An online forum has two small friend circles that overlap in a single shared…
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
An online forum has two small friend circles that overlap in a single shared moderator account. Circle one is {A,B,E}, all mutually connected; circle two is {E,C,D}, all mutually connected; E is the shared moderator and there are no other links. Treat the network as simple, undirected and unweighted.
((a)) Write the 5×5 adjacency matrix (order A,B,E,C,D), give the degrees and the mean degree.
((b)) Give the degree distribution pk and the heterogeneity ratio ⟨k2⟩/⟨k⟩2.
((c)) Compute the clustering coefficient C.
((d)) Starting from x(0)=(1,1,1,1,1), apply the adjacency matrix twice and report the ratio of E's score to A's score.