Four electrical substations are linked by high-voltage lines - , - , - , - , - ;…
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 electrical substations A,B,C,D are linked by high-voltage lines A-B, A-C, A-D, B-C, B-D; there is no line C-D. Treat the network as simple, undirected and unweighted.
((a)) Write the adjacency matrix using the node order 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 from triangles and connected triples.
((d)) Use the symmetry A↔B and C↔D to find the leading eigenvalue κ1.