Four clean-room sensors are wired in a closed loop: - , - , - , -
PHYSICS · Multi-part · Fermi University Physics · Thermal, Statistical & Complex Systems · Complex and collective systems · Complex and collective systems
Many Parts, One Behaviour, Ch Networks as graphs: degree, distance and clustering
Problem
Four clean-room sensors 1,2,3,4 are wired in a closed loop: 1-2, 2-3, 3-4, 4-1, with no other links. Treat the network as simple, undirected and unweighted.
((a)) Write the adjacency matrix using the node order 1,2,3,4, and state each node's degree and the mean degree ⟨k⟩.
((b)) Give the degree distribution pk and compute the heterogeneity ratio.
((c)) Compute the clustering coefficient C.
((d)) Find the leading eigenvalue κ1 by symmetry, using the fact that all four nodes play equivalent roles.