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Critical window for connectivity in the Configuration Model by Federico, Lorenzo; van der Hofstad, Remco is a scholarly article available to read on EtoBox.

What is Critical window for connectivity in the Configuration Model about?

We identify the asymptotic probability of a configuration model $\mathrm{CM}_n(\boldsymbol{d})$ to produce a connected graph within its critical window for connectivity that is identified by the number of vertices of degree 1 and 2, as well as the expected degree. In this window, the probability that the graph is connected converges to a non-trivial value, and the size of the complement of the giant component weakly converges to a finite random variable. Under a finite second moment condition we also derive the asymptotics of the connectivity probability conditioned on simplicity, from which the asymptotic number of simple connected graphs with a prescribed degree sequence follows.

Author

Federico, Lorenzo; van der Hofstad, Remco

Published

2016

Language

EN