General and exact approach to percolation on random graphs

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Antoine AllardLouis J Dubé

Abstract

We present a comprehensive and versatile theoretical framework to study site and bond percolation on clustered and correlated random graphs. Our contribution can be summarized in three main points. (i) We introduce a set of iterative equations that solve the exact distribution of the size and composition of components in finite-size quenched or random multitype graphs. (ii) We define a very general random graph ensemble that encompasses most of the models published to this day and also makes it possible to model structural properties not yet included in a theoretical framework. Site and bond percolation on this ensemble is solved exactly in the infinite-size limit using probability generating functions [i.e., the percolation threshold, the size, and the composition of the giant (extensive) and small components]. Several examples and applications are also provided. (iii) Our approach can be adapted to model interdependent graphs-whose most striking feature is the emergence of an extensive component via a discontinuous phase transition-in an equally general fashion. We show how a graph can successively undergo a continuous then a discontinuous phase transition, and preliminary results suggest that clustering increases the amplitu...Continue Reading

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Citations

Aug 10, 2017·Proceedings of the National Academy of Sciences of the United States of America·Antoine AllardLaurent Hébert-Dufresne
May 20, 2018·Physical Review. E·Edward LaurenceLouis J Dubé
Feb 18, 2017·Physical Review. E·Uttam BhatLaurent Hébert-Dufresne
Jan 27, 2019·Nature Communications·Ivan Kryven
Feb 20, 2021·Physical Review. E·Peter MannSimon Dobson
Feb 20, 2021·Physical Review. E·Peter MannSimon Dobson

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