A club of amateur radio operators is modelled as an Erdos-Renyi random graph with…
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
A club of amateur radio operators is modelled as an Erdos-Renyi random graph G(N,p) with N=8000 operators and mean degree c=3 (each pair of operators is linked, independently, with the same small probability, so that the mean number of contacts per operator is 3).
((a)) Using the Poisson limit pk=e−cck/k!, find the probability that a randomly chosen operator has no contacts (k=0) and the probability that they have exactly one contact (k=1).
((b)) Hence estimate the number of operators with no contacts at all.
((c)) Find the clustering coefficient C of this network.