Editing Perron–Frobenius theorem (section)

===Algebraic graph theory===
The theorem has particular use in [[algebraic graph theory]]. The "underlying graph" of a nonnegative ''n''-square matrix is the graph with vertices numbered 1, ..., ''n'' and arc ''ij'' if and only if ''A<sub>ij</sub>'' ≠ 0. If the underlying graph of such a matrix is strongly connected, then the matrix is irreducible, and thus the theorem applies. In particular, the [[adjacency matrix]] of a [[strongly connected component|strongly connected graph]] is irreducible.<ref>{{cite book |author-link=Richard A. Brualdi |first1=Richard A. |last1=Brualdi |author-link2=H. J. Ryser |first2=Herbert J. |last2=Ryser |title=Combinatorial Matrix Theory |url=https://archive.org/details/combinatorialmat0000brua_x9u3 |url-access=registration |location=Cambridge |publisher=Cambridge UP |year=1992 |isbn=978-0-521-32265-2 }}</ref><ref>{{cite book |author-link=Richard A. Brualdi |first1=Richard A. |last1=Brualdi |first2=Dragos |last2=Cvetkovic |title=A Combinatorial Approach to Matrix Theory and Its Applications |publisher=CRC Press |location=Boca Raton, FL |year=2009 |isbn=978-1-4200-8223-4 }}</ref>