000 02454nam a22003618i 4500
001 CR9780511546594
003 UkCbUP
005 20200124160236.0
006 m|||||o||d||||||||
007 cr||||||||||||
008 090508s2007||||enk o ||1 0|eng|d
020 _a9780511546594 (ebook)
020 _z9780521866569 (hardback)
020 _z9780521150163 (paperback)
040 _aUkCbUP
_beng
_erda
_cUkCbUP
050 0 0 _aQA166.17
_b.D87 2007
082 0 0 _a511/.5
_222
100 1 _aDurrett, Richard,
_d1951-
_eauthor.
245 1 0 _aRandom graph dynamics /
_cRick Durrett.
264 1 _aCambridge :
_bCambridge University Press,
_c2007.
300 _a1 online resource (ix, 212 pages) :
_bdigital, PDF file(s).
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
490 1 _aCambridge series on statistical and probabilistic mathematics ;
_v20
500 _aTitle from publisher's bibliographic system (viewed on 05 Oct 2015).
505 0 _aOverview -- Erdös-Rényi random graphs -- Fixed degree distributions -- Power laws -- Small worlds -- Random walks -- CHKNS model.
520 _aThe theory of random graphs began in the late 1950s in several papers by Erdos and Renyi. In the late twentieth century, the notion of six degrees of separation, meaning that any two people on the planet can be connected by a short chain of people who know each other, inspired Strogatz and Watts to define the small world random graph in which each site is connected to k close neighbors, but also has long-range connections. At a similar time, it was observed in human social and sexual networks and on the Internet that the number of neighbors of an individual or computer has a power law distribution. This inspired Barabasi and Albert to define the preferential attachment model, which has these properties. These two papers have led to an explosion of research. The purpose of this book is to use a wide variety of mathematical argument to obtain insights into the properties of these graphs. A unique feature is the interest in the dynamics of process taking place on the graph in addition to their geometric properties, such as connectedness and diameter.
650 0 _aRandom graphs.
776 0 8 _iPrint version:
_z9780521866569
830 0 _aCambridge series on statistical and probabilistic mathematics ;
_v20.
856 4 0 _uhttps://doi.org/10.1017/CBO9780511546594
999 _c518055
_d518053