Converse
Recently, Bilu and Linial showed that the converse holds as well: if a graph satisfies the conclusion of the expander mixing lemma, that is, for any two subsets ,
then its second-largest eigenvalue is .
Read more about this topic: Expander Mixing Lemma
Famous quotes containing the word converse:
“I lately met with an old volume from a London bookshop, containing the Greek Minor Poets, and it was a pleasure to read once more only the words Orpheus, Linus, Musæus,—those faint poetic sounds and echoes of a name, dying away on the ears of us modern men; and those hardly more substantial sounds, Mimnermus, Ibycus, Alcæus, Stesichorus, Menander. They lived not in vain. We can converse with these bodiless fames without reserve or personality.”
—Henry David Thoreau (1817–1862)
“Who can converse with a dumb show?”
—William Shakespeare (1564–1616)
“The Anglo-American can indeed cut down, and grub up all this waving forest, and make a stump speech, and vote for Buchanan on its ruins, but he cannot converse with the spirit of the tree he fells, he cannot read the poetry and mythology which retire as he advances. He ignorantly erases mythological tablets in order to print his handbills and town-meeting warrants on them.”
—Henry David Thoreau (1817–1862)