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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.
- Winter '11