nd largest/smallest eigenvalues) conceptually different from application point of view or might be used interchangeably?


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