Multivariate generating functions for information spread on multi-type random graphs

Yaron Oz*, Ittai Rubinstein, Muli Safra

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


We study the spread of information on multi-type directed random graphs. In such graphs the vertices are partitioned into distinct types (communities) that have different transmission rates between themselves and with other types. We construct multivariate generating functions and use multi-type branching processes to derive an equation for the size of the large out-components in multi-type random graphs with a general class of degree distributions. We use our methods to analyse the spread of epidemics and verify the results with population based simulations.

Original languageEnglish
Article number033501
JournalJournal of Statistical Mechanics: Theory and Experiment
Issue number3
StatePublished - 1 Mar 2022


FundersFunder number
IBM Einstein Fellowship
Israeli Science Foundation center of excellence
John and Maureen Hendricks Charitable Foundation
Horizon 2020 Framework Programme835152, BSF 2016414
European Research Council


    • epidemic modeling
    • network dynamics
    • random graphs, networks


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