A local quantitative measure for community detection in networks

Recently, it has been proved that the resolution of methods based on optimising the modularity Q is limited. In order to improve this limit, a novel local quantitative measure called normalised modularity density NMD is proposed and optimised by simulated annealing technique. Both theoretical certifications on some schematic examples and numerical results on a suit of computer-generated and real-world networks show that optimising NMD can detect communities with different scales, especially small dense communities that optimising Q cannot detect, which provides meaningful evidence that optimising NMD can improve the resolution limit in optimising modularity Q.