A budget airline network grows by adding one new destination at a time; each new…
PHYSICS · Subjective · Fermi University Physics · Thermal, Statistical & Complex Systems · Complex and collective systems · Complex and collective systems
Many Parts, One Behaviour, Ch Growing networks: preferential attachment and scale-free degree distributions
Problem
A budget airline network grows by adding one new destination at a time; each new destination opens m=4 routes to existing destinations, chosen with probability proportional to the number of routes they already have (a Barabási-Albert rule with attachment probability Πk=k/(2mt), t the number of destinations already served). (a) Write the rate equation for Nk(t), the expected number of destinations with exactly k routes. (b) Using the exact stationary degree distribution pk=2m(m+1)/[k(k+1)(k+2)], compute p4 (the fraction of destinations with the minimum possible number of routes) and p6.