The mutual-reply graph of an online discussion forum with members is modelled as an…
PHYSICS · Multi-part · 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 mutual-reply graph of an online discussion forum with N=5000 members is modelled as an Erdos-Renyi random graph with mean degree c=1.8.
((a)) Find the fraction of members with no replies to or from anyone else, and the expected number of such isolated members.
((b)) Find the fraction S of members in the giant connected component, by solving S=1−e−cS numerically to three significant figures.