A General Method To Generalize H-index And K-core Methods To Weighted Networks And Multilayer Networks

We proposes a unified framework to extend the k-core method and the h-index to weighted networks and multi-layer networks.First,from the theoretical point of view,we propose a general method to define the general degree,h-index and coreness of nodes in weighted networks and prove the relationships among them,that is,the zero order h-index is equal to the general degree and,the infinite order h-index is equal to the coreness.With these definitions,we show how to incorporate the existing k-core method for weighted networks into our framework.Besides,we design two additional k-core methods.With the relationships,we show how to design parallel or distributed algorithms for the calculation of coreness.In the numerical part,we evaluate the per-formance for four k-core methods by node influence spreading on four real networks.The numerical result shows that the first-order h-index is always optimal or suboptimal among all k-core methods.Finally,we extend the framework to multi-layer networks and propose the the definitions of the general degree,the h-index and the coreness for nodes in multi-layer networks.Similar relationships among the three indexes hold.Fi-nally,we briefly outlined some ways to define different coreness and h-index for different layer-layer relationships.