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Scientific Programming
Volume 2018, Article ID 3791075, 6 pages
Research Article

An Iterative Scheme to Compute Size Probabilities in Random Graphs and Branching Processes

Department of Mathematics, Computer Science, and Physics, University of Udine, Udine, Italy

Correspondence should be addressed to Paolo Serafini; ti.duinu@inifares.oloap

Received 25 September 2017; Revised 29 January 2018; Accepted 11 February 2018; Published 1 April 2018

Academic Editor: Fabrizio Riguzzi

Copyright © 2018 Paolo Serafini. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We deal with a functional equation that plays an important role in random graphs and in branching processes. In branching processes, the functional equation relates offspring probabilities to population size probabilities, while in random graph it relates degree probabilities to small component size probabilities. We present an iterative scheme that allows computing the size probabilities numerically. It is also theoretically possible to invert the iteration, although this inverse iteration is numerically unstable.