A network survey reports the following working: "We partitioned a collaboration…
PHYSICS · Multi-part · Fermi University Physics · Thermal, Statistical & Complex Systems · Complex and collective systems · Complex and collective systems
Many Parts, One Behaviour, Ch Communities: finding the groups in a network
Problem
A network survey reports the following working: "We partitioned a collaboration network of N=1500 people, mean degree ⟨k⟩=10, with the Louvain algorithm and found a partition with modularity Q=0.30. Since modularity ranges from −1 to 1 and our value is far above zero, this proves that the network has genuine community structure."
((a)) Find the error in this reasoning.
((b)) Using the fact that full Louvain optimisation on Erdos-Renyi graphs of N=2000 and mean degree c=10 (with no community structure at all) returns partitions with Q≈0.28, decide whether Q=0.30 is convincing evidence of real communities in the N=1500, ⟨k⟩=10 network, and state what further check would settle the question.