The paper gives new observations on irreducible nonnegative realizations of realizable spectra and characterizes the trace-zero case via graph theory, plus related positive realizations.
Spector, A characterization of trace zero symmetric nonnegative 5×5 matrices,Linear Al- gebra Appl.434 (2011), n 4, 1000-1017
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The INIEP: Irreducible and Positive Realizations
The paper gives new observations on irreducible nonnegative realizations of realizable spectra and characterizes the trace-zero case via graph theory, plus related positive realizations.