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 checkpoints along a hiking trail, labelled 1,2,3,4 in order, are joined only to their immediate neighbours: 1-2, 2-3, 3-4. 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)) Use the symmetry 1↔4, 2↔3 to find the leading eigenvalue κ1.