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Green's Classifications and Evolutions of Fixed-Order Networks

2018
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Mathematics
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It is shown that the set of all networks of fixed order n form a semigroup that is isomorphic to the semigroup BX of binary relations on a set X of cardinality n. Consequently, BX provides for Green's L,R,H, and D equivalence classifications of all networks of fixed order n. These classifications reveal that a fixed-order network which evolves within a Green's equivalence class maintains certain structural invariants during its evolution. The "Green's symmetry problem" is introduced and is

doi:10.3390/math6100174
fatcat:xi3nd5csyba3dds4xg3s3hgqwi