  Many real-world networks exhibit degree-degree correlations between nodes
separated by more than one step. Such long-range degree correlations (LRDCs)
can be fully described by one joint and four conditional probability
distributions with respect to degrees of two randomly chosen nodes and shortest
path distance between them. While LRDCs are induced by nearest-neighbor degree
correlations (NNDCs) between adjacent nodes, some networks possess intrinsic
LRDCs which cannot be generated by NNDCs. Here we develop a method to extract
intrinsic LRDC in a correlated network by comparing the probability
distributions for the given network with those for nearest-neighbor correlated
random networks. We also demonstrate the utility of our method by applying it
to several real-world networks.
