Five physicists have co-authored papers as follows: - , - , - , - , -
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
Five physicists P,Q,R,S,T have co-authored papers as follows: P-Q, P-R, Q-R, Q-S, S-T. Treat the coauthorship network as simple, undirected and unweighted.
((a)) Write the adjacency matrix using the node order P,Q,R,S,T, 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)) Starting from the uniform vector (1,1,1,1,1) in the order P,Q,R,S,T, carry out two steps of power iteration and use the ratio of the totals after each step, ∑ixi(2)/∑ixi(1), as an estimate of the leading eigenvalue κ1.