Statement
Let be a d-regular graph with normalized second-largest eigenvalue (in absolute value) of the adjacency matrix. Then for any two subsets, let denote the number of edges between S and T. If the two sets are not disjoint, edges in their intersection are counted twice, that is, . We have
For a proof, see references.
Read more about this topic: Expander Mixing Lemma
Famous quotes containing the word statement:
“Eroticism has its own moral justification because it says that pleasure is enough for me; it is a statement of the individual’s sovereignty.”
—Mario Vargas Llosa (b. 1936)
“The most distinct and beautiful statement of any truth must take at last the mathematical form.”
—Henry David Thoreau (1817–1862)
“He that writes to himself writes to an eternal public. That statement only is fit to be made public, which you have come at in attempting to satisfy your own curiosity.”
—Ralph Waldo Emerson (1803–1882)