A network of wireless sensor relays is built as a configuration model with degree…
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 network of wireless sensor relays is built as a configuration model with degree distribution p1=0.2, p2=0.3, p3=0.5 (no relay has more than three links).
((a)) Find the mean degree ⟨k⟩.
((b)) Find the excess degree distribution q0, q1, q2 (the distribution of the number of further links seen by an explorer who has just arrived at a relay along one of its edges), using qk=(k+1)pk+1/⟨k⟩.
((c)) Find the mean excess degree.