The acquaintance graph among the attendees of a large conference is modelled as an…

PHYSICS · Subjective · Fermi University Physics · Thermal, Statistical & Complex Systems · Complex and collective systems · Complex and collective systems

Many Parts, One Behaviour, Ch Random graphs, the giant component and percolation on networks

Problem

The acquaintance graph among the attendees of a large conference is modelled as an Erdos-Renyi random graph with mean degree c=2.5c = 2.5. Find the fraction SS of attendees who belong to the giant connected component, by solving S=1−e−cSS = 1 - e^{-cS} numerically by iteration, starting from S0=0.8S_0 = 0.8 and iterating Sn+1=1−e−cSnS_{n+1} = 1 - e^{-cS_n} until SS is stable to three significant figures.

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