Network robustness and fragility: percolation on random graphs

Physical Review Letters

Volumn 85, Issue 25, 2000, Pages 5468-5471

  Callaway, Duncan S ^a   Newman, M E J ^a,b   Strogatz, Steven H ^a   Watts, Duncan J ^b,c  

^a Cornell University ^*  (United States)

^b SANTA FE INSTITUTE   (United States)

^c Columbia University ^*  (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DATA COMMUNICATION SYSTEMS; ELECTRIC POWER TRANSMISSION; POISSON EQUATION; PROBABILITY DISTRIBUTIONS; RANDOM PROCESSES;

INTERNET ROUTERS; NETWORK RESILIENCE; NETWORK ROBUSTNESS; POISSON DEGREE DISTRIBUTION; POWER GRIDS; POWER LAW VERTEX DEGREE DISTRIBUTION; RANDOM GRAPHS; SOCIAL NETWORKS;

INTERNET;

ALGORITHM; ANIMAL; CELL FUNCTION; COMPUTER SIMULATION; HUMAN; INTERNET; PHYSIOLOGY; SIGNAL TRANSDUCTION; SOCIAL SUPPORT; STATISTICAL MODEL;

ALGORITHMS; ANIMALS; CELL PHYSIOLOGICAL PHENOMENA; COMPUTER SIMULATION; HUMANS; INTERNET; MODELS, STATISTICAL; SIGNAL TRANSDUCTION; SOCIAL SUPPORT;

EID: 4243939794     PISSN: 00319007     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevLett.85.5468     Document Type: Article

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19. The derivation of this equation assumes that all clusters other than the giant component contain no loops. It is straightforward to demonstrate that this assumption is exact in the limit of large system size for degree distributions with finite mean. See Refs. [7], [12], and [13] for discussions of this point.
20. ν was assumed equal to the value of q at which the derivative of the size of the larget cluster was greatest.
21. M. E. J. Newman, Proc. Natl. Acad. Sci. U.S.A. (to be published).
22. In fact, the approaches of Albert et al. [1] and Broder et al. [3] differ slightly. Broder et al. simply removed the highest degree vertices from the network, whereas Albert et al. recalculated vertex degrees after the removal of each vertex and its associated edges, and then removed the next highest degree vertex. Our calculations are equivalent to the method of Broder et al., although in practice there appears to be little difference in qualitative behavior between the two.