Distinct Degrees and Their Distribution in Complex Networks

الأصل · EN

We investigate a variety of statistical properties associated with the number of distinct degrees that exist in a typical network for various classes of networks. For a single realization of a network with N nodes that is drawn from an ensemble in which the number of nodes of degree k has an algebraic tail, Nₖ N/kⁿu for k>>1, the number of distinct degrees grows as N1/nu. Such an algebraic growth is also observed in scientific citation data. We also determine the N dependence of statistical quantities associated with the sparse, large-k range of the degree distribution, such as the location of the first hole (where Nₖ=0), the last doublet (two consecutive occupied degrees), triplet, dimer (Nₖ=2), trimer, etc.