Can also be written as k 2 2 k 0 which is the famous

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Unformatted text preview: portant, s → ∞ when 2 k = k 2 . This marks the onset of the giant component! Emergence of the giant component • s →∞ • This happens when: 2 k = k 2 , which can also be written as k = k2 − k • This means expected number of nearest neighbors k , first equals expected number of second nearest neighbors k2 − k . • Can also be written as k 2 − 2 k = 0, which is The famous Molloy and Reed criteria*, giant emerges when: k k (k − 2) Pk = 0. *GF approach is easier than Molloy Reed! GFs widely used in “network epidemiology” • Fragility of Power Law Random Graphs to targeted node removal / Robustness to random removal – Callaway PRL 2000 – Cohen PRL 2000 • Onset of epidemic threshold: – C Moore, MEJ Newman, Physical Review E, 2000 – MEJ Newman - Physical Review E, 2002 – Lauren Ancel Meyers, M.E.J. Newmanb, Babak Pourbohlou, Journal of Theoretical Biology, 2006 – JC Miller - Physical Review E, 2007 • Information flow in social networks F Wu, BA Huberman, LA Adamic, Physica A, 2004. • Cascades on random networks Watts PNAS 2002. Global Ca...
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This document was uploaded on 03/12/2014 for the course CSCI 289 at UC Davis.

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