In order to investigate the role of the weight in weighted networks, the collective behavior of the Ising system on weighted regular networks is studied by numerical simulation. In our model, the coupling strength between spins is inversely proportio
nal to the corresponding weighted shortest distance. Disordering link weights can effectively affect the process of phase transition even though the underlying binary topological structure remains unchanged. Specifically, based on regular networks with homogeneous weights initially, randomly disordering link weights will change the critical temperature of phase transition. The results suggest that the redistribution of link weights may provide an additional approach to optimize the dynamical behaviors of the system.
Modularity Q is an important function for identifying community structure in complex networks. In this paper, we prove that the modularity maximization problem is equivalent to a nonconvex quadratic programming problem. This result provide us a simpl
e way to improve the efficiency of heuristic algorithms for maximizing modularity Q. Many numerical results demonstrate that it is very effective.
