著者
Tomonori ANDO Yoshiyuki KABASHIMA Hisanao TAKAHASHI Osamu WATANABE Masaki YAMAMOTO
出版者
The Institute of Electronics, Information and Communication Engineers
雑誌
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences (ISSN:09168508)
巻号頁・発行日
vol.E94-A, no.6, pp.1247-1256, 2011-06-01

We study nn random symmetric matrices whose entries above the diagonal are iid random variables each of which takes 1 with probability p and 0 with probability 1-p, for a given density parameter p=α/n for sufficiently large α. For a given such matrix A, we consider a matrix A ' that is obtained by removing some rows and corresponding columns with too many value 1 entries. Then for this A', we show that the largest eigenvalue is asymptotically close to α+1 and its eigenvector is almost parallel to all one vector (1,...,1).