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)
““You are old, Father William,” the young man cried,
“And life must be hastening away;
You are cheerful, and love to converse upon death:
Now tell me the reason, I pray.”
“I am cheerful, young man,” Father William replied;
“Let the cause thy attention engage;
In the days of my youth I remembered my God,
And He hath not forgotten my age.””
—Robert Southey (1774–1843)