Combinatorics Probability Computing · 2007 · 32 citations · 8 references
Graph MinorCritical PhaseGraph TheoryRandom GraphStructural Graph TheoryFixed Degree SequenceProbabilistic Graph TheoryGiven Degree SequenceNetwork AnalysisEducationRandom GraphsProbability TheoryDiscrete MathematicsExtremal Graph TheoryCritical Phenomenon
We consider random graphs with a fixed degree sequence. Molloy and Reed [11, 12] studied how the size of the giant component changes according to degree conditions. They showed that there is a phase transition and investigated the order of components before and after the critical phase. In this paper we study more closely the order of components at the critical phase, using singularity analysis of a generating function for a branching process which models the random graph with a given degree sequence.
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Random graphs with arbitrary degree distributions and their applications
M. E. J. Newman, Steven H. Strogatz, Duncan J. Watts · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · 2001 · 3.7K citations · Full text
Engineering, Network Analysis, Poisson Degree Distributions +16