A household wifi router is joined directly to four devices ; no two devices are…
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
A household wifi router R is joined directly to four devices 1,2,3,4; no two devices are joined to each other. Treat the network as simple, undirected and unweighted.
((a)) Write the adjacency matrix using the node order R,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 ⟨k2⟩/⟨k⟩2.
((c)) Compute the clustering coefficient C.
((d)) Find the leading eigenvalue κ1 of the adjacency matrix and the ratio of the router's eigenvector centrality to a device's.