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
Two substations H1,H2 are joined directly to each other. H1 also feeds two households a,b, and H2 also feeds two households c,d; no household is joined to any other household or to the other substation. Treat the network as simple, undirected and unweighted.
((a)) Write the adjacency matrix using the node order H1,H2,a,b,c,d, 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 H1↔H2 and a↔b↔c↔d to find the leading eigenvalue κ1 and the ratio of a substation's centrality to a household's.